Maths-
General
Easy
Question
In the given figure if
then x =
![](data:image/png;base64,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)
- 75°
The correct answer is: ![37 fraction numerator 1 over denominator 2 end fraction 0](data:image/png;base64,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)
Related Questions to study
maths-
Which value of x will make AOB a straight line ?
![](data:image/png;base64,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)
Which value of x will make AOB a straight line ?
![](data:image/png;base64,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)
maths-General
maths-
In the figure, if
, then EFD is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWcAAAEJCAYAAABIRuanAAAgAElEQVR4nOzd11Nc157//ffu3E3TTYYGRA4CkRFCAZSMIrIk2xqHOXPx1FxNzT/w3M4fcqp+z8X85vjYlhWso2QJWcICRBBBIuccm9jQee/nwpbGPk5KVneL9apCVSpB69sNfHrttddaX0lRFAVBEAQhqKgCXYAgCILwSyKcBUEQgpAIZ0EQhCAkwlkQBCEIiXAWBEEIQiKcBUEQgpAIZ0EQhCAkwlkQBCEIiXAWBEEIQiKcBUEQgpAIZ0EQhCAkwlkQBCEIiXAWBEEIQiKcBUEQgpAIZ0EQhCAkwlkQBCEIiXAWBEEIQiKcBUEQgpAIZ0EQhCAkwlkQBCEIiXAWBEEIQiKcBUEQgpAIZ0EQhCCkCXQBQmApgHdtHbfbhRJuRms0oUe8awtCoIlw3uYkZZ3FvseMj9vx5hQTX5BFqgaMgS5MELY5Ec7bmgfFPc7449vcq59m44CJsrgsYhLAKIbOghBQIpy3M+8Gykw3c4NNtHTZmVCXo+QdoCIynBijFOjqBGFbE+OjbUxZX2ZlYBwPHuRYHfPTUwy19TO34kYJdHGCsM2JcN62vCzb1xga86FLTKOkOp0U/yxr7e0MzG0wDyKgBSGAxLTGdqR4wDvLwuIyA84konOTOGpagKFGuuY76BrYy46caKLDVGjF7IYgBIQYOW9H/g2w97C2tshCWDYkHSMvo5iD2QoJmmEGeiboHvDg9ge6UEHYvkQ4b0eKB9yLyIobb7gNdUQSMZZE0mMlrIZ1Vlcd2JcDXaQgbG9iWmM7UgCfjM/jRfZu4nYqOLRbbHkVvLKE4vMh+734MQS6UkH4X4qCgoLy480QCQVZ+d+/I6lQqVSo3pGpOBHO25Df7WNlYpnFsVlWvGEM9Gxg0PexseJhxSmzPjbO0tQUC/6dhGskcXklBJ4io7jsrCzOMzO3wur6Jh6/H7cs4ZMl1JIatSmaiPgdpKTHYXsHxhUinLcdP17nKqPjXpbsMtbYDXDOsuD0oo7NICpOJqzvKYt9WXTbs4hJ1BIZ6JIFAQXF68S1MMTk4zbaBleYlSOxxEQRb9GhkRRQNGhGx5iYySYtK42MeDORBlXIDi5EOG87U2w5Zhhx2/DH5XJgTyqRESZ0shcNGYSrr+OdbmZi8gmPB46Rbo0iMizQNQvbniQhGSKwmLREu0eZndrgsTaFI7uKqCqNRCVtsD7YQv/TVm59dx/Sqjhce5CjexKwAaE40yHCeRtRXPOsjH5HR0s/j2byiMwpIXVnGhkRzz4jEdNMG8Pmadq7v+Pbb8qJUO0jtiyG2DCNWFYnBJAKSWfBbLWQGOZDAlY1yUSnl7C7PBrYYivcgXZ9lK7GZtoG7ThMVgwxVo6nGLGEYNKF6ohfeGle/OvTzDzuoqOhm/GlFda0ahw/22mioNEYMEYY8K1PMtFaz+OOQfrtHlxyoOoWhJ+QVKg1atQaDSoJJOXZD6YJU+p+CmsucP5wCuX6XoaaGvj2+3EmN3wBLflVheD7ifCy7HY7iuLBojJhii8mszgZfXgecTkmwjUKMj/e9PNrMCaWUlD7//Av6avM6bNISbcQoVehFqNmIRgoCoqkRqVSoZFkFL8XmR9HmbpILOl72H/0EavTE7Q2PuVJ01N6qxJJjrRgDXDpL0uE8zvM7/czOjpKR0cH4eFm9u6pIKXqArZ9MrJKi1qrRav+yWoMtQVL5j4qUnZT/L4fP2pUGh06nQatuMYSQoKesIREdiTFYPFsMD83w9yWm00Q4SwEj6GhIa5cuUJ9fT27du0iO3cX1sjo3/mmS0hqHVq1Du07sBRJ2Ka8Hjx+L26NFslgJEyjwhToml6BGA+9g/x+P1NTU9y8eZPr168zNzeHTqdDUkJz7k0QXowX2THNdPcQT8e28CVmklGcR6bViCXQpb0CEc7vILvdzvfff8+1a9dYWlriyJEjnDt3jri4uECXJgivT1FQnn387B/W8Sw9pb1tgLYRMKXnU1yxixSrISSDLhRrFv7AxMQEN2/epKOjg5iYGN577z3Ky8sJCxMLloUQJ3uRPZtsORysbXpweX+6jMiJb2OS0eFxBie28OqtRMZFYtaHZsyJOed3iN/vZ2Njg8ePHzM2NkZycjIHDhwgIyMj0KUJwpuhNqA2xxAV6yJJa8ZqVP/kH7Wo9FYi4pNI3OHHbzVgUilISmguNRLh/I5QFIWOjg7u3LlDS0sLSUlJvP/++xw6dIjExMRAlycIb4YlFUvJh5yK8lGgyiQvy/KT3X9mdLGllJ/TE1Ep49+RT1ps6PbDlBRFEQ0v3gFLS0v89a9/5a9//Stms5n//M//pLa2lqSkpECXJgjCKwjR9xThpxRFobu7m7a2NpaXl0lJSaGsrEwEsyCEMDGtEeLm5uZoa2vjzp07OBwOamtrqampITMzM9ClCcIb4fF4WF1dZXl5Ga1Wi82WiMlkDHRZfzoRziHM5XJx7949vvjiC+bm5ti7dy8XLlwgPz+fiIiIP34AQQgBs7OzPH78mIGBARITE6mpqdkW4SymNULUxsYG9+/f5+LFi3R1dZGWlsbZs2fZu3cvkZGRSFJo3qEWhH82MDDAzZs3aWhoYG5uDp9ve2ymEuEcgrxeL+3t7XzxxRf09fVRVFTEJ598wsGDB1Gr1X/8AIIQIra2tnj8+DEtLS3IskxqaiomUyhuxn55IpxDjN/vp7e3l2vXrtHY2EhCQgKffPIJVVVVIpiFd4rH42F4eJjOzk7sdjtZWVns3r2b8PDwQJf2Vog55xAzMjLCpUuX+O6774iOjubs2bMcP36cqKioQJcmCG+U3W6noaGB8fFxEhMT2b1797baUCVGziFkZmaGuro6bty4gdfr5ezZs5w5c0YEs/BOGh4e5sGDB3g8Hvbu3cvOnTsDXdJbJcI5RKyvr3P79m2+/vprnE4nhw8f