Maths-
General
Easy
Question
The perimeter of a right triangle is 132 cm. and the sum of the squares of its sides is 6050 cm2. What is the sum of the perpendicular sides –
- 77 cm
- 55 cm
- 44 cm
- 33 cm
The correct answer is: 77 cm
We should find the sum of the perpendicular sides
let the sides be a b and c where c is the hypotenuse.
a²+b²=c²
the sum of squares of its sides is 6050.
a²+b²+c²=6050
a²+b²+a²+b²=6050
2(a²+b²)=6050
a²+b²=3025
c²=3025
c=√3025=55
The perimeter of a right triangle is 132cm.
a+b+c=132
a+b+55=132
a+b=77
Hence Choice 1 is correct
Related Questions to study
Maths-
In figure, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm, calculate the length of BC
![](data:image/png;base64,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)
For such questions, we should know the Pythagoras theorem of a triangle.
In figure, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm, calculate the length of BC
![](data:image/png;base64,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)
Maths-General
For such questions, we should know the Pythagoras theorem of a triangle.
Maths-
In DABC, AD is the median through A and E is the produced meets in F figure. Then the value of AF is equal to
![](data:image/png;base64,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)
Hence AF=(1/3)AC
In DABC, AD is the median through A and E is the produced meets in F figure. Then the value of AF is equal to
![](data:image/png;base64,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)
Maths-General
Hence AF=(1/3)AC
Maths-
In the figure shown below,
and
. Which one of the following is a true statement?
![](data:image/png;base64,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)
Hence Choice 1 is correct
In the figure shown below,
and
. Which one of the following is a true statement?
![](data:image/png;base64,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)
Maths-General
Hence Choice 1 is correct
Maths-
One of the angles of a triangle is
. If the difference of other two angles is
, the largest angle of this triangle has a measure of
One of the angles of a triangle is
. If the difference of other two angles is
, the largest angle of this triangle has a measure of
Maths-General
Maths-
In figure
If YO and ZO are bisectors of
and
respectively of
, find ![angle Y O Z](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence choice 4 is correct
In figure
If YO and ZO are bisectors of
and
respectively of
, find ![angle Y O Z](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Hence choice 4 is correct
Maths-
In figure if
and
, find x and y.
![](data:image/png;base64,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)
Hence choice 2 is correct
In figure if
and
, find x and y.
![](data:image/png;base64,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)
Maths-General
Hence choice 2 is correct
Maths-
In Figure. PS is the bisector of
and
. Then
is equal to
![](data:image/png;base64,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)
Hence Choice 2 is correct
In Figure. PS is the bisector of
and
. Then
is equal to
![](data:image/png;base64,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)
Maths-General
Hence Choice 2 is correct
physics-
Two identical blocks A and B are placed on two inclined planes as shown in diagram. Neglect air resistance and other friction. Choose the correct statement:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/494028/1/963307/Picture84.png)
Statement I: Kinetic energy of 'A' on sliding to J will be greater than the kinetic energy of B on falling to M.
Statement II: Acceleration of 'A' will be greater than acceleration of 'B' when both are released to slide on inclined plane. Statement III: Work done by external agent to move block slowly from position B to O is negative
Two identical blocks A and B are placed on two inclined planes as shown in diagram. Neglect air resistance and other friction. Choose the correct statement:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/494028/1/963307/Picture84.png)
Statement I: Kinetic energy of 'A' on sliding to J will be greater than the kinetic energy of B on falling to M.
Statement II: Acceleration of 'A' will be greater than acceleration of 'B' when both are released to slide on inclined plane. Statement III: Work done by external agent to move block slowly from position B to O is negative
physics-General
physics-
Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is (g = 10
):
![](data:image/png;base64,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)
Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is (g = 10
):
![](data:image/png;base64,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)
physics-General
physics-
A collar 'B' of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5m. The spring lying in the plane of the circular track and having spring constant 200
is undeformed when the collar is at 'A'. If the collar starts from rest at B' the normal reaction exerted by the track on the collar when it passes through 'A' is:
![](data:image/png;base64,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)
A collar 'B' of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5m. The spring lying in the plane of the circular track and having spring constant 200
is undeformed when the collar is at 'A'. If the collar starts from rest at B' the normal reaction exerted by the track on the collar when it passes through 'A' is:
![](data:image/png;base64,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)
physics-General
physics-
The blocks A and B shown in the figure have masses
. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is:
![](data:image/png;base64,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)
The blocks A and B shown in the figure have masses
. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is:
![](data:image/png;base64,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)
physics-General
physics-
Two bodies of mass
are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull
with constant velocity v is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKEAAADqCAYAAADKziUZAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAEChSURBVHhe7Z0FeFTX1oYvEkhwt+JOe1tavEjRUtzdCcXdggQPHiC4BQnu7sEtuBMgEIgbcRcC37++PTHazn97e9tkQs73PLsh58w5M+l5Z8m29S9o0pTC0iDUlOLSINSU4tIg1JTi0iDUlOLSINSU4tIg1JTi0iDUlOLSINSU4tIg1JTi0iDUlOLSINSU4jIoCD9+/IjY2Fh8+PBB/fvTJ0j7lHCMjf9mk1MJ10RHRSE6OhofeYGIr4uR32NjdfeJv0bdME4feSzunjExMYiWpu4rr+E53i86Okb3YjmmXsP3kPvFK/794sX7sfE1H2M/JtybnyPmQwyi5HOy8TjfQ/e6uJ9JPmfS90gLMhgI+T8/IiICISHBCAoKUv/++PGTemDxx4KDgxEijT8jIiPjzoXAy9MTXl5eCA8PVw/dz89PjnkgIMBf93q5NiQ4SMHKBxwl14bIscCAAHlNgHq9r68vAgMDERoaiiD56e7uru7Le0ZIe+/jo37n5+B7RMo9wuS1kfI5CTx/8n14bfx78n5swfLe/v5+8Pb2ho/cJzAwAKHyuXk9f/I92dTfJ78T1LQkg4CQ1of/893cXPHW8Q3evXXE+/fv1cMmgO/evYOT0zs57wYXZ2c4vnkDVxcXBcZrBwfY3biB27duwdnJCd4C44P793D96hU8f/oE7xwd5X5v4ST38H3vIxAFwtPDA2/lHryW7dWLF3hhb6/+zde/lH9fv3YVdnY35X2d1H3v37uLG9ev4emTJ3B3c1efhcddnNmcVeN7qPu9fAGHV6/kb3FU1zu9eyu/v8Tz589gb/8cr187qNe6ujjLPd6pz/Lm9Wu8efNaHeeXg/9P0ooMAsIP4qr4cI4eOYwD+/fh3NkzCgQ+jJcv7XHq5AlcuXwZTx4/VsAd2r8fRw4dxLUrV7Bz+3ZMnTwJs2ZMx2E5ZnvuHBbOn4spkyZi+9YtuGB7VgF5TRpBevzoIW7KPS7Y2sL27Fn1+tMnT+L4kSM4deIEzp4+hX17dmPeXAtYLl4kx47jmHyuRQvnY7Lcc82qFbh43hbXBciL58+r1x8/ekx+nsGlixdxYN9ebNq4Afvl5+VLF2F384Z8zss4e+Y0Thw/hhPHjuK4tDNyHT/TpQvnsX/vXths2YydO7arcwQ4Lblkg4AwOjpKwLiOjevXYevmTQLFCTx59EhZmlt2N3DwwD5cFeBevXiJO7dvY9f2bdhusxUXBCA+8JHDh2LC+DHYtXMHjhw+hNEjh6N/n17YsG6tPGRbucdNdf/ztgLcqZMKPgLE9yFwe3btxFG57ozAeOb0SezZvRNzZs/CwgXzFTT79uzCZLMJ6N+3N8ynmAk0u+VLcQkXBKCD8qWx3rAe+3bvkXtewGbrDZgza4b83Khec9vOTt7vjILr9KlT6gt17OgRBeQNsbYX5R78GyzmzMbsmTOwcrmV/I23NAiTW7SEz548VlaBLtRVXNwbcWtPHj/Cw4f3xcW9UrFbdFS0cttvxW29Fvfm6+MNF3FnDx/cw9OnjyWOExcp1+7fuwc7BFLe09/fV13D2OyaPHRa0EcP7sNbYka+1yEB/NSJY+Ky38DH21PcuSc8PNzxSu5Pt/leXDjd6RWxagf27RHLa4NzYtXohnnu/t07OHrokLLKdPP35PdDB/eLxb4u8Z+3xJrv5f0e4NHDByoeZOzJkMFT3iNIYkOGFPfv3VGfef3aNdgqFpGv1SBMZjH2OyrucPHCBQLJAVy9dEEsy06stFqGLWJRaM3oSh9KrMefN69fxTWxMnfESj4SAAmb/fOnEq+Ju755XSylDXaIK74sUD+gC5aHSljWrl6JmdPM1b1vy7XHjxzC3NkzsHyppUB0UQCywy25/qFA+uqFvYrtCMTNG9fE6p7B0YMHsE7usXbVSnHn53D3zi0JDfZhxbIl2L5lC+yuX8dpcd+brdfL8b3Kil+/elmFBbSmhPGZgH/vzm157TX1uWihadVXLFuqvMAlgZ0JkBYTJrOYaY4ZMxb58+fDjzWroVO7NmjWpBHq1KyOhvXqolP7tujdszv69u6JXj26oUvH9ujYtjW6dGiHHt26oG+vnsr9mvbtgx5dO6PZz43xS+OG6Mzr5PWmco4/f6rzI6pW/hYtm/2MPj27oX2blqhZ7Qf8VLsWunXuiJ7dOqNzx3byswuGDByAYYMHyut6oEunDnKvdmjfuiWaNPgJjX6qh07y3r16dEXrFs1Qr3ZNNGvcCL26d1Wfq3GDemjVvKm6Dz9r/bq18Yv8PQP69cGgAf3RvUsn9Teayu+8z7dfV0SNKj9ghnxBnsgXSeuiSQERwgEDBuBf//oX0qX7F3Jkz4ZsWUxgnDkTshhnRs7s2ZEnV07kzZ0bueVnTjmfPVtW5JCWM0d2dSxP7lzIm0fO58yBbFmzqOvjr8snx/nTRO6V2Sijui6vvJ7XmvA9TIyRS65j43vnkuMF8uVFQflSqPeT33mMP3nvrHJv/s5zvBfvm12O8zPweFa5Hz9f/LXGmYzUNfny5kF+uS+P8Tx/5/X8u3PI9QNN+4v1fRn3fyXtyCAgZF+cqampehhpuXXu0F7Ciudx/1fSjgwCwtDQEIwaORKZMmWCkZERMmbMqGtJ/p0hQ4aElnCex39zjr9/dj7JuYwZjRLuH38sKQTp06WTY7+/Z9L7JW18re7fiff8T+dVSzivez0/U6EC+SUEGKj6GdOaDAJCdtFcunQJy5cvT9Y2deoUlClTBukEwCyZM6Nju3aSHC38w9f+023DhvW4eOGC6htNazIICFNKHK1o0KCBsoI5JH5ctWI5YiQ+1ZS8StMQso+xYRIIly9biqiI8LizmpJLaRpC9jvWqV1bQZg1SxbVRUIw01IfnSEoTUN48/o11KpZU0GYxcQEE8aNxUv752muny6llaYh5MSCmjVqJEA4bvRo2D99qkGYzErTEHJ2TVIIx48egxdPn2kQJrM0CJNCOEYgfKZBmNzSIIyHUBKTiePHqYkLnz5pECan0jSEnG5Vq1ZcYiIQTplkBsfXDhqEyaw0DSEnztatU0dBmDVrVjU728PNNe6spuRSmoaQ60QaNWqkIMyWLRsWLZiHsOCguLOakktpCkLOdH4s1u/27VtqMimXA1SuXFlBmDmzMXr17IGdO7bh7NlzOGdri/Pnz6t248YNvHzxQs2S1vT368uH8NMnNQLi4+2NrZut1STYZk2boFH9uqhS+Vs1f5AQpk+fHnny5EHJEiXUpIakrW6dHzFq+FA1tZ8r43g/bVTl79MXC2FwcCDu3rmN3bt2Yt2a1ZhvMUfNuM6bKzuyZcmE3DmyIodJZhgbZUAGgdAkU0ZpRjDJbASjDOkVmElbmRLF1GzpaVMmqcVMu3ZsVyv2uBSVC901/XV9kRAGBfrj7JlTGDFsKGrVqI6SxYuiSMH8yGaSCVkyZ0SxIgXx3TcVUalsaQVjRoEsR5bMqFSuNH5u+BNaiKWs/kNllPiqML6S6/LlyoGsxrzWCIXy50Wl8mVRo1oV9OzWVa20e+PwCp+0vsW/rC8KQu6w8Oa1A44cPADTfn1RuFAhZMyYOHE1k1i4EsWKoH7dH9XakNrVqyGPAMb5hJyCX03AG/rrAMyYOgXDBg1E+9at0FyArPb9d8ifN/dnljFjhgxqIirvs3qFlVpoxS1ANP33+mIgdHdzxe6dOzFsyGA0bdIY+fPlU7Bw/UfFCuVRt3ZttGrRAr+a9oP51MnKrXZo1xYF4l5HqGoJlFPMJirrtsxyMcwmjMe4MaMxeOAAdO7YAT/LfTnrpkL5cmr9C6/jGpEa1ari1wGmmDd3Ll5IAqPpv1Oqh5DWj+uSOSG1du0fFRhGGTOqYTguXKpRVQAR8ObMnIFlS5dgw/p1KiveuG6dHO+PIoULfwbh1MlmajcErgG2mD1btUUL5mPJ4kVYtHCBWqDO+9Wo+gPy5c4FExNjeb8MaoEWp+qbm5vD1dVF7TOj6c8p1UPItb2jRwzHv7/5Wq3VIFCFCxRA7Zo10LplCwwSCzV10iTMnTMbC+fPw6qVK7DNxgbr16zBAHHZRQoX0kEoAP0o8ePUSWaSeFhj7erVmDNrlkA3E3MlqVkg17LNmzNH3W+IuOuOYkl/rFkdXxUqoO7BVqxYcbW088Txo2ojJE3/WakWQu6sxYXpo0cOU0szFUjp00sSUlziuJ8xZOCvmCTulBNVp5tPxZTJkzBJXC33mFm/Zi1WLFum1isXLlQwAcLatWrAXF63ZdMmrFm1CrNmzMDM6XK93MNc4sSpUyaLpRRXLtZu9sxZMJ8yRa0jbt60Mb6uUE4t5eS9soir5vFr166o3bY0/f9KtRByd4Sxo0YJdF+pB59eWkXJdtu3baPiQsZz0wQcQhjfpk2bqlzqRon5VotF7N+3DwonsYR1fqwp4E1T3TqbNm7EPAsLZUHZaBEJ5Yxp01SbOX2GwG2uJsISeC7QrymxIdcl837fVKqISRMnqE7xtLbV23+rVAlhWEgIdmy3wb+/rqQDKP2/VLdJV0keCN/M6dOlERZz9ZNjwrNnzcSc2TOxdMkSbNm8CRvWrsVAU1MUKRIXEwqE9erUFks5B4cku96+bZtaecd4kG2+JB1zBco5EiMSSL7HdPNpAvpUZR0nTRyv3PC/K1VQ9zMyyohKFcsrqLm/jSb9SlUQcp6fh4eH2kmLFs8ooxEyZ86M776ugN49uirLN9dCl0wwgWDj7lqM6ebNm4v58+ZhtbjZfWrDJBsMHzoERb/SWVJC2OCnupKALFQ7d+3bu1clMoR2qaUlFi9ahIULFqh70EIyXtS56+kC+3Q5NkfBzi0+ypQojkwCIe9bU5Kdvbt3qY2PNP2xUhWEfr6+2LNrF5r+3ERNvUqXLh0qSCzWp2d3ZXFoseaIxSMYBGSuJBFMJuiCFy9aqPYb3CzxHrdnOyzWbuzoUSherJjOcgmEjRvWx6rly3D54gUcOXxYkpiVWLlihWpWEkMSSEuBcRFhpGWU+/N9pk01V++7QECfKS6/W+dOKF+mlLpvtqxZ0aZVS7XHIXej1fR7pRoIuVUId9ZislGwQH71gEuKxWnXphUmjh+rgGDsFh+z0f3OFygI3tIllsqqWS1bqtzshfO2OHn8GCaMHfMZhE0aNcK6NavUvoEnT5zAOnHZayWL5k9aUAXj0qVYupiWcaECnPsKzqA1FLdPy7tAEh+GBO0EvAply6hhwJw5c0hiNFltKazp90oVENKCPH/2DMuWLEaThg3U8swc2bKpseDRI4apDSyZqTI+UwBKzMYsmBaQAC63WoYVy60EouXYuWMHLomlOyMul0AXL54IITu5N65fi9u37HDu7FlssraG9cYN0jZiw/r1Ckh28fB+tIp00fEgzhRXPE2ycMagDAtGDhuqdugqW7K4un+L5s3VvojMljWL+LlSBYRhYWHYIRbs58aNkF3goxsuXqQQ+vbsgWlTJqsZ0VMnT1HZ6mcASiy3XNwoLdia1asEotXYK/Ekt+nl5ANzuZazZhSEEsM1a/qzmmnDrh9uT7xt21a1aeXWLVsEyE0qq163do1YxZUC9XKxrkuVpSWIyjWLJVRZuEBoNn4chg8ehAZ168LE2Bhly5SGxawZYmWvqY3atVk4iUoVEHK3+4njxyBXzpwKmNy5c6NhvToYLzEdXSBhohUiBEkt4AorK2W5aME4UkKImPlyk/VrV64q61WqVMk4CI3QvFlTNV3rxQt72NnZYdfunZKFb5O2HTZbt6qsmpaR9yLQulhRB+LC+fNVwsLkhBDyM7HPsWunjmpkJZPc/4fvK0ssaSFW/almDZMoVUDI7Xu7du6gYGGrXq0qRgwdjFnsfhHwlBuUh88sOAFAcb+0WLRcGzdsUAnJFrFqJ44fVxNbuS803WjpUroEghC2atFcbdv77t1bPHjwAPv378Me7mm9e7dy49u32SjLuHmTtdwzEURaRA7rEURmzezcpkXkF2Twr6b4d8XyCkJm4BzFOXn8qCo7oUmnVAEhS0I0jpuGzzl/Hdu3U0NwTETUAxcY2RVDt7jEcrHKZJnZEkBaLrpTJiQ7dmzHuXNn1Sxp7uLP15ctXSYBwratW6ssljVQnj9nNYEjynIePLBfdetwQ3XusG+zle55I9avW6vcPIFfJjEivwB0y/xCxPdRThg3Ru3WWrqkzuKWl2RlpWTg2thyogweQnb0rhGLxhGIDOn+haKFC6gdTZntWgh4dH3MhJUbloyVx+mCEwHcrNwprRmtGpMS1hdhaQpazHJlyyZA2LF9ezUPkbVO+Jozp3VlH7jz/pHDB1V5C96DMPO+vH98jEjw6ZbnzbNQn4cQqjBBPt8USZzq16ur4s68uXKqbJ61VbT1zToZPIQXBZo2LVsid47syJHFGNWrVMaIYUOUJaS748NWkxMWzIelWEFmrnSTjP8Yw9GF7t61C/v37ROI9qukhEV7uC0c4alQvryCkBt09ujWVc5fVtsXs6IT65DYiuVkDZKTJ46rvkPeY/fuXZK02Ci3zPhwzerVKlEh1AsWxGXLYgVZX2W2WMVF8+eKlW2lIMxmYox+vXuqLwO7nTSlAgi3bN6MwgULql1UmRG3+OVnNV67YO5cBSFjQgb77LdbKlaQ3TB0k+xeYTLBWI6jH4cOHsThw4dUTROOXviIhbWWuK5SxYoKQuPMmdVG5nclVmS5MlaUYg2Sq1cuq1ojZ8+cUfEkQWSsuGvXTuWW2X2zds1aeV9aw6Xqc7Ajm1k6u434BaH77dq5kxpFyZQhg5oIyx39WUpCUyqAcKXEduzDIyjfVqqgdtKfPMkM8+OGzlQsOG+ecoWEgNYt0QpuU1bw4P4DKr47Lq71vsSXrD8X6O+numO+rqQbf84slrBPrx6q5APnKLJj2eEli/fcUt01F86fT3DPhw4dxF6JEbdL5syEZ/269fK+q8QKW6mYlAkKhw5nmJur4bwVYp179+yhZnEzpq1R5XtMnzpZZcmaUgGEq8TVmZiYqMVINav+oEpIEML4CadMBPjQ+fCXi8WhK2asZrNVV6aLVvDIocPKirGi0uPHj1RSEBwYoOqGxEPI/aMbNaiPVSusVJEdQhjg769q2V27elVc86WEilBHjx7BAUlWEq3hhrhMmS5Zl6DEjyXTEvJ3TqDldK+8AmLRwoXQrnVLNXKjKTVAKJYwO0tKmGRG4/p11UwVxlpMSggh++b4kJmQrGRCQlcssdo2m60KEsLCMl4EkPEdi9kQwkB/X7VqrpIkPISQHeAF8udXk1TZv/dCsmMW+Xnz5g1YC4+xJN0y6+7p4sND2LtHrKFYW7p+Du0xIeLnoEtmosRQgSEDP+vokSPwc8MGElIUFqtrhLKlSqgZ3poMGELWFvaVuIyTSVnzg6vlOrRpiRFDh6iMkxMG+HD5sPnQ6YpXiSteL4nC5riEZI8kEIcOHVAu9KzAw2Tghf1zVXbWxektli5eiNKldf2ESVvFcmVVZSnK1dUVd27dUhU+dYmKriDjMXHvTHYYczJu5bAeXTL7DHVxoWTJjFnFGvKzcjy5U/t2qFCmtHoPWkRaUE0GCiGHtAgga911kYCeY8UVypVRFZ3MJoxTmScbHy4XF8VDyHiQ2SrjQY50cIiOlT85GeG8ra2yZiz5GhjgD3uJx1hiLH4CQ9L2VcEC2B1npViD7v7du7C7eVMVeeR9aFWPHT2qMuVdO3UumR3izJLju2o4o4afj40umePb7C/8uryuS6hA3jzKgmoyUAg5pMUChnt27VAr3LIIhN9+8zUG/Wqq+t5oXXQjEjNVJqofwj0C4SGcEsvFxIKxHWdkMylhkUarJZb4Tu6bFMDCAmDbVi1wVZIR9uO5iyUkhLckU+b1ugTllOo7/CMI2UXE+JQd4Uya2GgVCWGHtq1RungxcIlprhy0hBvj/uK0LYOEkF0kLLy9U0Bq3KihgpCzqAea9pN40OwvQ0hLxpjwvY+32haE8woH9O2NQgXygeuTv5KEgZNSt6nuE2/1OVju9t7/CCGtIusvt27RHIUk7iTsxsbGEjqsj/uL07YM1hKy3CxnJKsJrJIdVypfDn17dldzAAmgLtaSmFASE07D5zy/hJhwk657hqMb7E6hO2YsxwyXXTQE3NvbS1V7Z/XNnt27oXrVKqqY4h6BimVuYz/Eqk5rVpm/e+cOboo7vnLlsqruyQyZyc4fxYT8MtAdcy4jExNCyMm2/PK0bP5LwnpozgjXINTJYGNC1gK+cP4cOnXsoCAsWayomp83bPAg3UhEXNb5nyA8ePCAWC1JTM7oKrMTJnbTsMw/raGXh4fqkCbw/MmaxPwSMDHy9PRU8xhZ6Js7c12+fAnnJcOmBWWVenb/cEhQ11e4TmXyywTC+MSEXxQO4SkIJ5mhVYtmkoHrINQsYaIMEkLq48dYtbXG4EEDFYQFJZBn+VmWk51sNjGui4YQ6mbOxI8Zc7QkHkI1XHdgv+qoTuqSb92yU26ZRbrDw8JUVwwb3S9/srPa09MDzwTA+/fuKVd8/dpVlV2zi0Z1WAvcTHyYhcd30XBGzVL5MsT3EzJ54peFEHJnB5a4ZZVPDcLPZbAQUh7urhg/fpzKjvPkyI7GP9VVLpOTWGlpdJ3VunHj+Olbus7qjRKn6YbsOLJxSOJCdlZztjS7Wa5fv6Z27HomGTInErDINSeacjjP3c1NWcnn9gKguG61l+H167hCKxjfWS1WcP++vaqfLz4e5JzF+M5qLoji5+J6Z2bHVvIFmSoxIesg586VQ0HIDngNQp0MGkLf9z6YItkwLSELIP5Y7QeVOHAHBE5goCVMupYkMTlJOnlhJ/ZLAkFryK6V8+dtlVsliHZ2NxVktHaPHj5U7eGDByoRYRwYv5nm1SuXxIraJg7biRXkrBzen++jm8Sgm9K1xNJSkpL5KhY0n6LrVOcsICYmtapXkS+UsQbhb2TwELKzmpML2K3Brdvat2ml3DEhpJX57WTWxAkMtIZb1NAds2ROYCBAZ86c1oEoFpH9hjcEMrpnxn3xje6XoyQEVTdubKtm0iRMYJCEJD4r1s0r1K094ZeA607iO6qZjMRDOG7MKLUmOX4pqIlJFg3COBk0hOxK4axpzkrmgytcMD+aNW2s5uOx24OBPye18kHHT2ilNaJVonXiVCs1fCfAMIlgdw2TlPghPA7D0Spek3iPwMU3dsUwE+Y0Mlt2TrNLRgDmUB0nuOqsICcvxE/lSpy8QCvIMEFN5ZKwgZ/RUhIVdi9x0RPnRPJvYbeTBqFOBg6hl4IwfqOj3DlzoJHEhePFqjAOpCWcIedpdZIO3zFBiJ9TyCSFGyARRFqwBBAlUWGSQatI2JK2CwLn+Qu2ahb2KYkB+frDYgEJIK0qM2J2y/D+ulhQN8Wf78/Pwf5LLrpi2MDJFpx61r51S7XpZsb06TQIfyMDd8feYunEEmbSQZhV4ihOgxo8wFRZPwb/ap2JWBtOJCWYtEYcOksKYmJ8qJvcStfMGJETEdjxTFebtDH2YzvJrpijR1RfI+NKAshkJ+msanbL6IbqEjuodVuE6FbdjRk1UsWxP1avimKFCiBT3LQ0DcJEpQIIzdWsZz44tmKFC+KXxg0xcviwhA5rrjWeJVaRVoiZaTyIupV2iSDSNRMiulMdjAdUjEfQjh07qkZB2Pi7Wl+i4NsnGfZuNSOHFnDrFt3Urfhp/XT/jEV13TLsG+RGSboF+Px8nHDRoG5tlC1RFEXy54Vx3N+iQZgog3fHTEy4ESWtIddnfFUoP8qWKo4mjRpi7OiRyhWrRe9qQgNn1cxVQDBL5RBaUhCZRNCK0T0TRlpGWjfGi5zyRXfLn/sI3p69Cla6cQ4BMgmha+d9dBZQtwg+fuoWhw/VFyJukyRuDcIuGm4/xy1BcmbJjPyc1Bq3w6sGYaIMGkJvLw9MnDBebaPBLTUYV3G9ccEC+dRGRt3EzTFT5ggKHzjd4GwFIucYLlQWKmmMyCSCINIqsh+RMNK66YDcqaDcJW3nzh3qOJMPWk+Cy+viY0C6YALI+ysA1YwZnUUmgJzWz6lbtILcKzFfnjwqIcmV1RiZ47JjDcJEGTSEnh5uGDliOAoVLIjePbpj97atmCwPt0zpUmov6kb162H4kIEqW2b8RQgIIuOyRItI17xUWS5msey+IUzs0OZIBxMMuljCxmZD6MTq8Tgtnw6+Deo6gkyg6ep5X95fATibichUTJFEhACaT56stifp0KYVqlb+DkUkFsyVLSuyZjZChvS68hRZsmTVIIyTQUPIERMO25UoXlxt6eHp5ooTEq/VqqmrzFlOYOSD5nbBnBvIrJRuOR5EukjuoMWkgSByRRwnGRAmutTPgUxsjPl4fMO6dWo4jtZvzWru0BW/9cdiZQHjE5EZ03VJCK3gzGnTMX70aDVt65tK5cUVl0bXTh3QtkVz5M2p28lVg/BzGTSE7q7OGGDaH6VKlRIrtQ2svunq9A6dOuh2Y2D/4ffffYv+vXupPWlUtizJQLxFZH8dQSQshIZxIq0YkwkCRbfK6VeELL6tU8CtVtsF8/yK5SsUvPHxH0dmaAGZidPtc6YM41b2C3K9C7uMunfprKbvZ5b4j2tY2C20QywsjyVCqLnjeBk0hG4uzjDtr4Nwx3bdTOcPMdGSQBxARwExnbg2Dun98N136Napo9pla65YplliERN36IrbKFOAIYyMFS0XLVZAEirCRcg+b1ZqHxu1DZy8zlJcbzx8dL8coWEXEe9Ny8u+TP7OLwAL7JQvp5s9zda8WTM4Ozvj9q2b8jn/nXDcRIMwQQYPIS0hd86ie4wXp3px2lXVKlWUNeSa5DIlS6Jj2zaYOI7xoW4LXx2Iuu04FIySPFiItZpnodu1ldZMZyF1UCY2+Z0uV4DlSj6CR6vHvkiOVdP68Z60enTDnO3Ngt09u3dFOUmgCBmXkNJKc/IClyrYnjujQahHBg8hi9RwHchyiemSVkzirq2Eo9oP36txZQb8ZUqVRJuWzTF04ECYjR+vkgRCyKbbpEjnphk7Eki67/nz2Lc4//MmFpNWk2PAfA1HZggeN8PkfdgUhAIgN0cfM3IE2rdprSoHcNMjrtxjJYCllovgKn8Dp4cdOrAfFcvpAGXT3HGiDB7Cgb+aqu6YRWKRoiMTdzqNio7GS3t7LBSIWK2TIPLhliheDC1+aapA5HAZLRUzV1orduXEW0iCpOvsnikWTjc3kW5bNTlGi0fQeO00gZklKCabmanGUhLTzbnHzERVfqxTuzYS7+k2PGKrLBZwwdw5quZdvFjCtkRR3SbtGoSfKxVAOEBByG0/IsI+38mKbpmTU1nBs27tWioRYCmJ0iVLoHGD+ujYrh369+mtCi2y3071JQp4BEw1ZRF1jf9ObLr1woRUgSrHdCMhUwXCCRg9aoSq6sQEhGuJK5QpBWOjjMoFVxHLzPe4d+cOoqMTS0ds37ZVdbRrEP5eqQZCusaIP9hOja6OO2gdO3wI7Vq3SnjIrCfC/kWu8/1ZgGTHMWfecEuOlSusdCMdkmjwGIfbLGZzz2vGixaq0SVbLlqAZUss1VQsZs3crth8shl6dOuMHyp/h6+KFEmol8xad21at1Z9jq8dHH632dE2my0oXEA3tV+D8HOleggTJFaRm6HT8rVo0Vx1jTBh4QPnjl4/1qyJzpJB9+vbBwP691MFcLgrArf1pZtmF890umlp7GymxRs3eqRa08ISYoPEvffq2R3NxdVXiFs7zMakqWHDhhg6dCiOHz2GkODguA/0uTQI9evLgVAUKTEjV9G9dXyjKjZV/aEyjDJkUMs5OZM5e/bsyJkjB/LkzIFSRb9CzapVBKqf1aL0Hl07q+6VHl27oHOH9mr3r5rVqqBcqRIokC8vcuXKqa7Nli2rmmTLvWu++7oiZkmywomw3MXr/9udX4NQv74oCJOKScEicaldxPrVq1sb5cQt582dS2I3IxU3stA297cpmD+/ZN9FxaIVRymJJUuJZStWtKjalyZ7tizIYmwEk0wZkD2riapvXLZ0KVVatn27tli6eIHayeHPSINQv75YCLnjP7Pn87ZnVVJguXC+uNaBaCnulEW0WdGdIMZDoa+VKl4U9evUQvfOHWEm2fbiBfOxeeMGnDtzGs7vuNvqn9sAXYNQv75YCCku4YyICFfb//qIm7a7cR3W69epafcsiMg1H7SG7N4xSp9OVYbPnDG9LtM1yiBWsbi46g5qFObAvj149vgxfLy8EBgQgAhJPDiM+GelQahfXzSEvxV3zHdxdlIr6rgYntt9sEN5/tw5am3wIrGWzJg5isKfnPrF1z17+lStd/lfpEGoX2kKwpSUBqF+aRAmkzQI9UuDMJmkQahfGoTJJA1C/dIgTCZpEOqXBmEySYNQvzQIk0kahPqlQZhM0iDULw3CZJIGoX5pECaTNAj1S4MwmaRBqF8ahMkkDUL90iBMJmkQ6pcGYTJJg1C/NAiTSRqE+qVBmEzSINQvDcJkkgahfmkQJpM0CPVLgzCZpEGoXxqEySQNQv3SIEwmaRDqlwZhMkmDUL80CJNJGoT6pUGYTNIg1C8NwmSSBqF+aRAmkzQI9cugIXR3dcGggb+iaFFC+PudWlOTNAj1y6Ah9PHywLChg1GsWFFYLlqED0m2301t0iDUL4OGMMDvPUaOGIbixXW79wOfdCdSoTQI9cugIfTycFNlxbhppeXChZol/EJlsBB+/PgB165cQquWzVWVzCEDB+KV/fO4s6lPGoT6ZXAQhoSEwMvTE1cuXYLZhHFqG18WymF1pIXz5uLe3Ttqr0C+7tPHP79JZUpLg1C/DApCNxcXLLVcjK5dOqN+/Z/EDX+V8NDSp0+H0qVKoXHjxujerSuWLlkMh1cv4640fGkQ6tdvIJTAPzYasVFhiAoPRVhYOELDwhARGoJgf194u3vA19cPEZFRiImNQVRkGIIDfOHp7gVv7wCERX74y6nD27eOKu6rkKQ4Ya6cOVG2TGlUKF9e1TjOkztXwrnyZctg1vRpqphOdFR03F0MVxqE+hUHIdFh+4iPYV7wd7yLJ3aXcPbsBZw+exEPbl2D3blj2LR6DWxsduHmvQd4+e4NXjy/h4sn9mP9inXYsPkwbj5+B//wxPpzf1YfYmKweuVKlCtdOuEhVapQDgP698WCeRawVNXVLTBsyCDUqVUDWbOYqH2mS4urnm8xGy7OznF3MlxpEOpXEgipWHzwfYxnJ1dg6dShaNO2K1q37wWr+TOxcvZ41KlZC1V/bIix02djzY7t2LTRCmaDu6LWD9+j+k/tMX35btx28cXntYz+s4ICAjBk8CD1cAhXg5/qYsnihbh9yw7OTu9UkUL+fPL4EbbbbEan9u2QxdhYvb5t61a4cvmi2iTdkKVBqF+/gfAjPgQ8xZPT8zGyR2PkzVsKBUvUwLQp02Gz2gIdf66GimVKol6zDug6ZgZmWy7FzHG/okHlEihbojQ6D5qKjZef42W43OdP+GWCExoaint3bqNF8+bqwbRo1hQ2WzbDSaD7KIkH69fF/6QCJCw4cugg2rdtg6xZs6BSxQqq3NfbN28+qyVnaNIg1K/fxYSfPrzHe9dDmDu5HyqUrYMf6ppiy96L8HF/ihdHLDB3cGs0btEd9fvNxeojd2D/8Db2WgzE0GZV0H/QGEzZfgOnHSMR+p8MkzAVHByMF/bPYb1hnSoDVlGA2rd3NwIDAxV0kRJ7+vv74f17H4lFfREVFakuDZXMePeuXSgu7tgkcyb06dkdRwVMlokwVGkQ6tdvIKRCER5+CauXTMCPNdujSYcZOHrZUR2H4y6cWDwY7boOwU8DVmDbdW/ESnLyYq/Ebb3qYsTwsRi94Sr2P41EUIzubnolEPr5+eGW3U2whANrGletWkVVSI+Xr5+vSljevHkNR8c3CsZ43bSzQ4UKFZT7ZmFFFrihyzZUaRDq1x9AGIjQYFusXmqGunW74OeOM3Do/EvxnQLAo404tGAguvUbi19GbMS2qx4I8fPGvc2TsaBHbYwZY4ZJNrdx5MUHBCsIxbLSlX4UlyrQsSVI/u3v74+7t2+rGiKlSpbEd99+izOnT6nTdMFeYtkIYHxj3bp4Xbh4EeXKlYNxpkzo3qWTqkni7OQUd9bwpEGoX38MYchFrF1ujvoNe6FZVwscuSAQxngLhNY4ajkUvQdNQstxW7H9uieCfT3xYMtkLOlbH5MnzcD03Q9x/LW4WkIYI1Y1wAdB/gHwD45CsHjTpLFicFAQHj98oGK6MpIZf/vvf+PUyZPqHCH0EctHCxjffJIUtDl//jzKli0LE+NM6NW9K3bt2CYJjEvcWcOTBqF+/QGEQYgMuwzrVdPRoFFftOy5EEcuOugs4bOtOLV8FEyHTUfbybuwy84HwX5eeLxtKlaYNsQ0c4kZDzzHWWcgRGLCKB9HvL13BY/v3sVDBy84+sUiaQ9OVGQk3rx2wNo1q1ChfDkVFx49cijuLOvThcLd3Q3Ozk5wc3NFSEhiGVdazDJlyiBnjmwYNKA/Dh/cD09Pz7izhicNQv36HYSfPrjBx2E7Zk/ohUpfN0TVhkOw5+QDxIa7w892IVaObIMmkpjU7DoHG868gp+XO84tG4lhjSuiS+de6L/gCHbeD0Vg5EeEOt7B3QPrcXT3TuyxfYBLDsHwjUg0hbR2LNF69MhhVKteVRXJnjnDHA4OLyXT1XVAMxkJCQ1JSEpiY2Pg7uaCeXMtkC9fPhT7qghmmE/BjWtXVUJjqNIg1K/fQPgJMe/v4ObOEWhduxQyZMgCk1xfY8OOkwjxfoXTC7uhZcWcyJo9D4zz18WstSfhJnHYksE9USxrBuTOlRdF6g3AxE234BkQgRjnO7i/czG2r16G+VtOY8s1ZzgHfJ6xsHK7o8R7HTq0Vw+nXLmyGDN6FG5cvyZnkwaROjGbnjZ1qiQl5dXra1SrBpstm+Dh5qbuZajSINSv30Po9xj3jy7ExMEd0axZM7Rs3QunL9gh1M8FF7fOwNjuzdC8eXP80moQbA5fg4+nN3ZYLkDbX5rK65uj5a+zsPzQPfgGRQBud/Hq4FLsWWeFmRtPYNV5Rzj6/r4vLyYmWlzyGlSMAyt37lzo2bM71q1ZjcOHDqqK7ocOHsDmTdYYPmw4ChYooF7HGHKehQWePnmMDzFaZ3VqVRyEiRbnU2woIgOd4OTwBA/uP8HDp2/w3j8MH2MjEeHnDPc3z/Ds2Qs8tHeGh184YqKj4OfigFeP7uL58xd46ugD16AoxEgG8snpNlxOrMaJHdZYsucKNt3wwLuAP4bl3du3ah1JieLFxQKnV9XVc+fMjrIli6PyN5VQpmQx5BM4s2XNCqOMGVGpUkWsWG6lMmJDHy2hNAj16w8Sk7+i37tN6uPbW/A4sx7nD+zAmiO3sP32ezgH6ilS/emTmoww2cwMNatXQ1aTzAkPLGkrkC8PfqpbB7NnzRQ3/ibuYsOXBqF+/U0Q/pF0ltDb1hqXj+zBhhP3sOuuH1yC9M8BZDLC8eEt4nbHjh6JerVrIUf2bEiXLh2+KlQI7Vu1gMWsGdizayfsnz+TJOXPVV03BGkQ6tc/CmG0wzU4Hl6KI1vXYdHOi7C+5oZ3/v9/8kDXGhIcDKd377DJegNqiFXMni2bGhU5eewofLy9ERYaKgAavgtOKg1C/foHIIxzzZ8+wv36fhye0ROTB/VFx9GWmLjlOp65hejO/wlxGK5vn94oUrgwZs+cocaMU6s0CPXrH4XQ6eZRHLAYjGmjhqCf2TLM3nENL90TO5z/k0KDg1R3TckSJbB65Yq4o6lTGoT69c9BKD8jfJzg/uQaHt+xw7UHr/DgnR8C/otJr74+3hg+bKia3MBp/7EfDLcf8D9Jg1C//kEIKSYhuuSBR/lb0rP/SW6uv9kGRNuB4YvUP5iY/O/S9qJJG9IgTCZpEOqXBmEySYNQvzQIk0kahPqlQZhM0iDULw3CZJIGoX5pECaTNAj1S4MwmaRBqF8ahMkkDUL90iBMJmkQ6pcGYTJJg1C/NAiTSRqE+qVBmEzSINQvDcJkkgahfhk0hK7OTvh1gKmCcJ7FHA3CL1QGDWFCRSeBcMG8uYgMD4s7k/qkQahfBg1hdHQkJk4Yj5IlS2Hd2jVxR1OnNAj1yzAh5O6ssbGIjIzApIkTUKpUKfXAki7xjN+5NbVIg1C/DApCQsblnm6urnjy6CHOnj6Fju3boUCBAhgzapQ6FuDvr1bdcZthbd3xlyGDgpAAXrt6BUstLTF08CB0aNcGpUqUgLFxZvxQ+TuMHD4Mq1csx+mTJ9SWcoa8AdJvpUGoXwYFIRe2W29Yj0YNGiBXrlzIYmKCDBkyqB0YjIyMkCN7dnxbqSLMJ5vh0YMHCdvHpQZpEOqXQUHIjdRPnTgB0759Ubxo0YQHlilDuoR/lypeDFZLLVXpMc0dfxkyKAi5aaa3l5fadbV7187Ikzu3emDGRunVz6zy4Dp3bB+3d2HqkgahfhkUhBRBfPzoASaMG6O2/+ADS58uzgqWLIHp5lNUPJjapEGoXwYHIeXm6oKF8+fhqyJFEh5a7lw50bRJI2zauAEe7u5xr0w92r5tK4oUyq9B+AcySAgD/PywbetWVK9WTSUkTEy+/boSzMaPxcUL5xEYEBD3ytSjnTu2odhXhRIgZGhhbW0ddzZtyyAhjIyIUBuhjxk5AiWKFYWxsbFYwcaqTISnh3uq2Jn1t+KeiiWLJ5bOzUYIN26MO5u2ZZAQcrTEy9MD+/fsRr06tcUV54Jpv354eP+eOpcadfzIYZQslghh5kyZsGjBAkTHVSVIyzJICKlYsXb2z56he7duqlTEpIkTJXM23Dolv9OnT6rgY4CEDu4Sw7IDPm/OHAkQZsyYEV07d8KJY0fVft2s4Zea+j3/ThkshFREeDjMJpqp3fpnz56lxpJTi0KCg3D7th2WWC5Gt25d8c03Xyv4jDKkR+4c2ZAnZ3YU/aoIqlWtijatWoL1/e7dvZOqRoH+Lhk0hNRGiZsaNWqITRLEs/smtYh7as+eNSOhLAYbu5jq/FgTLZo2RpMGP6FE8WIJ58qWKom58kV76/gm1U3O+F9l8BDevHkTa1avwp1bt+KOGL78fN9j65ZNqFe3jsrsM0n8V79eHUybMknVZtlsvVGNgY8ZNRI1q1eFkVFGpBcQ69etjfVr16SKSvZ/pwwewsDAAFU4kcUYU4NCQkJw7sxpdGzfVvUFmpiYYILEsxfO2+K1wyvJ7j3g5eUFV1cXVTJj+zYbNPvlZ0lUjJA1iwmqV/kB221sVEycVmTwEKYm0Y1euXwJfXr1RP58eRVUPzdpguf29nGv0I0IsfLAp0+60ILj5SyL1qRhA5gYGyvXPG7sGA1CTX9N7L+0mD0b2bNnB4uBV/3+O1guWqiKSFKsWspyuR4e7qqAePwEjHdv32DxgrmoVL6cgnDQoEEIl6QsrcgwIGQgHmcZUrPYxTJs6FAFUob06dClYzucPnlcTcIloJ6e7qpus4O4ZSendwpKKiwkGPv37FQxYcYMGdC1a1dVrYo1/1LTTKG/KgOBUAD8KC4qNgqx0RGIiQxDZGQkIqJiEBn9QT3cmJgoVUcvMioKYeFRiIiMEddmWFkkP+fwYcMUhFkyG6F/3964eMFWWTV2vTAOZAX7168dPoMwKMAfu3dsEwjrqLp9nTp2hP2zp6qfMbUVDforSnkIVXcEv+2xiArxgsvTG3hw6RSuXLoM2xsPcc/+LZwlMXFzegWHF49w+859nDp/Bzfvv0Zo2O8rhqakCOGokSMVhMZGGdS0M1YnDQ4OUrGgp6cH3r17q6yhi4uzwKlbPejj7YkN69agirhvZtP9+/eDr7hrXhMfO37JMgAI+T+ZEH6C97sH2DZnEH5t2RStWrZC847DMW2JDc5fuIizx7djpeU0DBs+Cg1aDcbY6Rvg4u6rbmEo+iDWbo7EhPny5kGWTBlR+duvYTFnlsSBPuo8LZ+Xl6dk+87w9vZCjEo+PsHhpT1mTTdHiaK6WUODBw9CtFj8tCIDgJAA6r7tbvY3sLB3TVTLkxU5cuRG1q8aoPtoK5y1vYiTh7dg/qwx6NW7D76t2QGmIxbinYu3us5QxHHt40ePom2rliiQNzcyGaXHLz83xoXz55VrpZhBc7w43sL5+r7H5k0b0aZlc5hkMkL69OkxduxYZVXTigwgJkyM64JdnuHsYlOMb1kZ9Rs0RZXOszF7mx3cPN/Dy8MZL188EXd8B/sPncW5C7cRFGxgi+EFMB+xcNbr16Fale+VVcubJzcGDxwIuxt/PBvc9txZNGhQXxUa5+vLlymDVStWpMqZQn9VhpGYxCn6/Vu8OjAHNmZtMXT4eHSbdwrbbv1+7uAHMSIRkrB8VPGk4Ymd0lMnm6FC+XLIbJQRhQsWRI9uXWFltQzr1q1Tk1nXrVuPFSuWo3OnTgo+xoJVq/yA2TNm4OH9+8piphUZFISR3m/weMdUrB3xC/r1H4K2U/Zi01VvxMrzoPsKDwyAv58/AsIjECEgGupjYmZ/55YdZphPRfUqVZDFxBgZxM1y5gxXDya29AnHq1WtgsULF6iumdQ0Rv53yKAgjPB+jUfbp2Dl4Ebo0rEr6plaYvVpB4RHxODty1ewPWWLW7cfwdMvMK5inuEqIiICD+7dw1xJVGrVrA7jzEbK4v22ZcmcCQ3q1cOcWbNwy84uTfQL/lYGBWHUe0c82WmO5QPqomm9OviqVjeMsdyFW3duw2r+YnFpg7Fo2WY8d3CKu8KwFR0VjWdPnmDLZmtMnjQRQwb9im6dO6Jls2Zo/ssvaj7hFDm+a8d2PH74EH5+fmnOClKGFRP6vsXTXdNgZVoL9at9j+zlmqDLaAvs2LUVg/oNQPVqv2DEhHm49ehF3BWG65LjRcsWHhamJmL4vn8P53fvFHD3xUq+dXRUxzlvkmPFaW0KV7wMKyb0eYNHO6ZgxcCf0L5lK1TtOBXmG07j/sP7OHXkMFYv34gDh8/ijYsndD1smr4EGRyEz8QSbhzdEoMGjUTXWUdhYycuKu58TFg4QoJDESZujvOP/wqEdHdMHEJD5D5hEWkyBjM0GVxMaL93BjaNaQ1T0+FoPWkv1l/0+CwJ+SQQxUr7PHL68zhGSGbt6PAadjfu4NHDFwgOSr27v34pMigIQz0ccH3dKMztVg3NfmmP73ssxsIDTxDDPprfSY7FRuFDRDDCgv3VJAA/3wD4SwsL8kNEqD+CQ4IRGBqJwLBohEboOn+5pvnciZOwWrwK27cdhrublzpO/V3u/dPHD/LRQhEd4ovoYB+x4P4ID/JHgM97+PsFICpG91liY8IR+N4H77394BsQjjB+xr/rQ6QiGQCE/L+ua16vbmH9yJ/RvHQm5M9XFJnKd8LQxcfgFxqjLN9nz+djFKlFgMtTPL5/HadOnsSm9TuwZa01Lh3bjpuX9uHYySPYe+Iijl16jLv2noj4IO/h7oKNK1egd1dTTJmyGM9evo274d/3/KMj/eH+wg43Dm/B+R2rcef0bpzevx0rli3HqjXWOH/9Jl67OeHhvUvYbb0SVktWYpX1QZy3ew6/8LS3BDTFIVRjqJ8Y4X2A06NTmNa1CsoZsw8tHf6V5Qd0Hb8BL7zCwZFUjpQkKNIP0Y438PrGQezevRETp5ijaaP2aF6nAeaM6gzLmX3Rp293tOw2FAOnrIXNiQfwDYuBh4sDllrMQtN6LWE6cDJuPHml4Psd5P+DwgLe4frB5TDvXB+/1vsWC4Z3xrA+bVGubDmUq1QZfYePwdItW7B44VR0bloNFUqXRoXvm2DkzLWwc/VWSVdakgFAKI/+E/+3x8LP9SmOb12KWRPGYezYMRg3YQFsDl+Fa6C4Xb4iCSVhbvaw32eFCzaW2Hv8ENbsPQqLxSthOdsCR3asxOYV09GlZQvUqN4CQ8ctxc1HToiUm/h4usBm3TqY9hyOKeZWePzqnbofb/13QRgR6Ip7h60wq92/MeynMtgyfyLWLzVHj+Y1UPu7CqjRuC3aDJuJuVarsGjKEHSoVxnfl/8a7ftPxLorL/FWwtS/67OkBhlUTChEquyVGWt8082pizufRP6v7uDKsvHYNnccth05jhOPHPHc4z0CA4MQHhqCx3ZXsFBg7tO+N+ZarMbzV84Sc0UjwPc9ju07APMJc7BkyRa8fOP6myTnf9fHiAB43TmE4zPbYde0TnB+fhuxIc5wPLUE681N0aRtP9TotQC7L79GpJcjbmyehVl9WuHXYWaYtPM+LrrqLDP/+/FDNCLCQtVwZWBQiJ74OHXLsCD8LxT1/hUcDy/GRvP+GDh0hLjcxVi7+xTuPXqBd28c8PD6KexcbYGpY4fDdOgkTF68DbefOsPfx0visA0w7dIHY8fMwuUHDuBcnL8TxE+RQXh//yjOzu2Ag3O6wfvtMzkaiIg71jiybAxadhmGqj2XYr+dh4QVvnh1cBFWDmuLYSMnYfTmuzglYapC7VMwQr1e49GNi9ixaSt27T+F526SeMmpL6ljKdVCiA8+iHY4ij1LRqFNs2ao9VNbmI6Yg83bj8D21EncOLcHl05bY+cOK/Qbbob6Hc2w7+RdBPp648BWgbBjFwwfaoYjN+3hK0/874zDPkYEwuvuIZyY2Qa7p3WAi/1dyVY8EHRjLY5ajUfHvuNRe8Aa7Lnugo9+7/Bk1yysGNoaI8dMxXibBzhDCElhtBe8nl/GcZsVmDBkIIaOmYEt8jc89wmD5GpfjFIvhAgBAp7g9mkbLJgxHePHzcCSFdtw/PQ13LhyE0/vXcXb1zdh/+ImNu3Yi/HT1sD28mNxbcF4ePMyrJcvh/WG7bjx3AV+Ylb+XgjFEj44ijMW7bFvZie4vhAIYzwRdmsDTq+dih6Dp6P+8E3Yd9Mdn/yd8GLfXKwb3QHjzGZh8q6nOO8ilu7jJ3yS7N/l4QWc37cKKxdMwLBR4zDAbBW2HHsIj4CYLyZuTMUQCjaxIQjwcYWD/XM8efwcr147wV3iQh9vXwT5+yJCLFJEZDBc3T3w+OlreHn542PsBwQH+MHl7Vs4O7nANygcUfI0/84H+kne0+/RcdjO74iDszrD7aUOwvDb1ji3YTp6D5uFBiO2YJ+dm3yRnOFwaCGsJ3SB2dS5MN9rr2JCdiXGBL2Hq1hRx4cn5W88guXL5qJyrR4YOHYjHFyCNQg16VdUkDceH12BBR2+xswudfDs3k2EBzjg9uYxmNmnMb6t1ggl6wzD9tNPEepuL3FjH/Sp9zXqNWiJRmNssPW6F6IJYXi4fMk8ESVJDeCKs6e244fq3dBrgBVevgvUINSkX8E+zji5ZhJ6fpMHPX+sgZs37ODj8gCbzNqi5bcFkDNXXhQq2hi7D9+El8MDzOldD5Xy5ECePCWQ/6cRmLfztsqCGRfqpnYxAPTF3Tu2GDl+JZasPgc370gNQk36FRH8Ho/P74G1+TBsmj8Hjm8cEeLrhCt7rWBlPgIjRozG+EnLcfexEwK93uHYBnHDI4bI8YkYMX8njt10lJgw7mZxignzwJuXT3Dmij0e2L+XMOPv7lhKOWkQ/gP6FBuDaAExyP0VgjzfIiYqXELYKEQFesDfwwlOzh546xGEoIiP+BQTiTBfV/g4v4aLqwecvMPgHyaAKTMnGVNsFCKDveH4+DYe3HmIN17hCPly+FPSIPxHRZL+mBie+dyd/sa5fowVaN3g43AHd22PwNpqOVas2oozt1/iXVAMIuTlv7ki1UqD0EDFrVBeXDuMHXOHYkTnJqj2XWWU+64BWvWZhLUHLsHBOwiRXwiFGoQGJx1ZUeEhuHdmD1ZO7It+berjx1o18E3VRqjf+lcsWrcfz118EP6FuGUNQgMV+zMDvN3h+PwBHt65gevXr+PyNTvcuPUQr9+6ITg86rMJHalZGoSaUlwahJpSXBqEmlJcGoSaUlwahJpSXBqEmlJcGoSaUlwahJpSXBqEmlJcGoSaUlwahJpSXBqEmlJcGoSaUlwahJpSXBqEmlJcGoSaUlwahJpSXBqEmlJcGoSaUlwahJpSXBqEmlJcGoSaUlwahJpSXBqEmlJYwP8BVDmMvCxlS+kAAAAASUVORK5CYII=)