5vTp09tqJCFsH5ubmzx58oSOjg6sVitHjhwhPT090GW9VSKcQ8Dm5iaNjY1cuXKF8fFxqqqq+OSTT8jKygp0aYLwxnm9Xvr7++ns7MTlcpGTk0NpaSmRkdurD7wI5xDQ0tLC//2//5eBgQGKi4upra2lpKQEvV4f6NIE4Y1bX1+nsbGRvr4+kpOTKS0txWazbbvloSKcg5jP56Ojo4NLly7R3NxMeno6n376KZWVlRgMolWJ8O5RFIWJiQnq6+tZXl5m79697N69G41m+61d2H7POISMjIzwxRdfUF9fj81mo7a2lsOHD2+7yzth+1hbW6O7u5v+/n5MJhOVlZXk5uYGuqyAECPnIDU6Oso333zDzZs3UalUz5fMiWAW3mUDAwM0NTXh8XjIzc0lPz9/22w6+WcinIPQ0tIS169f59q1awAcP36cs2fPbru71cL24nQ6efToER0dHSQnJ1NdXb2tW6uJcA4ydrude/fucfXqVWZnZ6murubChQtkZmaiUolvl/BuUhSFqakpWltbmZmZYdeuXRw8eBCLJRRbs74ZYs45iLhcLhoaGrh48SLT09Ps2bOHCxcuUFZWFujSBOFPtby8TGtrKyMjI1itVoqLi8nKytrWA5Lt+8yDjNvtpqOjg6tXr9Le3k5eXh6fffYZpaWlgS5NEP50Q0NDPHjwAKfTSWlpKTt37tzWwQwinINGT08PX3zxBS0tLaSlpXHu3DkOHTqE2WwOdGmC8Kdyu910dnby6NEjLBYL7733nri/ggjngFMUhbGxMW7fvk1dXR1ms5mPP/6Yo0ePbtu71ML24ff7GR8f58mTJywvL5ORkUFlZSXR0dGBLi3gRDgH2MLCApcvX+batWtotVqOHz/O8ePHRcdsYVtYX1/n0aNH9PX1ERsbS1FREampqeL4W0Q4B9Tq6urzlRkrKyucOHGC8+fPi8aswrYxMTHB/fv3WV5eprKykrKyMrRabaDLCgoinAPE5/Px3Xff8cUXXzA/P09lZSWnTp0SN0KEbcPpdNLX10d7eztqtZoDBw5QUFAQ6LKChkiBAHA6nTQ2NnLx4kW6u7spLi7m448/pqSkBJ1OF+jyBOGtGBkZoa2tDYfDQUZGBkVFRaIx8U+IcA6Arq4u/va3v9He3k5WVhZnz57lwIEDhIWFBbo0QXgrtra2ePToEZ2dnSQkJFBZWYnNZgt0WUFFhPNb1t3dzZUrV7h//z7R0dFcuHBBLJkTtp35+XkaGhoYHR2lsLCQgwcPbpvegC9K7BB8SxRFYXx8nCtXrlBXV4fFYuHMmTOcPn2a+Pj4QJcnCG+Nw+HgyZMn9Pf3o9PpKC0tZdeuXeJG4D8RI+e3ZGZmhjt37vCPf/yDra0tTp8+zblz50QwC9vO8PAwDx8+xOFwkJeXR35+vjif/FeIcH4L1tfXqaur4/Lly2xsbHD48GE++OADcnJyAl2aILxVPp+Px48f09jYSGRkJEePHiU1NTXQZQUlEc5/MofDQUtLC9988w2Dg4NUVlbyySefiGAWtqXZ2Vk6OzuZmJggJSWFqqoqYmNjA11WUBJzzn8iWZZpa2vjf/7nf+jp6SE/P5/z589TWVm5LdvuCNvb+vo6bW1t9Pf3YzabKSgoIDs7W8w1/wYxcv6T+P1++vr6uH79Oo2NjezYsYPPPvtMBLOwbU1MTPDdd9+xvLxMeXk5JSUlYq75d4hw/pNMTEzw5ZdfcvfuXaKiojh16hRHjhwhJiYm0KUJwlsny/LzFlSKolBdXU1hYWGgywpqIpz/BPPz89y8eZPr16+jKArnzp3j5MmTYm5N2JYURWFycpLOzk6WlpZITk5m9+7dYqXSHxDh/IZtbGxw/fp1Ll26hMvl4tChQ5w6dYqMjIxAlyYIAbG1tUVzczNdXV1ERUVRVlZGSkpKoMsKeiKc36DV1VW+++47Ll68yMTEBAcOHOCjjz4iLy9PzDML29bi4iL3799neHiYoqIiqqurt3VvwBclEuMNUBQFWZZpbm7mq6++Ynx8nOLiYs6dO0d5ebk4m1bYttxuN319fXR3dwNQUVFBUVGRGKy8APEKvQGrq6t0dnZy+fJlenp62LVrF5999hl79+4Vd6OFba27u5t79+6xsbFBYWEh5eXlREZGBrqskCCmNd4Ap9NJV1cXra2tbG5uUlJSwsGDB7FarYEuTRACamVlBbvdjk6nIyYmBoPBgKIogS4rJIhwfgMMBsPz4z4dDgdut1tMZQgCkJ2dTVlZGZIk0dvby+joKB6PJ9BlhQQRzq9JURRmZ2eZnJxEq9WSm5tLQkICbrc70KUJQsBZrVasVis+n4/V1VW2traQZTnQZYUEEc6vaWpqim+//ZabN2+i0Wj46KOPOHbsmJjSEAR+aCzR0NCASqWivLycnJwc9Hp9oMsKCSKcX8PS0hLXrl3jypUruN1uqqqqOH78OBkZGaLdlLDtOZ1OmpqaePjwIdHR0dTU1JCZmSl6ZL4g8Sq9oo2NDb7//nuuXLnC/Pw8x44d48MPPxTHHwoCP2zXHhkZ4enTp6yurrJz5052794t1je/BBHOr0CWZR48eMDf/vY3JicnKS8vp7a2loKCAnEjUBCAhYUFGhsbGR8fJyEhgcLCQpKSkgJdVkgR4fyS3G43LS0tfP3113R0dLBr1y4++eQTysrKxFyaIPxoYGCAuro6Njc3OXDggNh48gpEOL+k3t5ePv/8c1paWkhJSaG2tpaqqirRnFIQfuR2u+nt7aWzs5OwsDCqq6vJysoKdFkhR7yVvYSBgQGuXLnCnTt3sFgsfPTRR7z33ntEREQEujRBCAper5f+/n46OztxOp1kZWVRWlr6y8GL4se/aWd9ZYVVl4zBHElMTAxarQaP14/bJyOpVBi1atTbdAgpwvkFzczM8M033/Dtt99iMBg4deoUtbW1Yh5NEH5iZWWFBw8eMDAwQEZGBnv27Pn1o0H9btzTTxh6/IiOaQ9xuRUcPnQIq9aM1+vH4fahVmvQaVSokd7+EwkC2/Q96eXMzc1x9+5drl69ysrKCseOHeP8+fPs2LEDSdqePziC8Gvm5uaor69ndnaWsrKy3z5fRnbjnu5k8MGX3Lr0NxqbWthyOgHQaFSY9BoMOhUqCbbrZm8xcv4Dm5ubPHjwgMuXL2O32zlw4AAXLlygoKAg0KUJQlDZ2tqiu7ubwcFBTCYTFRUVvzPXrIAEksQPf0jwbICs12nQ655/1rYlwvl3bG1t0drayuXLl3ny5Al79+7ls88+Iz8/P9ClCUJQURSF7u5umpub8fv9FBYWkpeXh8lk+vUvUOnQ7yhj53vwfp6XmKxSwkzGX3zadr4uFeH8G2RZpqOjg7///e88efKEnJwcPvjgAw4cOCB2/wnCP3G73TQ2NtLc3ExCQgKHDx8mOTn5Nz5bAbUOQ1Ix2RFZJHpAazATZvxlOG9nIpx/hSzLDA8Pc+PGDe7fv4/NZuPTTz8VwSwIv2F6epqOjg5mZ2c5c+YMe/fu/Z3dgApIKlTGCMzGSMJ+nLsQt29+ToTzr5iamuKrr77i9u3bhIeHc/LkSY4dO0ZcXFygSxOEoLO0tERrayvDw8NYLBaKi4vJyMj4gzM0/neSWYTyrxOrNf6J3W7nzp07XLt2DbfbzdmzZ6mtrRWdggXhNwwODnLv3j22traoqKigoKDgj3fLKjKyzwWy9+0UGYJEOP+E0+nk1q1bXLx4kfX1dfbv38/JkyfF7iZB+A1+v5+enh5aWlowmUwcPHiQzMzMP/gqCcXvwTk/xNZ0L/i33kqtoUZMa/xoY2ODpqYmvvrqK4aGhqiqqnq+ZE6r1Qa6PEEIOj6fj/Hxcbq6urDb7RQVFVFZWUlUVNQffKWE4nfjnOpkeWYCv60ca1oJsTHRaDXi4LBnRDj/qLW1lc8//5y+vj7y8/M5f/48lZWV4gagIPyG1dVVGhoaGBgYICEhgdLSUlJTU1/ovGZJ9uFbGmK46Vt65AF27PNy4thhrOFhb6Hy0LDtpzV8Pt/zztkNDQ0kJyfz8ccfs3///ud9AQVB+KW5uTnq6uqe7wasqKh44ZMZJWSUzSVmBtppuF9HZ1c3Tpdo7fZT23rkLMsyQ0NDfP311zQ0NBATE8O5c+c4efKkaN8uCL/D5/PR399Pd3c3Wq2Wffv2kZOT8+IPoNKgjUjEkpRLtN+IxWxCrRLLNn5qW4fz1NQUt2/f5vr16yiKwrlz5zh9+rQIZkH4HbIs09/fT1tbGxsbGxQVFVFcXPwCc83PKKAJw5x/glJDFtHrKqyJWZjDfmM34Ta1bcN5cXGRW7duce3aNbxeLydOnOD8+fOkp6cHujRBCGoul4uGhgZaWlqIi4tj//79L38ImNqAIbmMrOQyxFqoX7ct55zX19dpbm7mypUrTExMcOjQIS5cuCCCWRBewLNNJ+Pj4+Tl5bFv376X7A34k1OOhN+07UbOXq+XhoYGPv/8c0ZHRyktLeX8+fOUl5eLrsCC8AfW19fp6uqiv78frVZLWVkZO3fu/NN6Zyps3xjfVuHs9/t5+vQp33zzDS0tLezatYvPPvuM0tJSEcyC8AKGh4epr6/H4XBQWFhIQUHBK3bUVlC8brweNx4/qLV69HotHreb5fUtVt1qDEYDCREGTNrtGc/bKpz7+/v5+9//zsOHD0lISODUqVNUV1eLNlOC8IK6u7t5+PAhBoOB6upqMjIyXu2BfJts9tXR0fSAlik/KSVHOHK4GueanZtNfXQsmcnIyuTCvgRM1u25CWzbhPP09DT/+Mc/uH37Nkaj8Xn/P7EyQxD+mCzLzM/P09XVxczMDAcOHODAgQMvsULjn/g9eBf6mWi7TWO3h3WdjX17K/B63EzOLNA57UYOT8Tpld/sEwkh2yKcl5aWuHz5MteuXQPg6NGjnD59mpSUlABXJgihYXV1lUePHtHb24vZbKaoqIicnJxX30Gr0qGLy2FHaQ17Yrwk52RhNBoJN8Sxp6wAjU2DLdFMuG77Tje+8+E8MzPDjRs3+Nvf/obdbuf06dOcP3/+BQ5nEQThmdnZWa5evcrQ0BBlZWWUl5f/dpeTF6E2YEitIC8sjdhNP0ZrLGFhYei0GvaVh5G14Uej1RBp3L5nbbyz4ez3+/F4PLS0tFBXV8fa2hp79uzhgw8+oKioKNDlCUJIUBQFv9/PwMAAQ0NDWCwWqquryc3Nfb0HVmlQm+OJMsViVRQkSY36x0OPIsNNhP94Ar96Gx/2LCmK8s71UOzr66OxsZGZmRk8Hg8mkwmtVkthYSFVVVUYRTscQfhDi4uLPHnyhJ6eHiYnJwHIzMzk8OHDZGRkoNG8s2O7oPBOvbqKojA5Ocm1a9e4cuUKsixz7tw5/vVf/5X4+Hg0Gs3L7WIShG2st7eXL774gvb2dsrKyviP//gPdu3aJUL5LXmnZtsXFxe5f/8+V69eZWlpicrKSt577z2Sk5PRarUimAXhBfl8Prq6umhqakKSJEpLS8nKyhLB/Ba9M+HscDj47rvvuHTpEsvLyxw6dIh/+7d/o7y8PNClCUJI8Xq9jI2N0dnZyerqKrt37+bIkSMvfByo8Ga8E+HsdDppb2/n0qVLdHd3U1lZyaeffkpeXl6gSxOEkLO0tMTDhw8ZGRkhPj6e0tJS0tLSxKj5LXsnwrm9vZ3PP/+cJ0+ekJ2dzfvvv8/evXvFjT9BeAWTk5PU1dWxvLxMeXk5RUVFolVbAIT0W6EsywwPD3Pt2jXu379PUlISn376Kfv27cNgMAS6PEEIOT6fj97eXrq6ujCbzRw8eJC0tLRAl7UthfTIeXJyki+++II7d+4QHh7OiRMnqKmpIT4+PtClCULI8Xg89Pf3097ezvr6OpmZmVRUVLz6Fm3htYRsOC8sLHDz5s3nh+WfOXOGU6dOkZCQEOjSBCEkORwO6uvrefr0KUlJSVRUVJCcnPynHQcq/L6QDOfNzU1u3rzJ5cuXcTgcVFdXc+bMGbElWxBew8LCAk1NTczOzlJcXMzu3bvFCo0ACrk552ft2L/66itGRkaedzEpLCwUZzILwitaW1vj6dOn9PT0oNfr2bdv3+tv0RZeS0iFsyzLtLa28tVXXzE8PExhYSEfffQRlZWVLxfMih+f14esSKDWoFarUEsAfmSfH69PQZHUqDUatM+v6BQUnw+fIv1wLoA6RC87BOFXDAwM0NjYiMvloqioiMLCQqxWa6DL2tZCJpy9Xi89PT1cuXKFhoYG0tPT+fjjj6msrHzJS68ttuYnGBu1s+o1YEzcQXxiHIkmNzgmmBqZZXBGwa2OwJaeQlZWJOEo4J5lYXyO6TU1XnMSibYodkSIeBZCn9/vp729nUePHhEVFcX+/ftJTk4WO2oDLCTCWVEUBgYGuHTpEo2NjcTGxnL+/HlOnDjxEu/uPvzORVYmRhganmFiWUIxRhFvjSNC2WJ9aYLV3k66px2MbujR+CfZ9DpwSLmkGBzo7YNMLjsYXlRwuWdZTs/AW5SBLUyDUWS0EKL8fj/T09O0t7czMzPDiRMn2L9/P2FhYYEubdsLiXCemZnhzp07XLt2DZVKxYcffsjJkydfIphlkCeZfdrC/bo+xuV44sr2kZ8RQ3q0kXDdDKMNrbTeH2MjdRcpRQkkrzxmar6F21MbhNsXyQmzoyrdhWJ1IDXfY3Bpmjmzjb1Z4eSJn2MhRK2srNDa2srAwABms5mSkpLXO0RfeGOCfsy3tLTE9evXny+ZO3r0KGfPniU1NfWFH0P2LGLvqKej/hFtc1qc8QXklRVRkp2ILUrBbO9ksPMJ9wYUVnQZFBXnUFIcgVWeYejeQ+59fo9HLZPMaeKwJkWSxDibM0N0TbiY3vwTn7wg/Mme7QZcWVmhuLiYwsLC1ztEX3hjgjqcHQ4HTU1NXL16lbm5OY4dO8a//Mu/kJ6e/hKP4sa52Ef7je9obJllI6mIHaV5ZIbL6AA2l3D1PmZidp4xYyIqSxzJBiOauGQMBh2m8T6ck4NMb7pYdMjIsg5LdDQRkRb0KhWS/0968oLwFvT29tLa2orJZBK7AYNM0E5r+P1+6uvr+fvf/87CwgKHDh3iL3/5C6WlpS/3QM4xNoZbeNQ6QvNUGLF5M6yOtPBoVk9keh427Rqq4QnWVrfwRsRgCLegQwvqaLQaPVbvEpZoL8RrsM9MM76qQtHmEJuVRnS6gWQxpSGEIJ/Px9TUFB0dHczNzVFVVUVVVRUxMTGBLk34UVCGs9fr5cmTJ1y9epXGxkZsNhtZWVlotVrsdjtarRadTodOp/uDJXQyynI/y4NP6Vs3sGhMIleyI01