Two bodies of mass
are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull
with constant velocity v is:
![](data:image/png;base64,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)
physics-General
physics-
A small block slides with velocity
on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point C. The angle q in the figure is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOsAAACxCAYAAAAlH0pEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAD4cSURBVHhe7Z0FeFVn1rZn2vmn8818M+1HBSjSUgoUWmgpFC0uQYq7u7sUCQ4BgrtbcPfiFtwtOBQpXuhQJLRI6frfe50cCCFAdoTkhPe5rn1BcjTn7Gcve9ZafxELxZ9//vn4CI7n/d7C4lXDktXg/v37cuvWLblz+7bcvXtXHjx4EHSL6P8DAwPl5s1fZc2a1XLp0uWgWywsXi0sWQ1+/+03uXzxknTw9paxY8bIb4awAGt67drPcvr0jzJx4gT54IMPZMeOHXqbhcWrhiWrwW+GrBDyq6++klQpU8rJEyf0948e/Sk7tm+TKX4TpVTJEpImTRpjeQP1NguLVw1LVgPc4OvXrkmzpk3krb//XRYumK+/f2B+v3D+fGnVvKkh8WeSN29eva+FRXTAkjUIDx88lAnjxsrf3nxTevr4yG0Tw/56478yfepkSf15SkmQIIFs2rQp6N4WFq8elqxBID71X79Ovk77laT7+mvZvMlf9u3dI5NNrJogfjypVKly0D0tLKIHlqxBgKznzp6RLp07yVtvvSXdu3aWmdOnyagRwyRu3A+kY8eOQfd04dGjR0H/s7B4NbBkDQbKNju2b5ckH38syZImlY7t2mgcGz9+fNm3b688+vOR7N27V6ZPny4rVqyQM2fOBD3SwiLqYckaAiSaWrVoLn/5y1+kkFc+KZA/v+TOnVst6UZ/f3n77bflvffek0SJEkmcOHGkdu3aWqO1sIhqWLKGwC/Xf9FSTYoUySRhgg8lUcIE0qOHj942Z/Zs+ec//ymrVq2SgIAAWb16tSRMmNDc3kNvt7CISliyhsCdO3dk966d0qplS/nrX/8qb7zxhixdulRv27Vzh7z9n//IxIkT9WfQpUsXyW+sr4VFVMOSNQQePnwov964IZs2bpSUKVNK+vTp5fTp0+oGX750Scs6WFc/Pz+5efOmNGvWTLJmzRr0aAuLqIMlawg8+vNPuXfvnkoOIem1n3/W3/O7e0GCiBEjRmjdNUuWLJI4cWKpUqWK/t7CIiphyRpGYHGDd94cPnxYM8Lr16+XCxcuBP3WwiLqYMkaRkBUrOsff/wR9BsLi1eLaCErJz4nPdbqVR283p9/RkzIQLvc7du31TX+9dcbEhh4V5sA7gYGyo0b/5X//vKL1Q5bRBmihayBdwPlzJnTcvToETl+/GiUH8eOHZFz584qqSCTEszEpOE5yBZv27JZ+vfxlcYN6kmNqpWlbauWMnhgf1m5Yrl5raPyyy/XldS///570EXCNq5bRBzRQtbjx49Jl47eUqViOalepaJUq1xBqlbiKB9Jh+v5eN7qlSvq73r26CrHjh6Vc2fOGLJtkU3+/rLRf4OjY9NGf9myeZOMGDZEShQpLJ+nSCofxf9Avvo8peTNmV3KlSohTRrWF9+ePWTu7Fmyd88eJS4W2RLWIqKIFrJu37rVnNzZJPGHH0ja1J9L5m/SSfYsGc2RSXJkDX5klpwc3wY/sjz5v7kth/k3+GOyc5jnypY5o2TJkE7SpflCEsePK0UKealF3Lhhg/j69JDO3u2lk8Ojc4f20qWDt1QuX1ZSp0wuSRLGl48+jGue/wNJFPd9SRTvffks6cf62vVq11Rd8a6dO1UVZbXEFhFF9JB121bJnzuHIenX0qxxQ+nn21vGjB4p48eO0Ta1SRPGid+E8eI3caJMmTRJpvqZY7I5pviZY7LrX/PzFPP7yZMmmvtNkEkTx8uk8eP08ePM84weNUIG9OsrrVo0kwxffynFCheUbVu36GNyZs0iX6ZKYY7PwnWk/DSJfJwgnhLVfShhDVn599OPE8k3aVNLpfJlZNTwYbJ/396nRsVYWIQH0UZWrzy5pEDe3CbWGyDLli41v9umVmjP7t2yb+9e2b9/nxw8cEAOBRyUwxyHA+TI4cNBxyE5fCjA3BYgAeY+Bw7slwPm/vuM27l71y7ZuWOHIeZWjSFHDh8ueXJ8K0ULFdDXXbNypbRp1UIa1q3t/KjnOiqWLS25jIX/PHlSJWjCuO/JJ4kTqDucL1d2qWrce16jT6+e5vWHyqIF83XixJ7du5S4uOMXzp+XWzdvavLLwiIsiDY32CtPTilauIBaxa0mhjx+7JicOnlSfvzxRzl79oyc++mcntCXLl6US5cuyeXLl+XKlStPDvMziqKLFy7I+fM/yU/nzmkXzI+nTsmJEyc0ecW8pBlTp4mXuSgUKZBfCfPz1avmNU6Z1zrh+Pjx1Ak5feqkLFm8UFo1byK5smWRZMaKpjCuLy53hTKlpHdPH1m5fJmc/+knfS/Tp06Rgf37GuL6KHmHmIsTf/OyH5bqxeXnq1fkjz+eruFaWISGaCVrse8KGXfWTy0hJzZkO2dId+GCIemli4aUl+Xnn69qqeSX69e1NPLf/7pKJNfNz8SCkI/7cX/ITdYX5dFJQ669e3bL7JkzpWC+3PJdEFnJ6JINJlPr9KDOSjYZC9mvT2+pVa2KVCxXRjp6t1P3e/WKFRJw8IBcNRcTYlQI3qNrZ6lfp5a6+z17dJPhQwbLMHP0Mv/v0LaNzJ0109zvpL4vC4sXIVrJWvy7ghp77txpyGqsHRb1J2ORLl68YCzpJSUihFSiGpKi2f3111/lhvlXSRtE2KvGOnF/HveTsciQ/pSxgHv37gkia57HZIVwEbViZ8zFYOH8eTJq5HCZaOJk3Pdr164/k0TCNa9fu6aULVFMWjRtYu47Vi3q3NmzpWf3rlK5Qlnp1qmjLDe/c8saLSyeh+gla5FCMm3KZI0zqbtCNNxaXFw3UbGikJSeUWqX7gMRPb/n9mtK2KtKWJd1PafuNLHv7FmzIp2sjC6FXHpRuXRZ5w2HFnu6yVqzaiUZ2K+v7Ny+XS8yvN/d5gKFNe7Vo7sMHzpYL1QWFi9CtJN1+pQpmlQ6a6whRCMOxY10u75YURIxgXfuqGIId5Gh27fNz/ye2+lBhQDEspCd+PW0Iev+fftkzuzIJ2tYAVkbGBeYeq+viVk3bliv7++iicO3bt4sY0aNlEED+mmGm99bWLwI0UrWEpB1ahBZz551WVVD1sdW1VghLCiqoSdx5j39V9VEQRaW+xHDYl2JXUnu4KpClrlzZkuh/NFF1v0ar5YuXkTFEpRxFi9cIIsXLVCS1q9TU60q/bNceCwsXoToJ+u0KZoIIjFE94paVkM6rKq6v4aQDNa+d+93rVXibpLkgbCBgca66sjQG8HI6nKFcSsp/cybC1nzRitZvyuQT8s9bVu3lL6+vTUr3Kh+HSlsft/bp5u+r5smFreweBFiHllN3Hk1yAUmmXT79h21opD14cMHqrWFtJDu7t075vZQyGqe55yx1DGDrDWlSEEvqVKhnHRo19ZY1P4yoF8frcOihGrfprXMmjlDL1IWFi9CjHCDlayGXE/IGsyyGstJjIolxaJC1Pv3cYV/U/eY24lbn7GsJgZGLBG9ZA2KWStVkN49e8j6dWv1ooTVR+yxauVyJW392rW05GNh8SKEiawPjTWDMGQ/ESlEtA0s1Jg1KMEE2SjFuGLWX9Q9vHPHtd3NHbfyLy4wWWGsrzvDyuN4f8Ss1Fo1ZiXBFG0xqyFr3VqaER4/drT5G08H3eJqE0TM0bpFU02A8d4sLF6El5PVnNeQ4uSJ47Jg3lxNkGDFIgI3WV2lmymu0o0h1wVDsksXyQZflmvGul7/BcLe0CQS7wFLykXDbVE1uRRkVa9dCxJHUGsNVrqZEwWlm7DCbVlrV6+qiaRDBw/KffP6HHgDyCVbNG0sxb8rpLVaC4sX4aVk5cRmq9qsGTPEu8330rNbV9W3Qp7wnvRPk3WynqhscYNkT5JMVwwBTeyqqiWXGMJda71508Sp5mct21BnNTGuWtUgF5g66ylDVgZyz54V+aKIsILSUZ0a1TQbXSlI6TR0yCA9+vXxlW6dO0mj+nXFu+33cvzY0aBHWViEjpeSlYTOurVrpF3rVtp72rJZE5k3Z7ZK5LgtPHhMVrfcMISCCcK63WEIi+XE1YWcrsMlOXxMVJUbBiWWDFFRMJ00728PcsNZMwxZn8gNXyVZjx09Ih3at9HSDXFzse8KSukSxfQoZX5XvkxJVTAtXbxIy1UWFi/CS8lKjIgkEJF6pw7tVdfap3dP7WgJb+zqJisnLy1rO3ZsV3kgKiYSMOeNdUQ4gHifpNHPhpDEpJDWffCzi6gui8r9eRz1WlzgE8ZtJxYm0xpdZMX6I9bnYrfKfF4rV6yQ1atW6rF29Srx91+v3UNclHhfFhYvwgvJSiKHk5/JCIjWZ06fKosXLdRxJvSL4paGBzsNOWmRK1aooPhNmijbtm2V44Zcp4x1VdkhhHVrhA0R3R03LuJe1X/dnTcklLCoEJWMMoklrP6xY8fUvWa5FK14RQp4mZ93yINX3JLGheGPPx5pku7hwydzp2wzuoVTvJCsJGzoNR02eJAMHtBPDh7YL5s3bdLxJUxNICEUln5MTtjgB03gWNYiBfPL2NGjZP36dVqTpJxBryru44njx9WVpRsHS0lMC5HJGvMvckJug5i0xB0396dPlMfzPMSLjG6hHS1/bvNaxrLSz4qnAFFCvqfoOoIjxI8WFk/hhWQ9euSItnIhQsftxYrt2rFDalWvqtvA161e/dJYC2sHYRgoNmzIIM2KUltM92VqneBADZKMaId2baRj+7bSybuda3xKR2/p2qmDdO3c0RydNBnTvYvr6MahvzeHuU8Xjo4d9HE8nufxbttG3yMDzdJ9+YVkNK+lg80G9Jeh5uLDe3lVBxMwZs2Yptn0JcYzCXksW7pEXeUd27bpBRHXmM+exB4SzFu3b8kfxipbvN54DlnNVd9Yny2bNkr1yhXEp2sXdSmpEyJGb9OyuWYxB/TtIwEHDwY9JnRsMFbz20wZJBHTFBJ9qId7dhEH41H4OaqO4ONX+Nn9Hl7JEfR633yVWr0IVExkh0MeDerW1gtJz+7dZMiggSbsGCqjR47QixxTJggb8CKI0UmwPdFLo+y6Z93q1wShkhWVECfG/LlzpXzpEtKoXl0ZY2JU5h0NGzJQWhpLWLFsKZ1OSKLkRVhrrC9WNM6//iFx47ytRzxzfPje/0l8c8R79x3XEXRbZB08X7w4rufmdfS1QtzH0fF/rn95vg/fjyMJPnhX/+Xn4LcHPz545z8S19yeJmVylRxCzBZNGj11NDcHIv86NatreYcMOTF2vlw5zL+5dBxN+dIlpXaNqtKyeRMlNERG7LF+3Rqt5VKuun0n/KU0C89AqGS9cydQZyKNHD5MLSiu5YRxY3SQGS7diKFDpG6t6jqhkNILiabnxa6s+ke0XrLod1K2ZHGPPYjT+RsgUbo0n8uniRMai5lGCuTLLSWLFdHbn31cCSVaw7p1dJM685gmG2sZ/GAw3NhRI6Vv717S7vtWGmKUKVlMs9fUZ70MYfOb13SRN7eUKVFMk30QHbd/YD9ftcA/LFksW7dsNi70IU3O3fj1RoSVZhYxC6GSFanf2NEjNRYcN2aUcYc3aYmE31P3JENLL2bBfHmlt08PnY+LoD40oDgiIXTi+DFVQXnqQWmJbPIEc7FiIFrqz5JL3Zo1TCw6XbXNjHAJ7XH83STDyFaTwdaSU/DDeDDE/ZSfVHllXgfRCXOKKfH8YOLZRQsXqlfDLCeEFY3NBbSC8WwK5csjORjhasKMfDmzSylzMWnWuJFaXn8TfvB89AE/+uNJQs3Cc/EMWflCSWxQnqlTo7qsMScMRA2J1StX6snarFFDtbavQ9cIDQaEA2WKF5UvPksmNY2FQyCCQCM03DYexy4Tb+KlMBOKODMsQGxyJ/COq5vIEJrPn4w4F4V1a1bLvLlz9DNnKwBeT9PGDdUi04ZXvkwpqVa5oibtSA5SduOCQq6BiwblOAvPxFNkhai4TsRBVSqWN3FSNdWzMsYk5FWZrCWZzmbGHSMzi2ootgMtL1pf3ODkSRJLnuzfatYaCxoaKD8xnZ95S/MNwRB8hAV81iSM3AfkdbcG0nFEUgnSQX4uFFxc/f391fp29G6r6igGpGdKl1ZnM+NSozybZkIW/oafDfndCaoHD+4/LmVZxGw8Q1ZOCEo0iB9WLF+mMj8ywyGB1C8g4KCxvKs048uiptgKiIImedXKFVLIK+/jTHPKTz+RiuVKa7Y2tBOexA9CEjqLNm/0V6VSVIDaMd8TNWis74rlP2gcS1seCSz6ZmmAJ3lVs2pl6dqpo0wysTJeE6tMwmrxLaIXz7jBnJhcuTk5aUsLjaiAkxNi32EekrlvWMQRngo+DwQXrMPAWpFZphRERjh39qwmppyvZHlkPrvgoMUPAQiJH0hx8+armwbxq3ktZifTM4sr3KheHZ0mSVIQrTJN8dSjSW5R46WuS+yMteW7tYh5CDVm5YC0L/vS3PfjCGlVYhOwPLQGNm5QV778PIWSFLIyiT9T+rTSv6+vZr1D6nvxNvbs2qWJKZRWz0vCRQX4TnCV0Scjy+T10UYvnD9XBvXvJ00a1BOv3Dkla4b0Uih/Pl0zgjQTl/qesdQWMQ/PkNXiWWBxmJuEFSVWReDhtqypP0umyR2mKDJxMTguqhs8Td1gNtBFd2cNnhDExW2fMW2KNmYwuxg5ZmGvfJow69O7l2agSUaxItMi5sCS9SXAu6AxngQNGWDWZXysyqi4kjRxAkn7RUpN4NCNRPY2OHCdiQ/ZWEdGlhJWdMLtCZFEZPrGpcuXtPOnb++e2lXFNr9M6b7S0tS0KX5y5FCAlt6YfWVd4+iHJetL8MCc2BcvnNfBbpRD2Eb3dWpXNrhsqeKqWaaEsnzZD88kakjCMR8Y2eZxQ1xkgjEJEJD9sTQ9LDZx96D+fTXbjcADNRXD3Cb7TRTWhXC/RxHcHG8RMViyvgRYISwmVpFsMKWawl55Ve+La0yZizIWDQshFUPEsLi+tPTd/PXmM7fHFGBxea9kr39YskgvQKWKFdF+Y2SOzDhm2RalKGJgrHNkgOchiYkwBAEHPch4IwhJaM1ENBJTP7PogCXrS4D1eaj1zftyxsRxkydN0kXJuL7Eo4gXmGtM+SRkkg3ZH4371D/9N6wPVVwSk0AN95fr1zRzzftFCdW0UQMpUbSwlCxSWDuj6BC6QeY7gglFPis8DeSRM6ZNlV49uqr2GR1604b1tYuKz5cyIt+BrQJbsjoCV/oF8+dJq+bNpEzJ4rJk8aKgW0IHVoKWPqwx42Wog3oKuPjQG0xyrFnjBlKkUAEpbkKA1uZvJ/5miwCqNZJW4QEXOHqj6TCiOQFhjU+3LtKjS2f9vNBJ9/LpIYsWLtAMNRfM1x2WrA7AeJn58+ZKy2ZNdY4SwpEXAb0w8Sy7WRcumKeLtzwFWD6ISAhAyQdSVSpX2rWYuqCX1miZHcU0jz8eOtsvy/NevHheevt017Wf6MuZqUymmjUiXATISPf17SXft2wuc2bNlN8C7UpMS1YHcEpWZh7v37tHVUWUQhCPeCJumL+DjfNLFi3Q7qC6tWqoZ1G9ckXp37ePbFi3ztH6DzyUDRvW6RACenzp2UXd5SY8/xA/87xMElmzepWKNV53WLI6gFOyEueibELJRL+pp6u8IBPdR1Mm+ylRKfVQo23f5nvtzMIi/nb35QooBBp+E8erq4v7+7wxrLResqmAyZc20WTJ6ghOyUp9FveROcGUdmLDWkcsHO48EsWB/ftp00Be4xpXKl9GhgwcqAPbb916cYkKKz1qxHANDyAtibjQwMUNb4Rar63zWrI6glOykhhhL2vPHt3N4+bo1MbYAkhEfXZAv77aKJAzayYpX7qU/r0bTPyJlX2eJ8EoIB3CN7C/JuyIVS1eDktWB3BKVoQEGzf6axmEIWjUKGMLqJFi8RgTyzC91i2a6eaDnN9mlmaNG8q8ObM0Ng0t8cRnweA8tunNnjlDk1ShgSYSklG8lpMEVmyFJasDOCUrmVRKHCrkN7HeqxTyv0og/Fi7Zo26tVUquNrxUEItMlaTDQshQZac2jOjbliB+TwZ5uVLF3Ui5KaNG+XuXds0b8nqAE7JyknMJH76ghnVQqIpNgKrd//Bfa0rQ0LWgtCKh4VdOG/eM0okxtswsobkUpvWLXQjA0omrCiuM2oqVqSsXbNKFVTMrGaq4+sOS1YHcEpWrCl6W2qtzAd+XiIltoDkEzOkUCTR+ECjft2a1ZXAZHTdYIsenwVD+Ljf0EEDtRGeSRpIDylz4R5Ty61VvYpMHD9W7nho2SsyYcnqAE7JypIsJjJMGDdW1q9dI1cux/45VVhGdL6LFszTOV7lSpeUurVrGMJOUEWUe+UK42RozHcrmIYOHqiKMCzuQuM+M6sapRizqWkvDNkr/DrCktUBnJJVFUC/3tDY1dVqFnunabiBS8zfzeb6/Xv3arMDtVi01GiLWW3C7Y8euZrjWYsyd/ZMnVXVtnUradGssaqWEF8wG5kJFmiIbenGktURnJIVQcSObVt1ax6dJC+rP8Y2EIfSHojel40E+fPkEJ9uXTU7Tj8tIJZltxEqJRr4p02dYlzgmXofSl9oiG0i2AVLVgdwStZjx45I984dpUuH9jJr5nRdP/I6ASvLONZ9e3ZL/Tq15LNPk0i61J8by9lCDhuXGLUT99HOJuN1YHHdBz8z08qWbJ7AktUBnJIVa4pY3ad7F5k3d7b2vL5uIGGE1UThlCje+5IkQXzjFudQt5fh8Na9DTssWR3AKVkvXbqo84KJvdhByzaD1wWQMNC4sKzZJG5lxlOKTz7SCRtpUqWQQubncWNGy/nzP1ndbxhhyeoATslKBpNuEprOUS+9TiclCbWjRw5rNjdvzuySN0c23cn7bcb08nXqlLqsrFaNajJ1ip8uw7Z4OSxZHcApWZm6wM4ZejWZhB9yoFpsBDEmFynKNMOHDFYlU+kSRXW6Bgu6qL0WzJ9HKpYrI6WLF9XNepRqaImLrHExsRWWrA7glKycsN5tWmvfJtv2Tp96IgyIjSAVdO/+PW1YYBNByaKFdZn1yGFDtdZMkzkb9xrWq6vdNvUNgbNnyahbAxiUjvdhE0rPhyWrAziOWS9e1MQSJQkEACRbYjOYy0QHDZv2yP5WKldW1UkH9u+XlcuXa+20lLGmnTp465C5ObNm6bwlyjrNmzbWecYxbQJkTIIlqwM4JStlC3o3dWfq+Z80joutIKF09cplVSCxGJq9Or19fHSL3t3AuzqS1benj1pWLCw1aNroSL7hDhctXECJTeMDYgmbJX4WlqwO4JSsrGskXqVRG+VObI5ZIRgrRtipwwJp73ZtZM/u3Sp+YPja5k0bH5OV/l5cXmqprLJkyXSNKpWkYL7cOnCckldsvrCFF5asDuCUrDqK1G+Sbjhn015MH0UaXrB2Ev1ux/btpLixkN5tv5dlPyx9rAMm4cTtj8navfvjmU2QfM+eXbpL9pu0aXTHLNsAzp/znOFyrwqWrA7glKx0j7gmIgzQaX1kPGMTSAZhHXdu3y5tWjaXsiWL64Lt1atWqLQS/S94EVlxd9lksNyQm880X67s6kZzf57bJpyewJLVAZySFVcPlQ7uoCdPN3weWFzFmNJ+fXx1rUiThvVNDDpbLlx4+qL0IrK6wUxllj2zbT9frhw6HobnDgy0u2PdsGR1AKdk5SS9fPmSHjRT08cZKxBUSyW2JMZknCiLrSaOH6cZbyxicISFrOwUolmffbEkp3CH+/XprSTG+loLa8nqCE7Jeub0jyoMGDJogK6dCGlxPBUM9UadRFN4iSKFpIIh1vSpk+X4sWMqwg+JsJAV0ONKSYfJhzwviaq1a1brhc5mhy1ZHcEpWU+ePKHWgZMUlU5smG4I8Uic0VRfv24tY1FLanKIuUr37oW+hDmsZAVMhGAxNS41i7EYIk799XnP/TrBkjUYcLW4guvxJ4drC7wbTslKlhQxxJbNm+TYsZi38tEp+CyYfczajJpVK2tsOWLoEDm4f7/8pn2nobuqTsjKczBvadqUydKofl0db8o0CSZFPu/5XxdYshoQYyFgoMeSuignFt0iDKy+eMG1xQw4JSv1RTpvOBABcNJ6KnB9r1+/Zv7mBcbq1ZMqFcuLd9vWsmPbNrWGL3JTnZAV4ErrIPDhw6Rg3txSp2Y1DSNe9/nClqwGkIqyCldzRoswUnO0iZvQ87J/1S0wd0pWJiXQw3ruzBm59vM1fR1PBBaNyYybN/lLR++2kjtbFmn3fWud5hAWoYdTsvJ6JOM2+ftr3FogTy4d9YKwgrj2dbWwlqwGkAolDbEXJYgeXTvr5rL1a9casrmykcApWZluyBjN/n2Dpht6YJ0VYlA+oYzSukVTqVC2lLRo2kh+WLJYXdOQmd/Q4JSsbpAJJtlUuUJZba+jZs30xHu/v57D0yxZDZjzQzKIgV75zUmBVd23Z4/WRm/e/FVM5Kr3c0pWNnljpbkIMKyaqX+eBi5k6HWHDBqoF7I61avK3DmzHY1VDS9ZEUvs27fXXDy7SC5jzWmzo5sHTfHrCEtWA3SokLVHt866t2Xjhg3qsuKKBe+xdEpWEkoHDxzQcgQWmpPPkwDJWK7Vq0d3KVW0iNQyRKVcA1lCK9E8D+ElKx4NwosVy3+QhnVrq3VFQ7zdxMm/G+v6urnDlqwGbrIyv5Ys597du4NueRpOycoYUtRLWCaGXHvS+gy8iUOHDsmYkSOkasXyUq5USRk/doz26DptEg8vWd3AHWYDe8mi30nOb7PI2NEjNbvu5IIRG2DJahCcrFy5d+/cGXTL03BK1osXL2rsy3T5rVs2m8dfDbolZoMkDvOiaEAoY/5Oyic9jSt/0rj1uiQq6H5hRUTJyjgcdrq2btFcsmXOKA2MlZ0/d7bHeSoRhSWrQVSRlYVLo0YO1zrhyuXLnrstLabhwvmfdIJ+vVo1pFC+vDKgb1+N4QPDSY6IkhWgs0bOWMmEKXlzZZcunTrIlSuXI+wKE+54ijttyWrwhKxdI5WsTIrAAsyZPdMjJkWQ2b1+7boufiY+xaq2bNpEtmzcKA+NyxnekzoyyMpzkJHu5dNDMqZPq6TdtnWr/Hrj2VEwxLq/m/uz9JnwgzY8wP0g562bN9XL8fX1lTRp0kjXrl09grCWrAaPyWpcvRpVKmuMGRqckhX3DRXTL+ag4yamx1gkxFAnsWuV7Gvb1i1k544dKuiIyMkcGWSFgNR02crnlSe3Tkxk8zp18JDvDVf9yJEjUrhQQWndsrmKUty/p+a9YtlS/a7ffPNNqVWrlmzZskVvj+mwZDW4f/+eEpGlwAgjnldicUpWFD8IBzasW+daphxDJ0VwskNIRq8w3K1sqeLSpEF9WTB/rjaQv0idFBZEBlld+FNXbTRp2EAK5M0llSuU083pPH9InDhxQhImTCjvvfeuIecyrc1ysVy6ZLF89eWX8sH770mKFCn0Qu0psGQ14GTlhMQS4iY9L9vplKzMXmr3fStDgOYy1c9PTgdbexhTwN+Om4ibTk24sFd+lRKuWrlCY0Knmd/QEHlkFZ3DTOKrepWKkiFdWunn21tLSfdDeC23bt/SJor/+Z//kZIlSsgF4xLz3Q4aMED+9re/yV/+8hfp06dP0L09A5asDuCUrCSUGAj2JBsc82LWO7fvSMDBA+JrYsFSxYq6xoROGK9qq4cPI8dtJxbm73dPN+zl4yO3b4WvER+RBhdBmtPTpflCJ1OsMDF2yHwA9dnV5oLzXeFC8u67cWTRwgWq/65Vo4YSNWXKlNpn7EmwZHUAp2TlhGGlIUkOLII70RETgEXFkzh6+LDWLatWLKcKpQnjxmmZJKLbAyAoLiYWFLXTvNmzNRYukC+3tG/zvbbUIVcknr93L+yvpckjYyEXLpgvBfPl0amIPbp00iaM4MCa87cNGzLIWNd/SNYsWXR0TJIkSeT/GctKUskNLkwR/XtfBSxZHcApWTmpqLViYRHChxZbRRc4OSERJZpSRQur8IGFxmwOIL4LmbRxCgQgdM7QxTRl0kSdI5w1Y3pJlTypZpkZ+k0NesXyZeEaJLdnz24dzFa4QD4pWfw7WbNqlX6+7veN+05Sb/26NSa+zS1/e/NNSZw4sfz1r3+VLFkyazKN76ZsuXLy+eefS6ZMmZTAK1eujLGtjJasDuCUrFfMSbh0ySIV8ZNhZsFwTAAnMlMrUAU1bdRAihuLin55z+5dkTYnirrorp07ZOTwYVoOy5whnXyS6EP56MO4kuHrL/XiQEMAlo+JGk5BhneRsa7E11kzfSOjR40wXsypxxdEN2nJFtepUVVyZssi//jHW+oC+xg3/CdzoUplSJozZ05ZsGCB9O3bV/+fOnXqGJsdtmR1AKdkJQPc7vuW8r1x/6b4TYoR6zMgKhcNxqVAGDaSd+7QXjb6u/TQEbWobkB6iNK1UwdJkzK5JEkYTz5OEE/J+nHC+GphmcSvyijjEjsFpCRr38m89yzGYrcynzH1Yff4UzfQNrPMuVyp4vL2f/6tZF26dKmsWLFCkiZNqhdUN/A2+I7D0kkUHbBkdQCnZCVORYROrMSUQ2qu0Q1IRLyH2IE5Ry2aNtaZxpEt2KBMwnOOGDpU5wEnMVY1cfwPlKwJ474nSRMnkBpVK6krHN6mcmJieo7Z/VqxXGkZNKCfXLt2LehWF/jMWd2BhS9TqpS88cZfpXnz5rJmzRr55ptvniF3TIYlqwM4jll/+824axdUyfTfX6J3UgQWk3Y/tpDTl5onx7fSsF4dmWvIElUnLK+JyIL1GF+mTKHLlCFrYvPvFyk+1b5hGgPCW+tkMzpZ5u7meQp75ZVmjRs8s7CazilG0fA6R4ynM3HiBFm2bJnGpvHixZP169fLWfOYU8br4ThtLHFMFa9YsjqA45jVWIwfFi+WxQsXmvhtp1yPxpj1jz8eypZNG3XCQ4kihXV86JLFC817pN0tatw+yEocjIwzd/Zv1aJiXZN9nEhyZM2km+S4UPwRTtEFmWFq11jXQvnzaJM6rjeNCObVH9+HhBlrPIJ3Pe0xns6HH34oqVKllMyZM0v69OklXbp0am23bdsWdK+YBUtWB3BKVq7y48eMkTGjRurCJrfs7VUDAX7Awf0yoK+vOanzSs2qVXQCA9rZqAZeBVMlypUq8Zis6b78QmpWq6KfSURiZLe3QLyty60Keen3Q/LsZaorHou6rFu3rrJhwwYJCAiQ/fv3y4EDB2KsqsmS1QGcktW168bPWBDXrhsUQa8SnJAklI4dParDuCuULilFCuTXsgnbxkkoRTVwKRmZ07RhA/kkIdngeLqAio1xlIkiRFZzQMpTJ06oS8+sJvbtQN6wJIn4bBiKt2njxpeSOybAktUBnJIVQQAxIq6gq/n81a7PgChHjx6R8WNHS5kSRTURw0wo9qVyokaEKE7AkO4B/fpq43iKpB+rphe9NFnpyHgHV69elYH9++pwNfbtTJ3ipxP+XwYITV6BrPLZM6e13BSTYcnqAE7JyqAxlDonzZUf/epvd+8G3fI0IA3EQuHEfbB4/PxnBK72tLRR9J80YZwuesL97da5oyHv0WfcvEePnsxLjgoC8zch92NwN5vO6YSBII/+iBxrRtxLN06bVi3NBSGT9PXtpcKGsPwt7ntAXC5gMRmWrA7glKy4Z/379JY+vXrKovnzjVsceozIiULGkrrs/n375MTx4/pa9yLgpiKhYwtA9coVpYiJ5RDRM8qT6QohT2Lqi1wgeL2ocAe58KBmYpVj4wb1dKVIZHYg8fx8fpMmjJdc2bJK29Yt5fixo8+9OHoqLFkdwClZGYNCrIhIfuE81mc8TVYoQzmHE/eUue+hgwe1f5Tly/4bNmjyxCkgPu4lrWCMQWFuUeP6dWXjhvVyI6gvFXJSf+T90WjPbbilqKxwWSMbXAD4G2kYQDW1ZvWqSI+X+bvXrVmtiSYm+ZPUItMdm2DJ6gBOycqk+mNHjshRc5ChZORpcHAS/9cQiz7aevXqSvbs2bWE8NlnKSR58mQycOAAx24pqye2bN6sQ7GzZ8mk4vnly5bqFna3q8t8JVriaCEjMYMckEFx3bt00oVTUQFeF/ebJcmohqLC5dy3d6+0bt5UJ/j79vLR2mpsgiWrAzglK9bjkolVdX0GKx/vPyuKQDTwYfz4kipVKqlWrZq09/ZWfeo7b78jf//7/5N+/fqFibBKhjuBSsKO3u10BWO1ShVlzqwZ6iK6291YcKzllKWLpYYhaNmSJVScwKqKxQvn6/sNLyAj1pu/m8QNFwgsdXB3/pbxFvgcsf6hWVda4Hgcz4Wg4a55Hv7P77GeLwL5gcED+kutalV0LM02D5kAEVZYsjqAU7K6ssF7ZO+e3doqFzIbjHUpXLiQJDBkZb6QG2wCYHtagfz5JVmyZGFSGHFCBxwM0JIIAgTmH9OkjTY2ONl5Taw8UyBKGBeZ5BOby5kUATkgfXjAazAylB1BbCJArMBCLn4mfmTmEa437j5b4TZv9NfPxN0pAxFJClFmQpWER0KGlskQjB09d+bsS7Ppl81Fcf7cObqQOX/unMYVXqJ/j0PnJMbCktUBnJKVBFM/316a3HGtfHw6ZoUgyT5NJjmN++ueIsHJxbKnkcOG6sjNuHHjyr59+/S20MB5SIKF1+rVvbuUK11SSxjDhw5W0oTsoYWs58//JEuMRWd6IVI9WvicutshwfMSJ+N+416zXa57l86a7Gn7fStNKpEA4vNoZVxV/jYGhkNE3iPZcj6jgf36SueO3voc/B+rP3TQAPVAnpegc4Pmci6OuP6Z0qVVPTAXpnuheDSeCEtWB3BM1pMnZYCxkH19exoXc4GKJIIDdy/Zp59KhvTpZO/uXbqpjQkKdMQwYqWuIdN7774rq1atCnrEsyBZRPZ4+pQpmlyhiwal0p5d5vlCiQvdZKW5oE3LFoZEg8KVyAoJLOPY0aN0NhJEpJuG0a5cEArmz2Pc0iq6noTyUfMmjYzlL6cdM5R0cMtZk9HFkBSyQ9D+fXylq7kv8XTThvW1Qf74sSNBrxY6uGgRD/OZkxVu36a1JrPCO0ImpsGS1QGckpU465yxphwkdULGaHTlpEiRXOLH/UCqV6sqbdq2kZYtWkj5cuUkX+5cUqRQAXn//fdkiXHnQgPkxr0cO2aUlC9TUpcPQwDGnvDaoVnL4GSFGPSTsjkgonCTlckNvj176AoSWgJnTpumyasmDerJCGNdDxzYr8olPkc8DlZz4CqvWrFC7zNuzGi9qP189aq6yxCXJnOEHbjTLwNuNX2udWpUk6qVKmjNNbpknpENS1YHcByzmhgMYTm10zMmniM7HBzEohkzZpB/vPWWJEnysSRPnlyPRIkSSuJEiaRQAS/597//LV988YU0a9bsmdgVt3rO7FlS18SdSO2wRExGIH59HtxkZd8p3TdMh4gMsj4wZEUDXbpYEfGbNEFXaEJg9L+UjiAd5RQ+E94fqi6GndGiB7mYVdWsUQNZMG9e0DMybPy8cWWHik/3ri6X2cSvLwMXKOJ/mgeKf1dI6teuJWd+dN7cHhNhyeoATsl69uwZGW+s3uiRI3R4V2hXeC+v/JIoYQJZtXK5/GysL3HsSmNliNe88ueXf//vv6V/v37aMI2bB8joQlwSKGQ+C3vl08Fhmzdt0vjvRUkiyEocR48nFou4LjLcYDdZkfvh2tI88NC8Fg3hTRu53FguXBCVRNH+vXtVLNKgTi2Z7DdJpk2drJMgIbRbucVFBZJiHcNKVjbWkxWm2Z/PpWTRInLEeBqxAZasDuCUrFg+kirjx41RoUNo0/TatvlepxcMGTzosWgBpVGFcmXlX//6l/Tx9Q265xNQSyWZ06p5E8mbI5smbCAFruPLAJH5O8gAQy4a0SNjZ8xjspYqbtz2heaicVcvDC6yNlDZIyomas1KVhOjEpdDVoiKWILEEIkkN7i4TTCfHTVTJ5aVBvS1a1Zpcz1ZYcagvuwi5gmwZHUAp2RFYM6A6WU6KWK3TvMLDk5mTqRv0qeTd+PEMXHZWLl04YJsWLdWPkqcWAoVKqi1WfdJxomIRd1hYrnvW7Ywbl5BqVi2lMyeOV2tI8/3MvAcZE0ps1A+wdpFRlO8m6xlShbTPllI+ZisDevLxMdkvRuMrD3URdY5VYakkBWLiPt79cplneFE/MvYGUgblpiV/Pjv936XgIADUqlcGcn5bWYt50D8l9VpYzosWR3AKVlxBckIM2MIqxqyjAIJqT36r18nmTJmlDfeeEOnxTdp3FjiGPIiiAAQDJD5pQZJlpVdpdUqVdBdOtQjORGD7vZSQCKSXbduueLHyLA4kBV3X8lqPpfHZP3hBxXwYxlDkrW3T3dp0aSRxq/79u7RbDDEpMyD29zbp4dmjckuu7LBYSErdP1Ty1FMVMyZNZMuBkPq6A4jPBWWrA7g2LJeuaKJHFw7Tshfrj87g4kTCPd36+ZN4jdxohQoUEB3sDBpj64ZN+jgIfZCa1y2VAmpaKzGkEEDdFMdJI5ukJmeZywYddVNOnzNuJ2GrFtMHN3HvGdKV9SS+T0XCIjHVriB/froxQzl1JJFi4x1HiGD+vc1BBuifyuEw90fZ2J/arJhBZ9px/ZtddyLJt7Wro1QY0RMgCWrAzglK9pUkjicwOzQOR1KVhKriQVyX/WJt6ir4qq6QUIJze64UaOkTPGiUjBvbhk9YrgcDjiosj635Y1OYJ2xjgvM50ODAKNVSBQhzKB9DXf7+rWf9e9EKXX18hXdrUPijbGgZIlZNbl9+zb9XHkM7itT/IltGd1Cq2FYQVhAWYpRpXT6ILv09C4cS1YHcG5Zr+peVo6AAweeImBYcc/EXyh3cCPLly6hml8sBR0ygcadjAlEBbwP9L6MsmGlIuTld8TYaJNx93G9+T0HIcG1n69qfEosj1uMNR0/ZrQmzyAxA8jpoPHp1kVje2rVYQVJM9aWUA5C0cVzv6ik5QmwZHUAp2QlI8rJS6x2cP9+7VelAyf4gfqIEg8nOiewm3z8i8WlfIGF4aTN8W1m6eTdXjZv3BhrVDlu4jIPidi2cwdvmT5tqtZdsYyouKgF/3TurCN3/7e75jnXr9NOIq+8OaV7106RUk+OTliyOoBTsjJzCcE8ErtqlStqrMnj3EeZksW1ORxZHImi48eOqYsIICoWh2wq8WnRQgWkZfOmsnrVCrVc3B5bAGFJwNFT6zdpogwwcezggQNk9MjhGj6QFcYqOvEiyHAfNWEI3UTZMmeU5k0bySXVQHtu+caS1QGckvXE8WPSzVzZUdJ8m+kbXcqkRC3uImup4kV0GRSa3sYN6up8pDWrVsqPJs5zq4wYAJY7ezapW7umlkTQ0cZGkM2mfowQn9ovGWXISyIqPMuceT5i5HlzZsu3Gb9RyePBg/s1UeepsGR1AKdkPXjwgCY3ICQWlF5L1D0LF85XiR3ZU6bIN6xbW+uB2Qyhud+40aNkmYnbEAzky5ld11xMnTxZpy1ghWIr+NtwdUkE4RoT45KQCs/f7A4jiHVpGURZtXLFslc+YTIyYcnqAE7JSkKErg+IicVEwE5CBbkf/6JwgtAkU0aNGG6el5UWhbWYj3zQK3dOqVCmpEw3riD12ogMUHtdcWDfXiljPJmyJYuJ34RxroxyzMjJOYYlqwM4JStWgfGWJIMQCTxPQYPluHnrprq95cuUkq++SClpUqbQdjd0sWRTLcKHE8eOSYN6dXQXDnVbykuWrK8BnJIVks2eNUNmzZiuUxN4/POA6B0xQfUqleSbr9JIzqyZNQtKBjmk8ski7GBSBs3sjLBhiTPfg4dy1ZLVCdjSTfKjVfNmmsmlHvgiIIIYOniQxqo/GKuJ+xsaiNPO/HhaJk+aKKWNu0aMSwcKtVR21DhNrlg8AYm6Qebzr1erpibxmIDoqZ+nJWsY4E5WIP+bPWumNG/cSEoVL6pW9sH9B/Lg4QMlVUhQjli