O0bngxzu2ic28gW3MzqZPj8lsxGjU8cMFhRaVomA0+rHEJRKxK5sIjYxqS4MvupiU7BQSMg3Eiak5IQRtbGzQ0NBAd3c30dHRlJaWkp6eLuaag0hQhnNfXx9ffvklXV1dmEwmtra2uH//PvPz8+zYsYP4+HhsNtvzj9885Ejx41uYYWFqjiVNHKbsw+zem0ZJZD8TDW1cb31A99IqOfoZlsKzURv06LUa4IfOXZLsQZJk/BEZhGceoizNTBoaTCYTEdFmrHo1YmOrEIoWFxd58OABU1NTlJWVUVZWJg4LCzJBF87j4+NcuXKFW7duERcXx+HDh5mammJwcBC73U5kZCRWqxWr1UpERATR0dHExMRgs9lISUkhMTHxJ8uAZHyrG6yvu5GtCcTurKCgJJuS2BhS/Qu0fd9K3+MBRtOX2QgvwIvqx0l4hR82pHjxelX4NPGY4/PIydOQE7BXRhDeDKfTSV9fH52dnahUKg4ePCjOPg9CQRXOc3NzXL16ldu3byNJEtXV1dTW1jI/P09zczMLCwusrq5it9sZGhpibW0Nt9uNVqslIyODqqoq3nvvPQoKCjGZjCCpQAKVRo3WaPphKkQFYMO8I5fUmKekGDbw6zVsSnq8Lg9+r+/Hatz4fApufxg6vQlruIQ4ZUAIdYqiMDo6SmtrK2tra+zcuZOSkhJiY2MDXWliULAAACAASURBVJrwT4ImnBcWFqirq+PSpUssLS1RW1vL6dOnKS4uZmtri6SkJBYXF1laWmJxcZHFxUXsdvvzv6+urnLv3j18Pj/R0TFkZmYAGjSRZqzRFtSzCp51Bz6vAoSjjUgg0mIlMcaCJ93IksnI5soG7k0XoAPWcXv9rGkSMFqi2GGVMYtJDCHE+f1+2traePToEVarlcrKSlJTU8XJcy/C68C5tsj84iorDg8+RUFWQFYUJAn8Hi9+vwpdpI2o5BQSIrRYXuNlDYpwdjqd1NfXc/nyZebn59m7dy8XLlygqKgISZIICwsjPz8fv9///EOWZfx+Pw6Hg9HRUZqamvjmm2+or39AeXkZ6elpqFQqNPFpxGVkYOtzsrg4wtxiHA6rBp99nS11FIbM3aTutqBzmOnpnmFrYYIZhxXLxhQrWxK+lDySMtPJsqgRJw0IoUxRFBYWFmhpaWF8fJwDBw6wb98+sRvwRfldeFYmme9u5/HgEpPucIzWSBKj9OjVEp6tNXxbW/hjdhErx6HSarFYXv2/C3g4O51OHj9+zKVLl+js7KS0tJRPP/2UoqKin72bq1QqVCrVL9rlREREYLPZiIyM5MmTJ3R1dfH06VOKiopJTLShiioiLs/Bvo6HdNrb6Oy2IK3JRK4NYg9LwLC3koK94RRM9RA7OcjGjIEb9QnELg4xs2Ekdl8FebuzSdarAv9iCcJrWF9f58mTJ/T09CBJEmVlZRQVFYkVGi9KY0RvCiPWP8XG1AiNy/lkl+ZyIG8HkToJ2TWDvDzI8KaL1UUv6zHAnx3OczMzgIKiyPh/HMYjK0haM/rwCCLC1bzKt1eWZbq6uvjqq6/o6uoiPT2djz76iEOHDr3UYUZqtZrc3FyqqqpYXl6mp6eHlpZWjh2rwWxOwpK6mwOVdsyjq0x4VplfkJH8RqJ2ZpKcXkp2lp6oMInw1Q3at9zY59eR1yIwJyewt3gX+VnRhIszYIQQNzk5yf3791leXmbnzp0UFhYSERER6LJChyYMgzWGHVYIk1wsesLJjs6luGIn0RJAOqxZsU5qGXdoCHvNzHihcO6o+4Y1r8S6rENjMGDUSkheL35tNGFJOeTk7CArVsfLtIBUFIXx8XFu3LjB3bt3iY6O5pNPPqG6uvqVDvjWarVUVlYyNTXFw4cPefiwnrKyEszmMNTmZFL3nyY8Z4k5h4JH0qAzmMiIiCUi0kKUETQ7isg1xRBud7DkVCGpCgmPjiYyPgar2M0qvAN6e3tpamrCYDBQVVUldgO+CpUarVaNVq0GJBQkVM9DOBz0WcTbJKwYCHvN3HixK/XBGzxdjqXbl0lOXibV2WFIvg1WJnsYGupmeLiY7PLdlKVEkPSCQ8zJyUkuXbrE7du30ev1nDp16rXbTGVlZbFnzx4aGxvp6+tjbGyM+Ph4DAYD2ugU4qN3EL+5gsOnw280Y9HB82r1VoyJVjJjnaS4vXgNFnSaIJj3EYTX5Pf7WVpaor29ndHRUfbu3cvhw4fFCo1XoYAiaVCrQON34FyZZ3rCDGEKy6ubLCxLREZFkJWhQfM2Rs65ulG+c5oY8cWyy1ZKdXUCKmWF2fov+P6bb7neMcajJTPUFmPLNf3hgR2rq6vcv3+fq1ev4nQ6+eCDD6itrX3t/n9hYWGkpqZisVhYWlpiamqKoqKinyyulyAsCvPvPYjWiFZrfKmrAEEIZg6Hg+bmZnp6ejCbzRQXF5Ofn4/RaAx0aaFHkpAkCUnxgXuN9cVZJsck1BFO+oeX6Z/SkZ6VTXxSJJGG1zu66IW+OsrgRaWScClG1AYLFrMZc/gOMnPSKEtRIS0M0fGom+5JO2t/8Fgul4tvv/2Wixcvsry8zL59+zh79iz5+fmv9USeMRgMyLLM1tYWTqfzjTymIIQyu93O/fv3mZqaoqCggLKyMhHMr0qlAkmFhAx+Dx7XJpsb62w6lllanGd61s7i6hYen/za/9WLXbVrjGg0WnQ+BUnx4ocfVvzqwrBGR2IN20DjdeH1efH8zsNsbm7S0tLC5cuXGR0dZc+ePXz88ccUFBS8sa4LLpeLzc1NPB7PD+9wopuDsI253W56e3t5/PgxGo2GgwcPvrGB0HYjA4rbjeL1IaMCjRGD2UpEVAwWiwmbTcOGX0NCTDh63etfe7/glKoKFAVJ8eHz+/GioGaJ2eFBHvcssEQ8cVlp7IiN/N2VIy0tLfz3f/837e3tpKamsn//fjIzM9nc3MTr9SLLr/5uo1arMZlMLC4u4nQ6cbvdrK2tMT8/j9frRaVS4feL8z2F4CfL8vPfBUmSUKlULzXIkCQJjUaDy+ViYmKC77//nqmpKTIzM8nIyMBgMLC0tISiKCiK8mc9jZD37DVXFAUFCR9qtGvzGLa28Es6JEMk1rgkUjKySTT6CQt3YEt2Y46IxKR9/dOYXyicFUmFyr+Fb3WK2bFenjyZI8w1TtvdRupaV1iIKSW/KIfc5Eh+7WJpY2ODwcFBvvzySy5dusTy8jJ6vZ62tjbm5+dxuVz4fL5f+coXp1arMRqNDAwM0Nvbi8Ph4Pr160xOTmIymVCr1SKchaD2LChVKhVqtRqVSoWigM8vg0qNTqdBjR/F68Hrk/HKCkgqVBr9DysIJB+yz4PHp6DW6JFlPwsLCzx69IixsTEArl+/TmtrK06nM6SC+VmtarUarVaLWq1GURQ8Hs/z7Hidq+SfvhZqtfpnp156vV78MsQkZ1Ac6yPH40Kn06M2WjFHxWGL/+E+ltkSS1KKgmd9BffCHC6jCY3FgoFXOzj/hcJZUqlQy078G7PMj/XR3WFEuzVFz9QaC7IZrd6IVeUGvxcFLf/8Eq2trdHU1ERfXx8qlQqdTsfExATLy8toNJrnO/5ex7MRhtvtxuVyIUkSHR0d9Pf3Pz9WNJR+GIXtR5Kk56PZZx+SJKFSq1GhIPv9+JUfB0sqCZUkISkKiuxHlhVkSfXD76okoVZJ+H+89+JwOFAUhcXFRS5fvvyzgUqo/E78bBT7kxH/T68qXue5PHuMZ1nh9/vx+XzIsvzDLuVwK/sP1WDbm0KKzonX68HnceHacrDulAkzqJAUGUXeYGFmmrmZDQzJScSHW9BKf2I4o8jIKj2qsGiiYhNJSY1E64nFoDOQGNdLy9AIE/Xf0RRlICIym3Qj/PTwQb1eT0pKCqdOnaK6uhq3243H4/nZu96boCgKWq0Wo9GISqXC5XK99nSJILwtWq0Wv9/P/Pw8IyMjzM8vEB0TSUFhJibHEoPtPQy6olClF5OfEUt2rAbJuczaYCsDw7MM+DOxphWzJ9NMlNZJb/8gj5pb0Ov11NTUkJub+/x+TKhRq9Wo1WoWFhYYGhpibm6OsLAwcnJySElJeT7CfVUqlQqNRoPBYMDhcNDe3k5TUxOKoqDTGyksKmZPUSYJVoW50QV6e8eZmjFijrHwIH2ZZLMW2bGAZ2OK/mk1K6pcyq0GUnj1dlMvFM4qZBSdBV1MNhkFlVQdTPlhR6Azk7WGdexP7nDx2028KTtJr8wm8Z/COTIyksOHD1NdXQ38coTwJj27CShJErIsh8zIQBB0Oh1+v5+uri7u3LnLk+5ectKj+eB4EdLCPNdNiSQadpF27CxHy1KoSNEhOaZZaL5EQ1M3t5dLsJW/z78dSkC/NcL//P0i9uUVEhIS+Pd//3dqamrwer34fL6Q+73QaDRoNBr6+vq4desWHR0dxMXFUVtby759+9BoNLjd7ld67GfB7/f7WV1d5enTpyiKwvr6Om63mwNVh7jw0XmqK/KR7P30LA6gMjvJjNcSrV5lfnoKwnX47aNsLo4x5c1ATo1HHxZFuMQvZhJe+Dm/UPEqQNIgaYzoTeb/3aptjMYaG4ZJ5cOz4WDT6cYlPTuq/if/iUaD2fy7q4sFQfiRzZZIVHQM1shoLJIL49wTxhd0jJjKSC6v5sNjJeRHS5gADDuxVJ9Gm5CD0mchMjWR7JRwuts2GRsfIyoqiurqaoqLi9Hr9a+0+zaYJCUlERMTg8ViITIyEpvNhuXH04VetzGt1+ulvr6eq1ev8uTJEzIzM9m/fz9Hjr5Hbk42Vms4mE2kHbLwYdYKB70mDOEWYiKMGHVqZGcq3q018qVopKgdpCf8cor3ZbxQOA+OzTEzOcq8q5v+pxF0pCQTpvLhWn6CvWOSMclGXEkxhdmJpOt5pXM2BEH4gdvtxuvz4fI4mRnuo316lh65hKHoavKz8ymOln6+SSp8J0mF8ewzOlCrPazMznPrzj1aWlopLi7hyJEj78wZGs7NTdxuNz6fD6/X+0b2MrhcLvr7+3nw4AG3bt1ifHycpKQkjh8/Tm1t7c+3uYclkJCfQMJbWI34QuHcPetnbXUVyTXMzKCRhw2TRKg3WRrtZWrEzlJ0MYXlJzm6O4N8/c+nNARBeDkGgwGz2YTXs8XIyDha7wLLO0qxFCQTGx/xK7tX9Wi08aRnRrG54aS9s4uOjk78fpldu3ZRUlLyzhwLqvDLm4Kvw+Px0NbWxqVLl6irq8Pr9VJVVcXp06fZs2dPQLe4v1A42w7+OzUOE7neaCJiY0iKN2JSu9HLagyRu8i05ZNeXEZpWjjhr7+8TxC2tcjISNLS0lAUmf7BGTwyhCUYsEZFYTX/1oWyhFanY9M1z/cP6xkfGyczM5OioqLnl/1v3wYbU8OM9Y0zviLji0ojKTubjEQz0c+Sx7/C4ugk87NrOHUWjEmpJCRHEAPgX2dzfp65ZR8+QzSxO+LwaNR4/X62NjdxOV2v1SRgYmKC+vp6bty4QXd3N0ajkZqaGs6cOUNlZWXAp4BeKJz3/9v/S6UiISsSkkr1wxIeSUH2y8iKhEqjRavT8gbWXQvCthcRYSUnO5uE2FhcfjUzLj8RLgkbKjR/kEV9fQM0NDSiKArV1dXk5ua+naL/ieJ34tuYYHawg46mDrpGV1m15JJQ6ubggXL2p2sw+udZneznaec0k7OrSGHhqNd82F1Z5MX70DumGR2eY3piBUxRLPkKcfolVIYw1BLMzc3S29tLeno6ZrP5hcPU7XYzMzPD9evX+eabbxgaGiInJ4fz589z7NgxduzYgUYT+CPPXqgCvSn8z65DEIQfSZJEXGwsJUV59OzKYqpvmIn1LQzrm8i/s4/KvrxMR0cHQ0NDZGVlUV1dTUpKytsr/CfcywssDg0xvSIhJ2aQwVOGhjrpuK7glcKIstqwzTUx+riHDmc2xpRccszzTI/28bijH1faOtqYaIbWbET6Z4lcaaXtkZf18GwSY9PYkZJI/fdN/H//5/8wNjbGoUOH2LNnzx92EPd6vTQ2NnLt2jXu37+Pz+fj4MGD1NbWsnfvXpKSkt7SK/TH1P/1X//1X4EuQhCEn1OrVeh0Ei7nGn1DAwwvesAYy47ocGxmL1uOdTbW1lhfX2NjY5XF+Vmampq5W3cPu91OVdUBzp07F7AbgZ6NZdaX1nFbdhCTt4viHAnd8gxdzSt4w80kZcJ6Sz0djdMspFWTe3g3Fcl+tjq76Ll7m8XZVvqJYURfQV6ci1Slm4dPPYw5EtlTYGNHlJaV1TXGxyeYnpnB4XDgcrmQZRm9Xv+LkJZlmampKe7du8fXX39NfX09kiRRU1PDX/7yF2pqarBag6sRXeDH7oIg/IJarSE7excV+49yp64BJgZYePg/3NNNsjmaSrQetH4vEgpatZ/V5SVaO/oYm5gld2ceFRUVREQELmz0EfHE7QwjQmNCE6bCJGViz5snpWUFs86OZs1Nb5+dngkjySfC2REbRriUTILBgdXbRf+0h0nLOiajDynNjF4dgUEtYfR6iIuKJjP7EClpGTQ1NfP48WP6+voYGBggOzubmpoa9u/f/7O59tHRUa5fv86VK1eYmpoiJyeHkydPcvjwYdLT05/vDAwmIpwFIUgZjWbyCnZTfaQG59Ymi9NP6ftujomeJKwmHSathE6jxmzSsmK30/m0n3hbEgf272f37vJf9Nt8m9SGMMyGZytE1vHMOPCporHtySYtw0fiVj8tc1tM+jLYaTYSpwINViJMClGRXlY3Y1lyaMiYG2AtysusOZaYdBtRlljiY8KIjrYSHRPLjh2ppKen8/jxYzo6Oujo6GBmZobe3l7Ky8uxWq3Y7Xbq6uqor69nZWWF8vJyzpw5Q01NTVA3HBDhLAhBLDYuntqzZ7FFGuhubWRwbIkVnxvFr0YymdDodWy4fMwtO3F5fCQlxlNWVkJKSiqvvjftTZLxLYwx3thKb7+PFUsG2REutOvruDw+tkxmNFotJn44hlinBW14FB5dIebwRDIlO+oVWDXYSCnIJ9aWQpT1f2MrOjqagwcPUlRURHt7O3fv3uXhw4cMDQ3R1dVFVFQU4+Pj9Pf3ExYWxrlz53j//ffZuXNnAFexvBgRzoIQxEwmE8XFZSTFRFJWVs7MjJ01F8hqLXqjAZ1WS0NDE7MzsyTabJQUF5OWlvZaS8zeHAX/xhxLo530P23nUZuLXoMGzaYBKWKdBbT4DEZ0mmcNohVUKhlZZcClSibGlseBIgPpkSpUEdGExdmwRmgx/dN7jtFoxGg0YrFYiIuLIyEhge+//57m5mbsdjs+n4/i4mLOnDnDe++9R1FRUQBei5cnwlkQgpgEhJnCCcsuIjX7l6HicDgYGexHq/Kzs7iAgwcPEhkZ+fYL/S1eF16/hBSbjMEwgNx9lwG/GU9hFOMeCyqthFb1bIyvIPu9eL0yfjmMyIRMdu1JJCPqxa4Anh2EtLi4yODgID09PUiSRGFhIX/5y1/44IMPguu1+QMinAUhhE1NTTEwMIDb7aKwsJC9e/cG0Tk2EipzLFHZByiJy8dsvUOycokRNhjbiGfZoSHO7AHFjxdQUPB6vXh9MjqDibBwK3rji0/NrK+v09DQwJdffklbWxuxsbF88MEHHDx4kPLy8pAKZhDhLAgha3p6mps3b9Lf309cXDwFBQXEx8cHuqyfkXThhMWGExabTpLOhXX0IXdXt1iy2DDJG1hdy7h9PjaBSLw4HT5cTh3WRAsxCS+2qcTn8zEwMEBdXR11dXUMDAxgs9k4duwYZ86cCdm2XCKcBSFEDQ4O8v333+Pz+Th06BA5OTmBLum5HxoAyCiokNRq1BI43WoISyUq0kR2bB7xU53o7ctsrK4y7fMT7lpgYV3LBikk70gkO1WL8Q/yWZZlurq6uHLlCtevX2dzc5OKigrOnz9PRUUFNpvt7TzhP4EIZ0EIQWtra3R2dvLkyRPS0tI4evQoqampgS7rRy7Wp3oZ6XjK2IYaT6SNSJOCyj7PHLnoUnZyKCcevTzP2OMhegb7ab61hls/Sv9mOOtJ2eTnZlAeC2G/s/x4aWmJBw8ecO3aNTo6OtBqtZw4cYLTp0+zb9++IJreeTUinAUhxHg8Hnp6eujs7ESWZXbu3ElRUVEQ7XDz4VmfZa7vMU9nYT0+l6RoDVatDndCEemphVSkaIg07yLCoLA0uMlG7wDTUQ6ccTkkZpdSnJlM9m8s03a73UxPT1NfX8/ly5fp6enBZrNx9uxZ3n//fTIzM4NyU8nLEuEsCCFmdXWVhoYGBgcHSUtLo6ysLMg2U+gIi00na/d+5DknK7o4rNFWYqIiMYXHERsTQZQRSCwla08CUvwGy+suNCY9OyxJWGOSSI359fmMZ51ivv76a+7fv4/D4aCyspKamhqqqqrIyMh4u0/1TyTCWRBCiCzLjI2NUV9fz+rqKh999BG7d+8OknXNz+gwxeeQHZlEwsYmDrcaVZgVi0XPzxZfSHGYE+MojlvH5fTjUMyEmbQYfyOVZmZmaG5u5ttvv+Xhw4dIkkR1dTUXLlxg3759f3joUagR4SwIIWR5eZnOzk5GRkawWCzs2bOHrKysQJf1K9SgsxAebSbMD6hUqH5rVZzGgiFcQYf0m81Qp6enuX79OpcvX2ZoaIjU1FTOnDnD4cOHyczMfOeCGUQ4C0JI6e3tpbm5GVmWyc/PJzc3N+CHwv8+FaoXGtT/ejB7PB5aW1u5ffs29+7dY3l5mcLCwudnYyQnJ7/heoOHCGdBCBEOh4NHjx7x9OlT0tPTOXjwINHR0YEu60+hKAorKyt0dnZy8eJF6uvrURSFo0eP8uGHH7Jnzx6MRmOgy/xTiXAWhBDg9/sZHx+ntbWV+fl5jhw5QnV1NeHh72YjjPHxcW7cuMHNmzcZHh4mOTmZ6upqTpw4QWFhYZBfLbwZIpwFIQTY7XYePXrE+Pg4MTExFP94wNG7Zn19nf7+furq6rh16xazs7Ps3LmTDz/8kJqampDeVPKyRDgLQggYGBh4vhuwoqKC7OzsQJf0xrlcLpqamrh48SKNjY3o9Xpqa2s5fvw4paWlQbZc8M8nwlkQgtzGxgbt7e20t7eTkJBATU1NEO0GfH1er5eRkRFaWlq4desWPT09REVFPe+EXVJSEugSA0KEsyAEMb/fz9TUFD09PdjtdiorK9m9ezdRUVGBLu2NmZ6e5tq1a3z11VdMTU2xe/duPvroI957771tN1r+qdDf4ygI7zC3283MzAyzs7NIkkRCQgKJiYlIUjB0OXl9brebrq4ubty4QXNzMxqNhr1793Lo0CFsNhsazfYdP27fZy4IIWBtbY3u7m5WV1fJyMggLS3tnQgsRVFYWFigpaWF69evMz8/T3FxMUeOHOHQoUPbesT8TOh/lwXhHTYzM0NDQwOrq6scP36cwsLCQJf0RkxOTnLt2jWuXr3K5OQk2dnZnDp1iqqqKlJTU9/JHX8vS4SzIASpZ6Pmnp4ezGYzBw4cIDMzM9BlvZaNjQ06OzufH4xvt9vJz8/n3LlzHD9+nLi4uECXGDREOAtCEPL5fPT09NDS0oLf7ycvL4+CgoIgOhb05a2srNDc3MyXX35JY2MjBoOB06dPc/r0aYqLi4mIiAh0iUFFhLMgBKFna37b2tpITExk//792Gy2kL0R2NfXx+3bt7l79y4jIyMkJydz6NAhTp48SUlJyTtx/vKbJsJZEIKMLMtMTU3R2trK4uIiBw4coKKiIiS3LDscDgYGBrhx4wY3btxgYWGB0tJSLly4wMGDB4Ou52EwEeEsCEFmaWmJx48fMzw8THh4OGVlZWRlZQXZmc1/bHNzk3v37nH58mVaWlowmUy8//77nDx5ktLSUmJiYgJdYlAT4SwIQWZ4eJi7d++ytbXF7t272bVrFyaTKdBlvTCPx0N/fz8NDQ3cvn2b/v5+IiMjqa2t5ezZsyHbDfttE+EsCEHkWTfpzs7O/7+9O39q6twfOP4OCQEhVZCCyCLbFyRsElYVAkZoQRZpaWe+v9yZ+9e1M7fToVK0oqKAgCyyiRDAgmyyKnsSQgI53x9663faq95WCQnwec34Y855zox5ezx5nucQGhpKUVERERERnh7WX+ZwOBgbG6O+vp67d++ytrZGTk4OFRUVFBcXy2OMv0HiLISX2NzcZHBwkCdPnqBSqbhy5QqFhYVHYobGzMwMXV1dTExMYLFYsFqtpKWlERISgtFopKCg4EhchzeROAvhJaanp/nhhx948eIFBoOB0tJS4uPjvXomw+7uLpOTkzQ3N1NfX8/8/Dx6vZ7q6moKCwsJDQ3F398frVbr6aEeORJnIbyA0+lkdHSU9vZ2tFotRUVFGAwGrw7zzs4OHR0d3Lp1i56eHpxO59t9MYxGI3FxcZ4e4pEmcRbCwxRFYXp6mmfPnmGxWMjJySErK8trHwMoisKrV6/o7Ozk7t27b2di3Lhxg2+++Yb09HS5Uz4AEmchPMxisdDV1cXw8DDh4eHk5OQQGRnp6WG919TUFPX19dy+ffvtY4zff/CLiYmRMB8QibMQHrawsEBraytzc3MYjUaMRiM6nc7Tw/oDRVF48+YNIyMjtLS00NraytbWFrm5udTU1FBSUkJwcLCnh3msSJyF8CCn08nU1BRmsxmHw0FmZiapqalet+DEarXS19fHd999R1tbG2fOnKGmpoaqqirS0tKO1Dzso8J7f20Q4gTY3t5mfn6etbU1/P39iY6O9so3ai8uLvL48WMePHjAwsICCQkJlJSUkJubK2F2E7lzFsKDpqenGR8fx8/Pj6SkJK/bZN5mszE9Pc39+/fp7e3l9OnT5OXlUVVVRXJy8pHdiOkokDgL4SGKojA0NERvby8hISFcvXrVq1bQ7ezs0N3dTV1dHR0dHWi1Wqqqqrhx4wapqale9w/JcSNxFsJDlpaW6O3tZWJigrKyMoqKirzixa2Korydc93S0sLw8DA6nQ6TycTNmzfJz8/39BBPBImzEB6wurpKZ2cnv/76K0FBQRgMBvR6vUe3Bd3f32d/f5+JiQkePHjAzz///HaqXE1NDUajkaioKI+N76SROAtxyBRFYWBggB9++AGLxUJlZSVFRUUeDfPi4iLt7e08f/6czc1NNBoNGRkZFBUVkZGRgdFolC0+D5nEWYhDtL+/z8LCAm1tbfT29r7deN5T22ju7OywvLzMo0ePaGhoYHR0lLi4uLdzl2NiYtBoNF69jPy4kjgLcYgsFgtPnz7l+fPn6HQ6Ll26RHJyskfiZ7fb6evr4969e7S2trKzs0NeXh6lpaVcvnyZxMTEQx+T+H8SZyEOkcPhYGBggOnpaWJiYtDr9Zw6dcojY5mamuLWrVt8//33bGxsUFVVxT/+8Q9KSkq8bhHMSST/VxHiEG1ubjI/P8/u7i6RkZGEh4d75K759evXDA4OMjQ0hNVqJSkpicLCQvR6vYTZS8idsxCHZHZ2lo6ODl69ekVUVBQFBQXExMSgKMqhLOawWq309/czMDDA69ev2d3dJSUlhYyMDBITEyksLCQsLMzt4xB/jcRZiEPgdDrp6uqioaEBu91OaWkpRqORiIgIt4fZ5XKxtbVFZ2cn9fX1dHR0oNPpKC0tpba2lqSkJE6dOoWfn5/8AP27BwAACx1JREFU8OdFJM5CHIL19XW6u7sZGBggPz+fa9euER0dfSh3zFNTUzQ2NnLnzh3m5uYIDw/HZDJx7do1MjMz8ff3d/sYxN8ncRbCzex2O2azmdHRUVQqFQaDgbS0NLeHeWtri/Hxce7du0dTUxNLS0tkZGTw1VdfUVZWRkhIiFvPLz6NxFkIN5uZmaGjo4O1tTWSkpJIT093+97H29vbdHR08OOPP9Ld3U1gYCDV1dVUVFSQnp4uYT4CJM5CuJnZbKa5uRmVSsW1a9fQ6/Vuu2tWFIWxsTGam5t59OgR4+PjhIWFUVJSQmVlJZmZmW45rzh4Emch3Gh1dZXh4WGmpqa4dOkShYWFhIeHu+VcDoeDkZER7ty5w507d1hfX8dgMFBbW8uVK1fcdl7hHhJnIdzEarXy7NkzRkZG8PX1JSUlhZSUFLfsobGxsUFLSwsNDQ0MDg6iVqspLy+nrKyMy5cvyyukjiCJsxBusry8TFNTEzMzM2RkZJCXl0dQUNCBnsPhcLCwsMDjx4/5+eefGR4e5ty5c1RUVPD111+TlJR0oOcTh0fiLISbzMzM0N3djdVqJT8/n0uXLh3o8V0uF6Ojo/z000/cv3+fzc1NsrOzKS8vp6CggLi4uAM9nzhcEmch3GBlZYVnz54xPz9PVFQUeXl5REZGHtjxl5aWePr0KQ8ePODJkye4XC4KCwv5+uuvMRqNBAYGHti5hGdInIU4YA6Hg6dPn9Lb24tOpyMrK4v4+Hg0mk//uimKwuLiIk1NTfz000+MjIwQERHBzZs3uX79OomJiRLmY0LiLMQB297epr29naGhIfR6PcXFxQfyvr39/X2ePn1KY2Mjra2trK6ucunSJcrKyigpKZHHGMeMxFmIA7S3t8fk5CTPnz/HZrORmZlJZmYmWq32k467vr7O4OAgt27d4vHjx+zv71NUVMS3335LXl4eAQEBB3QFwltInIU4QK9evaKrq4vl5WWioqLIyMj45PnFCwsLNDY20tDQwPj4OBEREZhMJsrKykhJSZEwH1MSZyEO0PDwMM3NzajVagoLC7l48eJH749ssVgwm820tLTw4MEDFhYWSEhIeLs3hrxs9XiTOAtxQCwWC0NDQ5jNZpKTkzEajZw/f/6jjrWzs0N3dzd1dXW0tbWhVqspKyujrKyMrKysA3mGLbybxFmIA7Czs4PZbGZ4eBiHw4Fer8dgMHzUzInJyUlaW1tpbGxkfHyc4OBgiouLqaqqIjs7W95UckJInIU4AMvLy7S0tDA3N0dSUhIGg+Fvv1XEbrczMzPDnTt3uH37NnNzc6SlpVFbW8v169cJDw+XMJ8gEmchDsDs7Cytra1sbW1x/fr1v70a0Gaz0d7eTn19PZ2dnajVakpLS6msrCQvL09eH3UCSZyF+ETb29uMjIzw8uVLzp8/z9WrV7lw4cJf+uze3h5zc3N0dXVx9+5dBgYGCAgIoLy8nJqaGrKystw8euGtJM5CfILd3V0GBgbo7+9HrVaTmpr6t6a3vXjxgtu3b3P79m1ev35Neno6X375JUVFRcTGxrp59MKbSZyF+AQWi4XW1laGhoaIj4+noKCAc+fO/dfPra6u0tfXxy+//EJPTw82m40rV65QU1NDUVGRbPEpJM5CfCxFUZibm6O/v5+NjQ1u3LhBVlbWB1cDulwu1tfXefToEXV1dfT19REWFsa3335LdXU1iYmJsqhEABJnIT7a0tIS/f39zM7OEhwcTFZWFjExMR/8zMjICHfv3uX+/fssLy+TnJxMeXk5JpMJvV5/SCMXR4HEWYiPNDIyQmtrKwC5ublcvHjxvW85WVtbY2hoiPv37/Pw4UMsFgv5+fnU1tZiMplkJznxHyTOQnwEu93O4OAgg4ODREZGfnA14MrKCk1NTdTV1TE6OkpoaCiVlZWUlJSQmpoqYRbvJHEWx9+eDfv2BmubNqx2Jy4FFBT2XS5U7ON0wj4BBJ4NITQ8iNNanw9+MRwOBxMTEwwNDbG5uckXX3xBXl7ef0TW4XAwOjrKw4cPefjwIS9fviQmJobKykoqKyuJj49373WLI03iLI4/pxXb60mmh0cZm93gzV4AWp2O4AAVGtUu1i0nNlsgwRdT0V/NIPFzPz40V2JlZYX29nZmZmaIiIggMzOT6OjoP6zeczqd9Pf3U1dXR1NTE06nE6PRyFdffUV2drbsjSH+K4mzOP7Ufmh9NQRujbM8NkPbTgoxqeFUJn7OGY2TnZUV1iYWsKwt8Go7mbNBfgR/4JsxOzvLo0eP2Nraori4mPT09D+EeXFxkebmZn755ReeP3+OTqejvLyc8vJy8vPz3fL2bXH8SJzF8af9jMCz57hweo8A1xaL9s+I/jyd7IJEwv19cL2e5k1QP5MEsq1WoSjvP9Tu7i5msxmz2UxoaCgmk4mEhATgt+fQU1NTPH78mPr6eiYmJoiPj+fmzZtUVlZy4cIFVCrVIV20OOokzuIEUKHS+OLvq0LjA/towDeAAH8fVIA6NJyQtCzY82U3yI/T79lb6PcwDw4Osru7S2JiIrm5ueh0OpxOJz09PdTV1fHkyROcTifFxcV88cUXXL58+S8v5xbidxJncTK4XLhUGnzUPvi6bOxuv2Fp3g98LFh39rAERqELDSDKH3zecwiLxUJLSwvDw8MkJCRgMpkIDw9nfn6eJ0+ecO/ePXp6evD396e0tJTa2lpycnLw9fU91EsVx4PEWZwMKhWgwkdxotg32H4zz8yLbeyWKea3NWz8TyCxiQF87g/vW9+3uLhIT08Pq6urVFVVkZaWxtzcHI2Njfz4449vtwutrq7GaDQSGxsrYRYfTeIsTojf4oxrH5wWbFurvF7chjcTzGyfYvPMFp9FR+J0gfYdt85ra2uMjIwwPT1NUFAQKSkprKys8K9//Yv29nbW19fJycmhuroak8kkW3yKTyZxFieMCnw0aLT+nNIFcEoJI9hPiyZQi