0YIGqeuixZDJESPDcLLCaMHaMTkXIneNb6dTBW+WJrgnxlqgRwSXzHdC43si4wtUqV9Cme0vWWAqsHmRavWKFDjFDq+qVN5dkzZBemjdprPrWaZP91L1CpB4cFOGZy7trxw7tsbwVbIuZGySaSEBBVBYrtWnVQhVPKH9ic+b3VYHQY7YJQ+j8KVX0O1k4f64la2wEXynlg6OHD0u7Nq0lU/q0kuKTj+SjBHF15f5XX6SSXNmyaAZ3mHF3qQcGB6WWXcaVpaiPRjb4pAcsNT8j8m/VrInky5VDG8nJHtOXaokaOSB0oUWRiRRk12dMm6oNBp4IS9aX4JG5CpMo6trJW8nKxm5WF7IUOEnC+ErYimVL66Y4MrrBgZSwl0931bZSnA++6JeTaNMmf2lhrDOLjWnQnjVjmooeHgbN+LWIOAglNvn767yprBnTa88trYueaF0tWcMA5H3uTWypkid9TNaEcd/VXaPt27SSdWtXqxY4OFzTDX21c4TYlf0zWExE5vSl9jAkZr0FTeR0lZyNwVu3PRUsUaZcQ7tchrRppI9vLw09YkJboVNYsoYBKGoYtYLGN70h54fvx1GyJvggjmTLnEFHt9AAHpJo6FNRzFy5fEWv8Gx2uxMYKAGHArTmhwSxcvkyMmrEsKC2sgceG0/FVFD2QgjBFMX0X6V2Zdl37gxXB1R0w5I1DIBEuKckKtgximX9OEE8SfpRAileuKCWA+4iNA8RZ0JWxo0y3gXdKyfI4cOHdJdolQrldMZu/769VcXE4y0iH64E4RUZMnCAXmjp4mEoW2iZ+ZgOS9YwAGuH+8ocW8QQyT5OpLFr+i9TS8O6dSTg4MGgez6N69evaZsWM5X27t6tIvXpUyfLdwW9pFC+PDrGhJm5JJusRY0auMMO9NZ8X8g3GZXqiQ0RlqwOQAzaybudZoA/S5pExQtcsUOuxXCDbeesfkCsTwKK2bk1qlZSorZt1VK2b936TAbZIvJBDXyq3yTJmO4r1QgzIoa41dNgyeoATL+fO3um1KxWWb5M9ZlOIWDVxfMWA9MwTT9l104dtH7KUuP8uXNoqYaZv5ExVdAibKCZPUeWTDptY9zokTpQzdNgyeoAxJX0V/p07SIZ0n6pWV6s6vNI505u6IhO4z5jkdn5snb1Ko2ZbC311WHRwvlSyCuvVKlYToeyIUP0NFiyOgCxJfEPIzfTpflCG5r54lmtyLzb0A7m3TZuUN+4YGkl7ReppKiJV9mQhls2dXLoj7FH5B2UxFCYueus+XJl1yQTkyGnTfEL9THPO5gJxTBy1lFGByxZwwFGjaT+LJmKIlIl+0Q+T570uUeqZEkleZKP9L4cJKZSfpok1PvaI+oOlGefJIovn5jPP3mSxOY7ePH3FtrxmXmOr9N8bi60fkFnwquFJWs4gEVM9nFCeedf/5D33v6XvPef5xxv/6+8/87/Stw4/5H47/2fHnHjvC3vm9+Hen97ROrB5/z+O/+WD8zB587nH+/dd8L9Hbz9z7ckQdx3ZYzxrKIDlqzhAJ0b6IEZF8IulZAH0/K98uQy/89h7pNVB3ZlyZBeRRD0qebPlUPvE9pj7RFZh+uzz24+e9zfLBnS6cH/s2fJqO4w35HrCO3xzx55cmTTgQAsfY4OWLKGA+h6GdHCKkeGVz859uv+0YPmYF3Drp07ZfXKldp8zt5Rv4njtcNm544dejv31cc89Rz2iOjB589uoTWrVujs4PFjx+jYHBJ9LAmbM3Omyj35Dg4ecH8PoT9X8GO/OXhMdAkqLFmjALdv35KAgIOyYf06XRJM3+sUv4l6otD1wUSIkFvQLSIXSEwgFr3EkJVdOdS6afBnSzzfCQJ/BgR4yqR+S9ZIBCok1uRv9F+vG8hr16imo0SosyIkr1e7pq5zYHX/5IkT5Yax0HYIWtTANZF/prRu0Vw/bwaId/Ruq9pgvodC+fNKpXJlVdSCsswTymiWrJEIBqKtX7dWenTtopMK+ZeFTBs3rNeuHOb+ssmbrWjsHMW1ii2T9WMa2FTHoi9G8HQ33wPrR9jCztLqObNm6nwryjk0/TNA4MKFC7o0KybDkjUSERh4V6fIM7Tbt6ePIekGFe+zgpBJ8LqV+9QpFfLT5zp3zizdrGYR+XCTlXUchB64xIhX2HbHoG/GxELaUsWKSOeOHXTszo0bMVv6ackaSeAkYMVjrx7d5DuvfGpRQxvNQvfNhvVrNeHR09yXrWkWkY/HZO3orQk+pkTyHSmCGjO2b9umG/5on2MMLCFMTIYlaySBGOno0SPSrXMn7ezYuX170C1Pgx2hbIVDEcMYF6YeWkQ+gpN15vRpcujgwWf6jSFw/76+OiCA7QjB9+HGRFiyRhJI59Og7tO9qzRr3FDj0dDAFZ3BatOmTBGv3LnURbOIfISFrEeOHJbBgwbI4IH9Zf68OTG+bc6SNZLAkDOSSCxPrlW9qvavhgZOGBYmoycuWbSwzmayiHyEhax4QqyVhKxYVkvW1wQIJRhH2rp5UylepLCsXrVKpxSEbCpnnhPTDlnuy9BpduBYRD5CkvVwQMAz60uohTOTiX7jJYsX6cjZmAxL1kgCe1UvmFjUp1tXlRMSCzGoO2Q54MyZ0xojkdggK7x/796gWywiE26ydunYQWbPmCFHDh16JtnHUur6tWtqq+NucwGN6cuWLVkjEUw35MSobdxgTgKGgiM5/MmQmIMN6PPmzpa6NatrM/qK5cs8sgnaEwBZUSu1bd1KBvXvJwsXzJP9+/fLUROnBhw4oKUalE0IJCaMG6urTZgRHZNhyRqJoN/1x1OnVDlTuXxZ7V1lTf6kCeNk2tTJOnqUif40oDPR8KI5QTxxJKYnALKSxGvaqKF+3uzJxSXu3rWzeLdtLbVrVNXfEa+yMeG+iWdj+hwsS9ZIBF82mV4I6565xMjRQcbdZRYTbu/woYM1hkJo/rsd6xJlYEoHi5RHjxyp9Wyy9Fqm6ddH+vn2VlHKhPFjdQgeAglPgCVrJAPCkshAuXTy5AndW8O0ginGJdvov0HOnTsrgXcC7UTDKAbfwaVLl7SrhsSf/4b1+vnz77atW4w7fERFLKElAWMqLFmjCJwAxLCcEGfPnJHTp0/raNLff7fW9FWAzx8BChdNJkj+cv26+fxdxw3zc2BgoA5d9yRYslpYeAgsWS0sPASWrBYWHgJLVgsLD4Elq4WFh8CS1cLCQ2DJamHhIbBktbDwEFiyWlh4CCxZLSw8BJasFhYeAktWCwsPgSWrhYWHwJLVwsJDYMlqYeEhsGS1sPAIiPx/L48TcGYcg/YAAAAASUVORK5CYII=)
A small block slides with velocity
on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point C. The angle q in the figure is:
![](data:image/png;base64,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)
physics-General
physics-
A bob hangs from a rigid support by an inextensible string of length
If it is displaced through a distance
(from the lowest position) keeping the string straight & released, the speed of the bob at the lowest position is:
![](data:image/png;base64,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)
A bob hangs from a rigid support by an inextensible string of length
If it is displaced through a distance
(from the lowest position) keeping the string straight & released, the speed of the bob at the lowest position is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAP4AAADeCAYAAAAdOr1nAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAEQ9SURBVHhe7Z2FexXplu7vf3DnzsyZ6T6nDXd3d3d3d4IEd3d3CO7uGpzgEEKAACEEgrtbcHrd77eSStN9upsAKSL7e3nqCdm1q3btSr3f8rX+j1hYWHgcLPEtLDwQlvgWFh4IS3wLCw+EJb6FhQfCEt/CwgNhiW9h4YGwxI+H+PXXX+Xly5fy+PFjef78ubx9+1Y+fPgQuff3+1+8ePG7/fx89+6tOe6Z7n/16pX8qnt+O+7Zs2cSbo57/fq1vH//PnKvmOPeyRNzzP179+Tpkyd/uv/x40fy8OFD3eeAz+T38PBw87kv9Of79+8i94peH+d9/OiRvo/3cy0O3rx5I0/M57Hxf2c/G5/JNbPvhbkXzvcEvJfvwj3ie/Je57y8j+t4+OCB3ouPjwO//mr2m3vw4P59cw+fRx3HT84b8V2e68835vo/3s/rDx8+0H1//C5xBZb48RCQ7VLYRdm1c4ecOnlCHhmi8TA6Dxj7L4SGyp7du+R0UNDv9kMsHsoTJ47LXr/dcuXK5ajjIGBYWJgEBPhL8NkzcuPGdUOmF7oPQK69e3bL6pUr5Mjhw3Lj+nUlh4NHhrh+Zr/vls1y69atyFfFkO6lvvdc8FlzvScl9Px5JYcDyLXXb4/s3b1bbt+8KW8iye/g3t27sm/vXjl48IDcvXsn6rvwk0XmQuh5ObB/v5w5HaQEB+y/c/u2BPj7y8nAQLl29ape/4fIheqV+YyQc+dk08YN5l4E6rkccDfevHktZ0+flk0b1stpc9535t4AruuuuZ7gM2ck6FSQnuO+uX7nermHfB73gH3cb+f+xiVY4sdDvHv7Tk4EHpc5s2fqgxt89qxKLkf6Itn8jxyReXNmy5bNEQ8g0pSH8/XrV4aUN2X92jUyZdIEOXrksHl/xEPNQwoJOOdW8+AePnxIyeMA0i2cN1cG9O0t8+fOkcOGiJDSAeedM2uGjBs90pDilJKAhx6t48KFUEPOfbLKLBq+mzfJnTu/nRdSLlowT+bMnCGBAQF6zo+JePnSJVmyaKFup4NOyYMH9/W78h5IeOjQAZkxbapsWLdWyQ343MuXwpS4G9evk4MHDsglcx7nvEjj/fv2yshhQ/VesGg50hmaokXs2rFDhg0eJFs2bZSnT5/qPu7tVXO9h8z5eH3jxvVyPuRc1L3n/m7z3SwTxo2VHdu3yW1z/5zFKC7BEj8egocPYi1aMF8WGCKuW71apdPbyIea/cf8j8rc2bOUqDygFw3x3r+PeLCRsLNnTBfvtl6y3pAF6cvrSNqzRpJtMcScbUg4zxzPouLg3r27hvCzpUtHb+nbq4fMmuGj0tsBGsLkieOlT8/ustM89DeN9Oahf/3qtZIZ4kOkUcOHSaiR0g6uX7tqvsc8mTB2jKxasVz8jx5VU8LBpcuXZLH5rpB7oyFy0KmTSlyumZ97du2SDu3byrgxo+ROpKYBia9euWJIuEUWL1ygi8r+vX5RGgqLHBpTz25dzPeYLufN4vjMkPs3Ar/WRaNj+zZmAZ2li8/Ll+F6b7kPJ80CyetDBw0UP6NZscgBvu+WTZtkxNCh5l7N1QXnY+0nrsASPx4C+xgibzaS2WfqFCUSDzFSCvBwnjYLwcrly2TKxAm6IdmdhxqpON2QqFmjBiq5r1+7pg/127dvlCyYCCPNOfv26qmSzQEmAsTs1b2rNGvcQLp06qAkhYDg1q0bMsNnmvQ1xF+2ZJEEHDtmJOlD1VDCw1/KUWMedPJuL+3NghN4PCDqetAU1qxaJeMN8ceMHCErli39nUZw/fo1WbdmtX7XaZMnqRqNfwJwjj27dur19OvdU0KMOQH53pt7cPfOHTlktBIWsF7du5nzLjHfPeI4iLrPLAT9+/SSiUY679yx3ZhPYVEERjNgwezk3dYsZuOMaROh/XBv8QlcvHhB72ur5k1ltbknaDUgYkHZKePHjJZxo0bJfLPwspjGNVjix0NANMgbauz4mT4+0qpZU1ls1GAcWUDtUPPQY99OGj9OOnfwls3mIeahBTykEI2HftZ0H5XEt4x0xv5lATgXHCyDB/STpmZh2ObrG0XsF+aBDzjmr8fUrl5VqpQvr4RxCIy5sdVIWJ8pk5WgLDyo8RzPdsYsRt27dJK2rVuqze7Y3I/Nz8Djx2Xh/Hni3cZLhg4eqBLWASRHwi5bulh69+imiwsqPuC8/ka76dunpwwfOlh279qhfgsI+NosAGgTLEIN6tTSe4GZALjmYLNILFuy2CwoXO9E1QiiFk+zWLFYTjEazJRJE/Wzg4yZwcLA/WURZPFsVL+Oal04PHmd4/CPrFm1UgaZe8giif8irsESP56Chwyio+43rFdHpSGqNZKKfTz0kI6HtmnDBrJs8WIlPERBIiLJZ82YIVPNfuzr4DNnowiOaort27BebX2AISgPPKbAbbNv+1ZfqVe7hhTJn1dWGXLjPGRRwat+9sxpYz6sMSr9QBk9crg69BwgUUcMHSLdOndQNfrihQvy0qjqkPSOWajQYJo0qGfI31qJ7nwXfrIfE6RtqxZ6bjQTwDWHGBt79qwZMnHCOCXh4UMHo5yH4eEvZMP6tVKrehUZPmSwLgpoTO/Mhs8iwCwac2bO1AWJhcrxEbAghZnrw0fCIjZy+FCzqOzUawWvzAKBz8GrZXOZaRZCvufTp0/k/Yf3agqwaLCwNjJ/m7WrV+lxfJe4Akv8eAwIgc2LRIfgxwOOmYcuQvJACBxWkLtJw/pq70NajoHEly5elB3btqojbmC/PuoVd4BUxMbv3KG92tZ4sCOcgxEONbzn7Q05ixcuoAsODjekNqYCtvnRI4cMkTpKe69Wek0OUOmXLl4kY0eNUMcjRMLfwLVy3oNG88D8aN6koezYvlVu3464XvbjNCOi0KJpI+nds5tqJUht/BYsVJxrrrG5kbIQGBMD8F3Z18YsGJAXjYXvx+uv37xWki4ymkb92jVlqpH63D/wq7mHhBhxjPpMmSStWzST5cZUeGkWTfDm9RvZbu4fWgYaDpoOWgr3nnPz/0H9+0nl8mXVh8C9D4/UJuICLPHjMXjIDh88qB7kycbeXG2kM844R/VGbV25fLl0bN9O1dKTJ05o6AnpjGQj1Dfa2PKYCkhTxxRAciGRkdgzp08TX2MmXDMS1tEIbt68odKzZrXK+uBjRhCuI/YNzp8PMVK9oyFxfVVzuQ5diB4/koMH9quWMnrUcJkX6V9wwAKC47BV8ybqezh+PCDKfAGQtpN3O+nTq4fa7vfv39OFAemOs3CFITwSGAejE43gXhwzJs+wIYPU+bdx/XqVzo6nne+MRG5Yt7b6F7h2HIAfzIKCnwBthkWwfu1aSmB+574T3lPzw5gRREemT5uii5xzjzB7xo8dLTWqVjL3cYRGWTC/nP2xDUv8eAweojAjuXF2oY6iRu/euVMlDkC9hHjYtlPNfhYG1OIISfleSTdm1Eipb+xfnHao6pq4YtTvwIDjsnzpUn14Of70qVNRDy1SeoXZ16dHd/XgQzQksLMfNRxTAZISGrxifodobJgf27ZukZ7dOqtEvPBRVCAs7KJMMVK3p7GLBw+MkNyOLQ9CzgXrZ0HQlcuXqoPwuVkY+C4sZHxWnZrV1D/hmAJoBOQ0rFyxTG15NCM0AMcU4FicfBwz0XzP7Vu36j117iGmwvKlS1TiT586Vc0T7hPHocGwALHwYips37Yt6h6weOJM7Nqxg/Tv21vmzZ6ttn9cUfct8eMxeMjIlMNrTKjL26u1Sj0eVsDDCyHXrV0jkyaMVwl+yNi/PLQA6eVjJFXTRg3VsXb18hU9luSVmzduapx7+JAh0tlIYSS1cxxk8zc27JxZM5XcXY3N7n/0SNRDfffObVXlBw/or6E0bG4SbXRReRmu7+3Yvq0eS96Ac15U+00b18soc514y1HNib0Dvivhwk0bNqhNPd5Ib+L2SFbAZ+/ZvVsaGMlNqDEo6KRKbiQ66jzaAtdE+G7p4oVRUQGOQ0taaiT3NKPST582Tb8rZgDgHpLTwDlZPPfv26fXwTWzkJHwxIKBI3T1ypWqgQDu4749ezRi0LVTB+neuZPeT0erim1Y4sdzoHLiUeah5uFDLeV3XufhfGCIgcccye3VsplKRefhI25NmGxg/77muOniZ4hz4/oN3c8DfD4kxNj/faVureoaD3ceahYGwm1+e3apJMTDT7LKG2PjA0hFeHGWuRYWHDzi1yJV+g+G/PgIenXrqgsKZMB/wGei1pMlR2JSpXJl9NxBJ08o6fku+A9Y5Aj3sWhg3mA7A94DuSEoZsi2rb7qnIOcaD5379w15F6sXnjChiwGznH8H+2BBaWLkdCYRx+HRglLkgeAI5S8CFR8rifi2Hvq52hUv64smj9fFyIWC3wSocZswIxoY8wPvs/a1SvN9cQNO98SPwGAhxTve/s2XiqVsJWdTD4e3OvXrqu6Xs8QGBISlgOo9EcOHdJFA8cWnnFCbk5aK6QaOWyI1K1ZXc/PQw75OS+ecVRvCFi9ckVZYx5qCMTnaUjw3DmVzqjso0cMVxPDASo9Dj7i7khtMt+IOHAsdjtRgXKlS0gds6Ds3L5VvwsRBRKU0Bx8N29WJyCL0qVLYXpOFhTsc2L2kyaMk7lGGzmwd2+USs9CSLJSg7q1dGEg5ZnvgsR3ogoLDXFxHs7y8YkKz/Fdr1y+rAlJmAmDjXlCRh/XClis8O7j7GTRRZ3HsQj5+Ymjs51XKymQJ6f6S/CPOP6F2IQlfgIAD/DRw4eMDTpFpvtMU5IibRxgk5Jxh0awaOF8uW2kNQ80wAmGajth3Bjp1aOrquUOeKjx6mO/Eg5kQfnY2Xb/3n1VZfHeYyoEnYxQrwHhxBOBgXosiwPHOoDIkNBnyhQ1F3bu2G5s9AjVG+AII6xXr1YNTQFGwrKYOMCh2aJJI+nTs4dZYIKjTAyIRkIRkhczAx8BBTYODhg1vUfXzhrJOGbe55gJACKjDXVo66Veeg01Rkp9inAgP/e3eeOGWqvg4P2797LPz08X1lnTp8vmjRvVp+GAEOsgo1EVLZjPLDiD5JC513HByWeJnwAA8UnCGWNsY1RostSIZxNLJqefxJQhA/tL9UoVNc9+7drV+rCyWKDe45nG5sYDjZ3rHEfBDX4BVFWkKym6OOZQqdm/20i+fr17SdOG9aVPj24y0yw6qPzHAwI0Pr7KqMx1DXmrVaogC+bPVa83225jBhBlIIyI/YtWQTjshDFJULmXGglaq1plKW+kPteFU47EHPax4fHnnHzukoUL1DmHz4Hrxc4eZiR6w7p1pG/vHmpycN7jRl1Hs8Hrj4mBer5h/TrNJuScfGcch3j3u5nFioQopDzJQaQ/8716desipYoVVqckiw8mFPkQ3GvuD8k6fCccn/gx8F+wqHm3aSP5cmZTLQVzgUXQ0apiC5b4CQA4zBbMmyNlSxaTXFkzS54c2aRk0UJStWJ5qVGlklQuX0YK5M4pGdOklHy5spv3FdfX2I/tWbpYEXNcJsmUNpVKJuc49hXKl1uyZ84g+XPnkOKFC0qFMqUM6SL2VyxbWvLmzC5ZM6STvOYzixUqIBXMa5CSc5QuXlQyp0ujn8v1VKtcQTeOK1Yov15L7uxZpGDeXIbkJdVk4FjIxbWkT5Vcv0+xgvmlYrnSUftLFCkoGcw5+dxSRQtLZXOdzncpYz4TtTpLhrR6bXyWc1zxIoXMd8koubJl0XOWK1VcqlQsp/s5vkiBfHpcnuxZ9Ro4ltfZ+N55cmSVtCmSmXuRU6pUiDiuSoWy5noK6XfJa/Zzn0oXL6LHVDf3iPuRM0smSZnkF8mcPo0eQyqwYyrEFizxEwCwj3FYpU6eRP73P/+v/Ot//kv++Y//lO//+//J9//1H/qT13743/+O2MfrH22819n/78f9p3n9v35/zt/t/+i8Ufsj9vE7+347L6//tk+PNZtz7D//8dvrP373D/np+/+RH//t3H923shr0n2/vyZ9Xa/1PyKP++vv4pz33/ZHbrzuXI++9tFxvOZsUcd+dI/4Pt+Z37NlTG80mkWqpcUmLPETACA+seS0KZPpw8bD6RDj4+3H78z2J6/rPjaz/0/3ReO4v/3MvzzvPyK27yNIzvbz9/8rP//zzzddCMz7I4796/Oy/dU1/dXrzvZ3+yO+q7neP7wetS9y+9N95jgWnxxGe8KUscS3+GoQIsKh16RBfVWla1atHDc3Y7dHbeb3ykZdLmXMDFTydCmTS5Kff5BffvjuT0nPljFtSqOel/j388aTjb+NV4tm6ndwEoRiC5b4CQA4ivDOUz12IjBATp44Hke3QDl5MlCCTp3QfgIkw5DgQ/Yffgds+iQ//UulI+qxSkskrNkgPnY1C5ye50/PH7c3/jYUMRFNsF59C48CMfOHD+5rPwG88XNmz5IunTqq8w+HHo7AHFky6u84ALOkTyPJEv0kiX/8pzRuUE/DdxZfD0t8i2+GV69ea9Xajm2+MmLYYK0aLFmssGTLlF5SJPlZ0qZIKkUK5JWWTRtrzT+psOTesxCkSPyzlrjGxaYW8RGW+BauAXWW1FVUWwpfSBRavHC+9O3dUyqULanSnDAXKj4hvdrVqmouPclAqMTYwu3atNYQWaqkibTvAJmFFl8PS3wL14Baf1sr2PZr6Wqb1i01Np4rW2Z15qVLmUzj9BCe9mH0FqB0mLRWMu5od+Xdzkvy5swmKS3xYxSW+BYxBiQ83mqKaVDpjx49os44quzI4IPAqPNpUyTRJBiSamj4SQ78/r175eaNG2ax+C3MRXYgmXuW+DEPS3yLGAO177Shxg5HXe/WuZNmsJEJh4RPnSyxOu/KlCiqnny68ZAOe+3aVa3Qo3jFybsHlvjuwRLf4ouBhCf1lCIgOvCQm07tOk1BKKmlNVf61MnVPkelJy23RdPG6tijvx5lvy8iewf8GSzx3YMlvsVXgSo8BkxQbUcXm1rVqmitQIY0qZSsbOTOt/dqra2r6O1Hw0v6BFD99rGE/yMs8d2DJb7FZ0E99a9ea0uskOBgre6bP2+OVtlVKFNSi1gS/fCdZEmfVot66teuoXX3NM9g3BemQHRhie8eLPEtog2kM7XpNOjYtWO7TBw3Rpo1bqiJNlS9ZUidQsNzxN1p6T129CiN2dOEg7Za1PLj/Itu1polvnuwxLf4JCI649zXcVmo6gyhoK6/do0qki1zBkn68w+SKV1qKVogn9bRI/1p503cnt71f6fO/x0s8d2DJb7FXwLJjKee7jjE1OmWQxspvPLE4km8SZ7oJ021rVm1kgzs30c2rFunyTc0pKTz7es3EX3xoyvlP4YlvnuwxLf4N7x7914bZhKLp5XVujVrZNSIYdK8caOILLpkiTQsx/8pnGExmDxhvGw3aj1tremN9yVE/yMs8d2DJb7Fv4GMO9py01uuR7cuEd1nDPkiHHffSwpjx9P5BlIuWbxIAgMDtIsuiTvUmccE6YElvnuwxLdQotLM49bNW1ouy2w8eu95t20jxYsUVAlPk4/smTJIqeJFtHccE3TorMuIKWLxMUX2j2GJ7x4s8T0ZylXCcwyGYJbeNkPoIVKvdk3tSUdIDsKlNhv96Jo1aaSNL/f57VFHHzPoaNGN888SP37BEt9DAdkf3L+n9e2MlKIuvnf3blKpXFltCpkmeVLJmDaVZt8xNZcxUEzVpSMtI6K/RbNIS3z3YInvUYjwrhNLZ+7bkSOHVKVv2ayJlClRTBtBpkmR1JA+iXa/pV3UyOG0vt6shLt3964OqOD4Lw3RfQ4s8d2DJb6HgBHWhOUYFMFgCQpkhg0ZqOOhaY2dPnUKrZwrlC+P1KlRTbp16ai951HrCc05wyW+JSzx3YMlvgcA6QzpGXm1ZNEC6eTdXj312TKm0wKa5Il+jlTrC+kwDibnnjpxQkdiIeGZieeMwP6WsMR3D5b4CRSMyMJTf/XqFTl29IgObxw3drS0bN5UihbKLxkji2jyGJWe0llmv5Fi67t5k4SGhPxuVFZswRLfPVjiJ0Ag4ZHUV69clo0b1+vsNqrmmOhCth118eTV0+6qbeuWOgmW9FrmvJG488qo9c5svdiEJb57sMRPIMBp9+b1G7lz+5YOr9xiJPeMaVOkU4d2Ur5MSc2lJ/kG9Z7RUTS0HDJoQJRa//EAybgCS3z3YIkfzwHh6av/Mvyl9tb3271LJhiVniQbJDqx+HRGyuOtz54pvc5xZ1Y+AyHDwsLk4f37OuGWMdJuxOK/Bpb47sESPx4DdZyqueCzZ3Vm+/w5c7SlFWp97uyZJekvP0pmI+lLFimkpGEftfOHDh7QhpZxQZ3/O1jiuwdL/HgIPOzv3r1VOz4g4Jgm37Tzai3FCubTltXE4cmnR9JTRMMI5w3r1sqFC6HqqQ8Pf/FZdfGxBUt892CJH4/ghOXCLl6QA/v3yvKlS2TY4IE6mIL4O00wcNrx/9o1qkqXjh3EZ8oUne1OSi7FN3Gd7B/DEt89WOLHA0BW1PKXL8M1xXb1qpXSu0c3nQWfM0tG7U/PmCli8sx17+TdTmfSnT51SrvlPH/+TEtlv0W2XUzCEt89WOLHceB4o9/88WPHZP26NTJh3Gitf4fgSHhy6mmKwaCKtq1ayLjRo1StDz57RuP4v8Yzsn8MS3z3YIkfx/Cr+Ydkfv/+nRbSXLoUph54GmGgvhc2anzmdGk0Fo+EL5I/r/a9mzppkhzYt18uXbwYEYs3x6IlxCfV/o+wxHcPlvhxDG+MHY4D7kxQkPhu3qz58t27dJQqFcqqh558+qwZ0krp4kWkRZNGauMvW7pYjvn7y/1797QRRkKBJb57sMSPA0AqI+UpdSUWf/TIYZk5bao0a9RQShQpqMk3SHcdTJEti9SoUkmGDx6kmgAdbB89eqjZdm7VxccWLPHdgyV+LIOwGqp5aMh5rYufP2e2DOjTW+rVqiF5cmSVDGlSauUcjTAa1a8j/fr01KaX+/z8dHoNPoCECkt892CJH0tQT/2H9zozjsEUhOY6tGsjZUsWUwlPxRyeeppilChcQLp37qStrs6cDjIS/pEOtVAbPh477z4FS3z3YIn/jeGk1167clUOHYjoUT9i6BBpbuz1wvnzaqvqVMkSq7SvVb2KdOvcUaZOmiBbfbdIaOh5bVntKbDEdw+W+N8AThwetf5JZNtqyl8H9esrtQ25icXjtEudPImR8KnNApBHWrdsrhl5hw4elDt37ui8+DdvIqS8p8AS3z1Y4n8D0P3m9u3bml67ds0qmTB2jA6RLF+yhLa7SvbLj5I1YzqpVK5MZF38CFm3ZrWcOnVSPfwJyWH3ObDEdw+W+C7B8dKTT0/23L59+2QCs+YaNZR85kEm246KOVJsc2TJpC2wxo8ZpZ56ps/SCIM4PvF8S3xL/JiGJb4LgPTUt58+HSS+WzaLzzRi8Z2lepVK+hDjtMuQOqWOooqoix8oSxcv1DFV169fS1Cx+K+BJb57sMSPISCVITyFMEjrIKOmz5s726juXlIob26V7lTMpUjys1bPlS9dQgb07aNz5S9fvqzjoyE85/BUCf9HWOK7B0v8GAA0hewMmaARxvy5c5TUPKh46lMlTSxpUyQXpsnWr1NL+vTsJrNnztC4/cULobHSwTY+wBLfPVjifyEcT71KeCOtGSXFrLl+vXtK2ZLFJWuG9MaOj+hvhz1fsmhE1dwCsyicDjqp6bUU0XyrHvXxEZb47sES/wtBEQz2OHY5yTcjhg6WVs2aSKliRTQOj5QnFl+tUgXp0tFbpk6aqH3wSMB5+vSJJXs0YInvHizxowlHwhNLZ17c5UthsmPbVhkzaoTUrl5Vh1LQshr7PXWyJFIoX25NypkyYbwcPnhAblzDUx9hx2vGnTmfteX/Hpb47sESP5ogNHf37h05dfKErFu7RhtWkmJL7J12V5A9R+YMUr5UCWnv1UrGjR4pa1avkuMBxzQW/9YsGBafB0t892CJ/1cw0hh1HMIj5e/evauz5nDKUf+ORKenXfJEP0mKxD9LzqyZdNbckIEDZPfOnZqdh8OPOLyq9Va6fzYs8d2DJf5f4L0hPFVz58+FaJ789GlTpWe3LtoMIy9Vc6lTqGqPp765WQiGDh4oSxYtlIP798n1a9fiffebuABLfPdgiR8J7G0ks+Opv3//npwOCpKVy5frrDmmydIAg3ZX1MXTo57XOnfw1qEUPJDUxeOld2x4i6+DJb57sMSPBC2raWaJp36v3x4Nuw3s10caN6inan3GNCklbcpk6qmvW7uG9OnVQ9X+XTu2ywWtmntsPfUxDEt89+CxxHe86tjwhOYePHggoaGhsm2rrwwa0E+HUuTKlknj8GmSJzbSPp0UL1xAZ8lD+EOHIqrm0A44B6S3Uj5mYYnvHjxa4qOW43H3P3okokf9kMGG2I2ldPGiks0QHbU+i1Hvq1YqL107dZCpkyfK5k0bjQlwSp19EN7CPVjiuwePIz6SGS892XY3jFrPOKlJ48ZK00b1JXf2rJL8lx/Vhsd5xwhpnHm0rEalxwx4bY51JLyFu7DEdw8eRXxUcRphBJ06JRvXrdO6eGLxVSuWMw9XVpXwNMRgmmzb1i1kLLH4lSvkmP9R9dTbnPpvC0t895Dgif/h1w+q0hNee3D/vlbNLZg3Vx8oQnFId6rmGEyRKV0a7XnXv08vWbt6lY6qwuHHnLpfP9hMu28NS3z3kOCJD3EvhIbITqOqz/SJiMXXrVVDB1NAdohfpEBeHR89eGB/Wbxwvuzb6ycXDemfP3tmzmDJHluwxHcPCY742N6OhGf2+/lz51Rdp2V1xbKldCgF1XJUztHBtmTRQvpwzZ09S06dOKFdb+lRH9H5BjveEj+2YInvHhIc8d8Y0tNvHqcdKn1/Q3imyTKYAvudFFsy72pUrazz4ufMnKHTZJkxT6aeddrFHVjiu4d4T3wnFo/jjSSaS2Fhsn3bVhk7ZqTUqVlNsmfOIOlTJdcOtkj5gnlzSYumDWXi+LFy8MB+bYJJtR1tr60NH7dgie8eEgTxiamfCAyUlcuXyvAhg6R186ba2ipL+rRaQJM9UwapUKaUdPZuL9MmT5JNG9fLyROBcufObZ1VZ3Pq4yYs8d1DvCR+RCz+jUpqyEvvecZKUf9OXXza5Em1ZTXhuexZMmjV3MB+fWX7Vl+NxYeHJ9yxUwkJlvjuIf4RPzIWfz4kRDZv3KAtqzt5t5VqlStqHn3aFMkkc9pUUrRgfmndoqmMHTVSi2iOHj4k165dlfAXz7WIxiLuwxLfPcQL4kd56p8/12mygcePG7V+mXTr3EHHRWfLlD4q+SZXtsxSsWxp7W+3fMkSOXvmjLa6durirR0ff2CJ7x7iBfFx3N28cUP89uyWmdN9pGe3rlK3ZnV11EWE5pIp4RvUqSWDB/SXRQvm6zTZCxcu6Kw5m1MfP2GJ7x7iJPGJn5MtRyz+3t27Ehx8VqvmaHaBvZ47WxZNvCEBB2lPg8sWTRvJTJ9pcuTQIZ1c89ZWzMV7WOK7hzhJfCT0g4cPxN//qCxauCCiR33d2lK8cMGI/nZJE2siDh1se3bvGlEXv3O7BJ89I/fu3dNSWYv4D0t89xAniI9U/vDhvc6KQzW/cvmyeuqnTJogTRvWV0/9L//6LnL0VArJlyuH1suPHjHcEH6HFtDYkFzCgyW+e4gTxEclf/7sqVbNrVm9UkYOHyatmzfR2DulsTpCOlliKVuquHi39ZLJE8bLpg3rJTAgQLP0MAksEh4s8d1DrBEfKU/nm8ePn2hdfGBggI6e6tiujebPM5ACT32GNCmV/BXKlJS+vXvKmlUr5dy5cxrD17CcteETLCzx3UOsEZ/wHBVwJNUgwZHk1StXkPxGjScWnyLRz1I4fx5p1qShagBrVq2Sw4cO6iALJtFEFNBYJGRY4ruHLyK+kzn34sVzefjwoWbPoXJja3+83bx5U4dQkHBDSA4pjQ1/y7xOUQzSe0Df3lKlQjltZomXHhs+Z9bM2v6qY/t2MnfOLB1KQcecN6/fyAcj4a2n3jPgJvF5hniGnz9/LuFajelZ042+iPh4zQmzMVVmo7G1Z/hMkyED+0u/3r20iYX+NIQePXKEptLu2bVLLlwIlZDgYDmwb6++1q1LR43FFymQT4tnkvz0Lw3T0eqK7rZLFi/SuvjQ8yHatprFxsKz4DbxKdA6fuyYZoFSmclCYIn/J1DPuyH9tatXlZRzZhoCd+4kNatVlgJ5chjiZta0WTb+WMTX69WuofF3Mu0WL1wgo0cMkwa1a0aOnUosqZMnlkxpU0nhvBGz5qia2793r9y/f9/8Id5GfrKFJ8IV4htia0KY0TpJCGNQyuaNG+XqlSvqJKZK0xPwWcQnZfbKlcuqotOrrnKFslIgby7JkSWjZEqXWpNpIH0+84fiJ69TFktb6hpVKmm3WhYDquWoi2cfs+eQ/mgBDKE8a/6wpOW+omrO2vEeDTeI/94IL8zM+XNna7UmzyQVnXzWI2O2ekodR7SJj6rNqrh1y2bp3rWzkjpFkp81XRabvJghNznyxNeZHgvReY0+dimT/iKJf/yn/PzP/9UN0mdOn1az8Ab376fjo9Eiwm1YzuIjxDTxeYaR6r7meWvZtLFGi3gWvVo2kwP793lUy/RoEd9x5u3auVO823jpZBn+ELkM4evVqi59enaT6T5TdXbcyhXLtBpumbHRx48Zpe9n1BRqPaRP8tMPUqxQfvXiz5szWwKO+WsePqRnXp2FhYOYJv6LF+Gqsc4wzypaKKXbCCSvls1l/769OiDFEv8jsEpeu3pNfKZOkQK5c0ZK7DQq3ceOGqHJNMyZCwsL06w7tosXLugqSsFMl04dpFTRQpIhVQqNzZOYM6h/X/HbvduYD1bKW/w5Ypr4mJA4l/v17qnmZqIfvtfx5p07tNcW6lbV/wh4ORn5vH7tWrXrMxvVHdu8fp2aMsaQ3m/3Li19xQy4YSQ30vvWzRsa3gsJCZGjR48YLWC5DBk0QCqXL6vEx7FXuXwZtbOIDtj6eIs/Q0wT/8zpIJk+bYq2XsuXK7tkzZhOc0VGjxyuz+9b69X/Daj5xNHxzENWBkeiuo8aMUy2bd2i0h3bCDWJ8MitWzfNz1u6uuI5vWJsd3rZY8d379xJchu7KpUhP3H7wQP6ybmzZ43Uf6afY2HxMWKK+FGm6o7t0sGcr3rlilKpXGl1LDMAdf68Odqv0ZMQLeIT9sAZwiqJM48JsnS/ORccbIh+SyviCL/xk1l0jJhmCCUDLO6aBQHHHTH/ObNm6Cx5imyw+Tu0baNFNmgJnhJGsYg+YoT4hO/Cw/U5pYU6vRghPOp9j66dpXuXzrJ+3VpN5PEkfJL4ONzwgpJdR958+lTJlLCBxwNU0rNBejL4SLR5/PiRWT0faVotPep5/YFZEFClOM9AY9uXLVXCqPyJpFmjhhoaxB9gHXsWf0RMEB/V/f6D+9q1adjgQRpmLl+6pA5PmTRhnPhMmWzs/v1aN+JJ+ATxzWr5KtysiGuknCFrmuRJtFKuQ1uv3xPfEJv2Vk+fPtW0XJpZ8n/Scx8Z8rMwXCEU6LtZbf3yZUpqI43mjRtFjqq6aIlv8W+ICeKjsfJ8rV65Uicekylazkj9zh291d7fuX2b7qd2xJPwt8RntWQE1bq1q6VsyeK/Iz52P3b9x8Qnn/7ly1eROflPNQ0Sie8Qf/OmDZrKW6ZkMf1Dkqm3zhLf4i8QU8Q/YaT9mJHDpWWzJupgJtPUu10brQY9H3JOBZSnOZg/qeqzEm7ZtFEqG1U/feoUSnxvr9YS4O+vxFfyG+Jj0yPduYkO4XWLtPWJDKxauULj94Xz55UUiX+RFob4URL/vSW+xe8RE8SH0Ht275LWLZpJg7q1pJ1XSy39ZobiavM84o969w7Se1bhV7Sce9w41HI64aRLkUyaNKini8G5c8HqmEPqOw4+Z1NHHz/NPkJ7QSdPah5ArepVJHtmuuImkvZerXTqDZV8NqRn8UfEBPERXGiaVStVkCoVyprztVE/05SJE2T/Xj/N2/dERIv4x409j2MENYlKOvLthxpbnRDd1atXVaIr8ZH8EB/SR2549WmWyXu7demkhTwkAGE2DOjXRyMDz1+88Jj4qUX0ERPEp6hs/do16lcqlDeXVKtU3jzLAzW5jPJwT+3A/GniG0KSkbd61QqjJrWSjGlSSZYMaTUfn553e/38tOiBmXXXr12NqsUnNZJS3FOnTsqG9etk5PChWhBBmuSP3/1DnXs4WDieUIs6Vyz5LT7C1xL/3dt3Koho2EqaeP7cObUUfNYMH9VU0TI9VeB8kviQkeSG8+dDZNyYUZIzS2ZJ+vMPki1jOqlasbz06tFNnSSU0tIDD28/oZNj/v6y1XeLxu47ebdXLYFFI9G/vlPikyNN+m+LZk3Uzn/0gKEXVt23+A1fQ3zojL+J9zNNKUfmDKqxTpk0SY4cPqxRJ0/WMj9NfAMcb4ToCOvVqVHdkD69quqkPDLJpm3rljJp/Hhtcz3bEJ0S25nTp8tQYx5QAAHpSfyhuw6DL7DxqcFnqGWJIoVk1nQfNQ9Qu/hjsADwf7sQeDa+ivjmOSKFHB9St84d9fmjRTu/37xx0+PCd39EtIhPXTzkp2896Y3t27TWeCg1+KTwUvDA78WLFNTe98yip/oJiU5ef1ZjGpCqy9jqHt26qMnA/ynLJaSHxCdzij8WhKdS79nTZ5pmaeG5+Briv3//QYKDg2XmjOnmuNpqWrYy2iXRqOfPbIp4tIjvgPAcVXjLly6Wnl07S/3aNaVMiaJSME8uyZU1k1GnMv5uy5sjqxTOl0dNAsIokyaOk43G3l+6ZJFMnjhexo4eKT5TJ4u//xHtqU84MDT0vBw1qhjtuk4GnjCr9nXND2BB8PQ/lqfha4jP83Lq5EmZOH6cdoEi65R08R3btqnPij6R1JWQUUoUyibw/A24Oc/MannTkPF00CkN861YukTGjR4lXTt2UE2AOH17Ly9N66X8ceK4sSrRWWnDwi5GFO8YFezSpTC5eCFUu+biQyBRyP/oEZk2ZZI5vrUxKapJ7x5dZZlZZKiqYr9V/T0LX0p8NEcECc8NPiZM0YJ5c6uGSeboksULNWOPOD7PG8U7pJrTWs5T8FnE/yNeGLufefMQdv2a1bJi2VLtrbdi6TJZtXy5bN+6VQKOHdMqPVSvvwO50ocPHjCLyEiNGOQ0GkTZksXMYtJKZht17cihg7pCW/J7Dr6U+GiGhPGILNHOjfLxejWra71JLfNstTMLwZAB/bUnRN9ePWTd2jVGm32gJq2nOPy+mPiOPU7lE8U5xERRyz/eiOGjvr8Mf6l/jL+7qZyLRB86oYw2f6iIDrx5JXf2rFKmZHFpbzSJnWZl9rRiCk/G10j89+Z5Q0u8a1R6KkAH9e9nBEoVdS7TG7JYoXyawjt18kQ5cviQppk7x3oCvkrixyTIF+DmYwbsMGrY+LGjpUWzxlocRCkl9pnvls36nlfmD0q3lNtGA+D9hGZwPnpucCZh4mts/I9x+fIlWbdujbZtpxa/dLEimsWHKbp1yxbNQbE2fiwCNf7Vy5ca2sPJt89vj5btLl28SFabn6Hnz+v+q1ev6FSdtatXyvKlS9TfwHAPawYkLMQU8REWNIk5GRgovps2ybrVq7WlNrkmvM5+T3McxynifwxUrqdPmKt3XZ2AbPzOH4khCAvmz5U+PbtrpSCNPvfs2imnTwepyWG79SYMxBTxHThCBbKTTv7sWUQI2RMRZ4kPsPvxzkJ2NiQ6av2mDRuke9dO2gIsa4Z06gvAJ4DHdsO6tUa1u+yxf9CEhJgmPs8PuSE4/vjpyRpinCb+n4GOv/v8/DQNs1H9upoklD5Vck0HrmPIP37MaO3xh+r2/t17td3Y+CPbxSB+IaaJb/Eb4h3xITCRgpBzwRqGoWEnzj+yCKnA6turp+YMQHy0BAZ2RjQIsXkA8Q2W+O4h3hHfAWYAWVckYqDiN2nYwDwk7WTShPH6cKAZnDkTJLu2b9duwH57dpnXgzQXAB+Alf5xH5b47iHeEh+JTg7Bvbt31KtP/P/Avn3aEgwHDnkElF8SBiRji3ztEcOG6PAPwjdq43mYJze+wRLfPcRb4n8MnDU4/YjtU39NWjHdgQYZM6BogXySPlUK7eNP5lbvnt211uBEYKCaDBZxF5b47iFBEB/pj+qvmYQvX2r6JTP5IH7p4kUlXerkkeOSEpuHKLvUMBrA0EEDVfW3iLuwxHcPCYL4H4PGifT0Dwk5p7UDdPVt2qiBlCtVXEuD2apWrCCD+vWVIGMisFAQ/gs5d047B6E12HLguAFLfPeQ4IiPzy6icQj2/92IDMC9frJg7myd/dekYX1tELJuzWodBErK7+KFCzRFeM3qVfqwMQjEIvZhie8eEhzx/wyE9OgLSHtvxihRC0DXX1p+Hzp4ULp27mDU/0r6kE0YO0ZHKgUcPaoTfvAZWA0gdmCJ7x4SPPGx/5mCSoefu3fvaErvo4ePtCX4yROBsnDeXKlWqYLODCALkE6sOAE7tGsrc2fNlCOHDlkNIJZgie8ePELi/xlIBb4QGqqtl4n/0xeQNmG0EmNoSLGC+aVPzx7aMQiTAVASzHG/2jDgN4ElvnvwWOJDXoiMQ2/3rl0yddIk7clW1BCexoy5smUR7zZesnzJYh37TdYf/QXQFKzq/21gie8ePJb4DpDgt27ekmPGpsfJR8MGkn5aNW8qkyeMl+1bfeX61aty6dIl7TJMh6GjRw5r1iAORDIAbRagO7DEdw8eT3x8AEhwUnyZ80dW38H9+8Rvzx6d8sPvOPmo4aYCkOGhmAD8Tvqvob05iyW+G7DEdw8eT/w/AulNRt+9e3eNRDeLwcOHugAQDShRuKCx/5Mp+Tt3aK8agjM8lMWDRcQi5mCJ7x4s8f8AiP/2zVslMna9hgLPnJGF8+dpE1BmBGRMm0p9ALQF69e7l/ZsY0Kwp7VvchuW+O7BEv8TILMPByBJQJMmjJP2bbykauUKUrJIISmUN7d4t20jhw8e1PoAiM+CQfYfpcBWA/g6WOK7B0v8T8DxAVAExEgm/6NHVfoPHtBfnYDDhwyW8+fOqXbw9u0brQzkgT0XfFb7AFrn35fDEt89WOJ/Juj7R3EP2X8k//hu2qhx/hfh4eoIpJXzhLGjdVIQDR0DzcN74/o11QhsI5DPgyW+e7DE/0x8MOR99eqlPH/+TJ2AEYR+pzn/9AKkAxBjw/LmyCa1qleRIQMH6NgmCoEoH7aIPizx3YMlfgyBnH5s/WlTJkvdWjWEPgAF8+aS6pUr6LSWtWtWa3dXpL5V/aMHS3z3YIkfQ6AXwJOnT7TUd9GC+dK1UwdNA86VLZMUypdbenXrqg8tzkK0BsiP/0AdgHYh+FNY4rsHS/wYBPSloIeHkxqAkcOGSCfz4Hq1aCaTJ03QoaHPn79QR+HlsDA5dPCAHA8I0MIhEogsfg9LfPdgiR+DQIpHdQF68ECuXb0qZ4KC5NCBA+aBDVJy4xOgHJgJQd27dJThQwbpTEAcgwx8QAOwpkAELPHdgyW+mzAEhswsAkQDIDXSfdeOHdoWvEzxolKpXGnp2bWLzPCZJlt9N2sYkMVBTQAPhyW+e7DEdxkQGC3AITLpvz5Tp+gwkMzp00iKRD9JhtQppFjhAtK0UX2ZN3e2JgyRDOTp5LfEdw+W+N8YzALcvm2rjB09SpoYouP9T5cqmWTLnEHKlS4hE8ePk2uG+CwWJA49N9KfpCB+epoJYInvHizxvzGQ5M+ePZXgs2eMnb9CB3+WKVFUihTMJ5UrlJWpUyZp3T9hP8yDy5fCJMD/qFwKu6h5AJDfU+hvie8eLPFjCSQAXTh/Xrb5btEsv5HDh8rYUSNUG3hiCM80V+r+ly5aqElAPlMmm/f66kRgKgdJIkroGoAlvnuwxI8lINFpAgLJ79y+JVcuX5bQkBDz/9vyykj2s0YjmDVjunYFypUtsxQvXEBaNW8i04xGcOTwQe0FkNBTgC3x3YMlfhyBhgHDw9UU4P/BwcEyb85sad6kkWRInVJ7AebLlV2zAgkB+u3epWHDhAxLfPdgif+FQMnG6w5RISD9+74mHZfjHC8+P3HwbdvqKwP795VSxQpLlvRpJE3yJJIxbUopVbSQpgZTK8B7WSj4bDZ+TygmgCW+e7DE/0K8ef1G4/O06F62dIkO47gQel6n+HytCg55aQByHh+AIf/USROlW6cOUr92Taldo6p4tWgqq1Ys03g/LcNPnTqpSUL79+2TCxdC1f7/8CH+mwGW+O7BEv9LYCSqpuaeCpLp06ZImRLFpFb1qtqK++rVK2ZR+PoqPMiPNkFDT9p/0QeAVl9zZs2UFWahOXXihHr5WXhmTfeRAX37SJ9ePXQBwv5/+TJcawK41vgKS3z3YIn/mXhnyIg0ZignXXjrGZubPvwM52RW36VLYeq0i2k8eHBfzp45rYQPPnNW8wFYEFavXCHNGzfSPoClSxSVtq1biM/UybJr53YJu3hBnpprZRGJj7DEdw+W+J+J58+eq/edLjyVypfRCbxJfvqXVC5fVtYaaUvbbTeIjx3PefElsBHjpxaAxYfhH2T/MQ+AnoD83qtHN+0PEHbxomoO8RGW+O7BEv8zcefObfHdvEl6G2LlyJxBfvr+fwz5E0mTBvW0Lx9NNyGp2yCr78GDB9r3f/DA/tKicUOpUKaU5MyaSdKlSi7VKleQEUMHy8GDB+JtAxBLfPdgif8ZwFtO0g2DNevUqCqZ0qaWlEkSSe5sWaR7547ae+9bedT5HJyILDQXjUrvu3mjjBoxTOrVrqndf8oY1b+tV0vZvGmDzg1ESyBnIPxFuC4aLE5xPQJgie8eLPGjCUhC2I5W2t5tW0upooW10y62NUM3Rw4dYtT8y5Hv/nZwrovPPrB/vyxZtFDGjh4pE8ePlflz58gx/6Ny69Yto43sjXAMLlsme3bvlpCQczo8NC6bAZb47sESP5pAStJUc+P6tVK1YjlNpmlm1OsuHb2lU4d2mmVH373YgCP9I6YCP1NHINdKRiA/0URGmIWJuYA1KleUHl27qCPyzOkzai5wbFyU/Jb47sESP5p48uSxSk9SZiuXLyPFCuXX+XrU1asXfcd29bLHBfz66wd5H+kMpL9/qDFPqAeoXKGclDSaSpmSRaVpw/oyoF8fzQ5kXBidgOMaLPHdgyV+NEFsHCmJU69WtcpS1ZCoZdPGMtrY1du3+ar3nJh7bCNCckf08keS0/WHOoB1a1ZL757dpaqR+DmyZpRMaVOpb6JOzeoycthQXdSYIPz+g9EcIjMBOUdsagKW+O7BEj+auHz5ktrN7bxaaay8VYumKjXpq8cDSr3827fue/M/F5goJBvRAGTnjm0yd84sGWS0lOZNGpoFrIp08sZM8VFCYe/fuHFd30tp8Nt3sWv/W+K7B0v8aCLkXLD0691TGtevozFysuRQ9ceNHqX98uIqkNgfZwFi/5PWu37dWpk2eZIsWbRI9vrt0ZwAIgR79uw2ry2Qgwf26yJAvsCbN69jxQ9gie8eLPE/AUjDduyYv7Rp1cLYx8WkZbMm0r93L7Wbt2/dqjn78QUfjP3PAsBiRYdfBoLyf+d3QoKN69fVacATxo2R9WtXy4njAVou/ObN229Kfkt892CJ/wk4knLP7l1Sp0Y1TZCpYuz7gX37yIF9e9VrHhO5+d8SjhbABCB+EuMPDQ2VdWvXSNNGDSR9quSakQjhWjdrKjN9pkmgWRScqUHfCpb47sES/xMg642Q18YN66Vi2dKSI0tGHZYJGUJDzyvpUYPjMyD/g4cPtcrPZ9pUDVMWyptL04AL5M6pWYmrViyXa9euavHPt4IlvnuwxP8Ewl+80Nr4ZUsW62Qc4veEwSiXvX//foLpfwf50Wxo7bV86RJpa8ya/LlzSIZUhvx5csrUyRPl3Llgzf5DC2IoCOFLogY4EN3wAVjiuwdL/E+AB5zGmGS90QW3SoWyKv3w8lP3npAA+YkA4MikxHj8mFHi3dZL2rdpLVs2bdSEIBqFXrt6RQeCTJk4QTZtWCcnjgfq7ECOj0kEGQ2EqAOLrUP8s2fORO61+BpY4n8CtLbe57dHxowcLhXKlJQmDeuL/9EjRuq90Qedjbx3tm/t9XYDfB8k+JPHT3TM145tW5Xk1APgC3j8+JGO/mrbuqUUzJtbFwWGgZDKzFBQ2odxjujcC97DfeO8ZByiTXB+Nv6/f6+fOlRzZ88iKZP8Ig3q1jaLwakYX2A8EZb4fwHHAXYhNFQ74PDQkfBSu3pV2bt7j8btcXRh896+dUs74ZAym1DAd6cG4Pr163oPcOzxO4lKdP+h+i/Zzz+qGVCzWmXp3NFbpk+bKseP+WtLMBaPTwH/CYlRxwOOaUkzDUWIlBBNIGeie5dOUrJYYe03mOSnH7Tf4JHDh9UkSQiLbGzCEv8voGmvhtiom8y8L1GkkHq7y5YoptNwzwSd1tx8+t4fNdKO9714/jzy6IQBZ/FzJKz6AMz3nD93tkY4aECC9z918iSSPnUKqVqxvGY33rxx3bz3hR6HP4Dtvfm/Q1aV9OY1NIT9+/bqZKEWTRppb8ECeXIZCZ9V8uTIJtkypdfzJ/7xn/LLv76TqhXKy7o1azQTkUXIkv/LYYn/N4D8t41du2vnDs3QK1+6pBTKl0eaNW4gfXp0lzEjhmsjjKmTJ6kNjJ2bkIEUJ6Pv+PEATfLp36en1KtdQ4t/cmTOKNUrV5RNGzdofQDS/JlZCIPPnjWL5Cl59PBhFFEhLfUD+BFII0Z7oJSYNOKsGdNJziwZJW/O7Ib8WZX8aVIkkUQ/fG80rszStmVzXXhCzoeoYzG+R1RiC5b4nwAPFvZ8oHnYVfU0kj9nlsySy6j9JYsU1tZbvL5s6WJNcknogLwa4jSL3KmTJ4x9P1U6tGtr1P0qau8fNao4kl6ThIw2tHL5Mlk4b6566ImCYMuTJUjtQK/uXSVfrhzawQgbPku6NMJIsQqlS+kiUqNyJe1yVKRAXtUoUiVNpIsD4UXGkGN2YHI5GolF9GGJH00g+TesWytDBw2URvXqGlW3urT3ai1jRo7Q18+cOZ3gVP2/xq+6GBLOw9m2c/s27f1HZyJs9vDwl3L29Gmt/fc2i0HdmjWkW+eOMmn8OHUULlo4XxeJkkULqSqfMU1KqVGlonTt6C1jRo1UW3/e7Nkyb84srSMYNniQ5haUKFxQzQu0A+YNkEvB52vXozhYJxGXYYkfTRC6u3rtquyLtEnHjx0ji80DfGD/Ps3ei41c9tgE3xVJi1ceDYAuP2y8hkfeb9cuTf8tV6q4pE2Z3JA7lZoErZo30+lAOEpTGCmfPnVyHRU+xryXLkJoBkQQiChcDLuoJgF+gFnTp+tiUSB3DiV/2hTJVNtasniRjhYn38Ii+rDEjyboU4/6ikOKDDdUf+LddLeJjgfbE+AsfDj26AhMIlAbY5MXzJtLVfkUiX+RfMZ2JzEItZ3GoMwKGDV8mM4QPHf2jI4IZyEljHrX/CRicj4kRPb6+cnc2bOkc8f2Ur50iaiWZ4QVly+JMLM8aeH9WljifwYipFxEnTsb0s3al/+Od+/eGjMgYtjITKO2Q05s97TJk0ryRD+pTZ8s0Y/qxR8/ZrTWQYSGnJe7d24r4fEfYEaQKg35iZ5cvHBRcwVWLF+qPhWciamSJpb8uXJIv149jWYQop9ryR89WOJbxDiIhqD+379/T1OAt27eLD5TJkk7swBQ5ER4LrOR9g3q1pLVK5Zr/T/5ApCeHADmFhAZwGRgAVDy37yp5cQBAf4ye+Z0qV6lkmTLlEEbnrZu0UwC/P011yAhTBD6FrDEt3AXRgDjycduZxJQmeJFJdkvP6q6Tzrw3j271VzChIL4kB1fAWYV4Tp+dyQ/77lhpD9mATn8RYwWkTpZErX1/cx50BTwOVh8Gpb4Fq4DAlPJuGDeHCldvEgU8Tu0ayN+fnvklpHm2PLY9hCd96MxEO9H+kNox95H7d++bZvOEsTLT/KQJf7nwxLfwnUQ5oT4C+fPldLFikjSnw3xjW2Ol55x3x8TH1XfmQMA8QnVoQngvON9jA7b5usrnb3b68Qglfi1a2gXISW+TeiJFizxLVwHPQseP3osvlu2aE8DnHuk5OL0o+7h9q3bSmyITzcjyE5ijpb+moXgniE+aj7ExxewccM6adaogfoLUiT+WSMD+/z8zLEPtbuwxadhiW/hOoh84G0/euSI1KhaWRIb4mfLmF67/WzeuFEuX7qkKjzpwOrVN+RH8uPYI9vPce5dvnxZU4AXzJsrlSuU1doJwoIsAnj8MRNsCm/0YIlv4TqcEBtVeHVrVVevPqE4knuowqPsmfRbogAQH7I74Tyk/R2zICDpTwae0CIdGp3SnAPSE9br3rmTNgmhGMiG86IHS3wL1+GQke45Hdq3keyZ0quDL3umDBqKI9+fGv+wsIva5OPmjZvq6UfKQ/iwsDBNzaWoZ/DAAVoXkCZFUkmfOqVUKV9WC6Vu3byln2ERPVjiW3wzYMdvWL9WunfprJV2JPNQgYdzjsm+JOdgq5MVSeouP+n8u337VpnuM0XHlVHAg5QnC7BMiWI60IQpxU+ePon8FIvowBLf4puBkV6k5NLTn3r+dCmTSzJD/qwZ0mk1HoU8lDgT719iNmoh+D9DQBkAUqJIQS3oIe+fqABtuXbv3KGFQTZt+vNgiW/xzfDh/Qd5Gf5SexhOmzxRnXL5c+eUDIbM1N3TzadcqRLa0IMJxNUqlZeqZitVvIjkzJpRsmVMp/H/+rVrqaTf6rtFTQPCfu/NuS2iD0t8i28OGnrSt5CBnWTvVShbWgmN5M+SIa1kTJtKPfbU4Ec158iayaj2RaVV8yYyZdIEbfGFI/D1ayvpvwSW+BbfHHjf8eBTWMOoLpp1jB4xXItv2nm11Ek+DC1B6jdqEDHVZ6SR8AsXzFfVHo2BIqA3hvS2SOrLYIlvEet49OixBAYel21bt8iqlctl1szpWqo7euRwLcjZtGG9nDx5QpN4rC0fM7DEt4h1QGaGeV6/fk3bdYWEnJNTJ09qA1P+T6suMvpo3W0TdGIGlvgWFh4IS3wLCw+EJb6FhQfCEt/CwgNhiW9h4YGwxLew8EBY4ltYeCAs8S0sPBCW+BYWHghLfAsLD4QlvoWFB8IS38LCA2GJb2HhgbDEt7DwQFjiW1h4ICzxLSw8EJb4FhYeCEt8CwsPhCW+hYUHwhLfwsIDYYlvYeGBsMS3sPBAWOJbWHggLPEtLDwQlvgWFh4Hkf8Pm/mMvuRkMUYAAAAASUVORK5CYII=)
physics-General
Maths-
The angle of rotation of the axes so that the equation
may be reduced to the form ![X equals 3 square root of 2 text is end text](data:image/png;base64,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)
The angle of rotation of the axes so that the equation
may be reduced to the form ![X equals 3 square root of 2 text is end text](data:image/png;base64,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)
Maths-General