079W8LfZWxsjM7OThwOB+fOnePNmzcMDg7y8OFDNBoNFRUV1NTUYDAYZDaGOBASZ3EyKAooLlw+vqhOhXAm9AJxyec4RwShln22PgsiWPvuL8T+/j5DQ0P09PSgUqmwWCzcunULh8NBXFwcRqPx7Wo/jUa+UuJgyN8kcTL4+KBWq/DR+OFz6iynPz9PTFwsZ333OO+wY3H4odL85xfC6XQyOzvLs2fPGBsbQ6fTsbe3h8vlIj09ndraWq5du0ZISIhHLkscXxJncTIoLvZdv/1xuVwoLgUXABpUWh2f+f52c6360/Pm31cDms1mNjc3sdlsxMbGUlJSgslkIi0tjbNnz3rggsRxJ3EWx5/Lzs7qHNPTM/z6YoK5zShCXqYz9iqEzOjT6DSA6t8TOv5kdnaWhoYG+vr6CAgIwGAw8M0331BeXs7FixcP/VLEySFxFsefy459e40VC9hcWoLUNnx211lct5EU8e84/4miKOzt7TE5OcnExAQAV69e5Z///Cfl5eWcOXPmkC9CnDQSZ3H8qfzwC0kg8ur/UhGxRube55yOTiQxNIBT71kNaLVaGR8fZ2JigsjISLKzs6mqqsJoNMpjDHEoVIryoZ0EhDiZVldXaWtrY3x8nKCgIHJzczEYDLI3hjg0cucsxDuo1WrCwsI4ffo0sbGxREdHS5jFoZI7ZyHewW63s7m5iVarlTdhC4+QOAvxDoqi4HK58PHxkTtm4RESZyGE8ELv2x1RCCGEB0mchRDCC0mchRDCC0mchRDCC0mchRDCC0mchRDCC0mchRDCC0mchRDCC0mchRDCC/0ftblfm5sE9mEAAAAASUVORK5CYII=)
In the figure, if
, then EFD is
![](data:image/png;base64,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)
maths-General
maths-
AB is parallel to CD. If
and
then
![](data:image/png;base64,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)
AB is parallel to CD. If
and
then
![](data:image/png;base64,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)
maths-General
maths-
In the figure, if ![Error converting from MathML to accessible text.](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUcAAADlCAYAAADA6jU6AAAgAElEQVR4nOzdZ3eUR57///fVOQepW6mVs4SQBAiBBJhsMDAOY8+ZXe/u7O7ZJ7KPY+fGb9M5s7bHnj9hSEZkEAIlJAQo55zV3ep8Xf8bjHrsMeCAhAL1OvbxOVaru9Th01VXVX1LUhRFQRAEQfge1Xo3QBAEYSMS4SgIgvASIhwFQRBeQoSjIAjCS4hwFARBeAkRjoIgCC8hwlEQBOElRDgKgiC8hAhHQRCElxDhKAiC8BIiHAVBEF5ChKMgCMJLiHAUBEF4CRGOgiAILyHCURAE4SVEOAqCILyECEdBEISXEOEoCILwEiIcBUEQXkKEoyAIwkuIcBQEQXgJEY6CIAgvIcJREAThJUQ4CoIgvIRmvRuwlmKxGEtLS4yPj7OwsIDJZCI9PR2Xy7XeTRMEYYPb0uEYDofp7+/n/PnzNDU1kZCQwKlTpzh48CDJycnr3TxBEDawLR2OkiSh1+tJTEzEYrEwPDzM2bNn6evro7a2loqKCux2+3o3UxCEDUhSFEVZ70asFUVRCIVC+P1+BgYGqKur4/bt28zNzVFZWcmZM2fYs2cPdrsdjWZLf08IgvAzbelw/FvPnj3j/v37PHz4kKGhIYxGI7t27eLo0aNUVVWJgBQEIU797//+7/++3o14W9xuN6WlpWRkZOD3++ns7KS3txefz0c0GsVoNGI0GlGr1evdVEEQ1tk71XNcEQqF6O3tpbm5mTt37tDX14fBYOC9997j9OnTlJaWrncTBUFYZ+9Uz3GFRqPB7XZTVFSExWLB7/czNjbG8PAwExMTLC8vYzAYcDgc691UQRDWyTvZc/yulWB89OgR165d4+nTp6SkpHDq1CmOHDlCbm4uKpVYKy8I75p3PhxXzM7OUl9fz61bt3j27BkqlYq8vDzee+89amtrxbpIQXjHvJPD6pcxmUzk5eVRUlKCVqtlcHCQp0+fMjU1hSzLWK1W9Ho9Op1uvZsqCMJbIHqOLzE8PMzjx4+pr6+no6MDn89HWVkZH3zwAfv27cNisax3EwVBWGOi5/gSdrudwsJCPB4P0WiU4eFhBgYGmJ2dZWlpCa1Wi8ViQavVrndTBUFYI6Ln+BrRaJTJyUmePXtGXV0djY2NRKNRamtrOXXqFLt37xbDbEHYosSWkNfQaDR4PB48Hg82mw2Hw0FjYyOtra1MTEzQ0dHBvn37KC0tRZKk9W6uIAirSITjT7Rz507y8vLYsWMHly5doqGhgcHBQebn51leXo6vmRTLfgRhaxDD6p/J5/PR2tpKfX09TU1NzM3NkZKSwqFDhzhy5AjZ2dnr3URBEFaBmJD5mXQ6HZmZmWzbtg2TycTk5CR9fX1MTEywuLiISqVCr9djNpvXu6mCILwB0XN8A7Ozs/T29lJfX8/Dhw8ZHBwkJyeH06dPc/ToUdxu93o3URCEX0j0HN+AyWTC4/GQkZGBWq1mcXGR0dFRhoeHmZycJBaLYbfbMRgM691UQRB+JtFzXAWKorC0tERfXx91dXVcv36dhYUFdu7cycmTJ6mtrcVut4tSaIKwiYhwXGWdnZ3U19dz//59xsfH0Wq17Ny5kyNHjlBdXS0K6grCJiGG1avM5XJRVlZGamoqgUAgXlB3aWkJRVEwGAyioK4gbAKi57hGgsEgfX19NDc3c//+fZ4/f47JZOLQoUOcOHGC7du3r3cTBUF4DdFzXCMrBXWLi4uxWq3xupEr/4qCuoKwsYme41uwvLzM5OQkDx484MaNGzx58gS3283Jkyc5ceIEGRkZooiFIGwwIhzform5uXhB3efPnyPLMkVFRezbt4/a2lpSUlLWu4mCIPyFGFa/RUajkby8PIqLizEajfT19dHR0cH09DSyLGM2mzEYDKLSjyBsAKLnuE5GR0dpa2vj3r17PHv2DK/XS3FxMSdPnuTQoUOYTKb1bqIgvNNEz3Gd2Gw2CgoKSE9PR5ZlhoeHGRoaYnJyEp/Ph1qtxmq1imuRwsYTW2JhdICh/jHG5kMEJQ16gw7tFqvat67hKMsyY2NjTE9PI0kSer3+nauL6HA4yMzMJDMzE4D29naam5tZXFzEarWSnJwsFo4Lr7RSkHl6ehpFUdDpdGtcNm+R5alntN6u5/btDjpG/IRNVhJSHVjUElvp07tun7ru7m5aWlpoa2sjHA6Tl5fH3r17KS0tfad6S2q1mrS0NFJSUnC5XFgsFh4+fMjjx4+ZmZnh6dOn7N27V6yLFF5qbGyMK1eu0NXVhdVqpaSkhIqKCgoKCtagoyETGW5ntKOR9gmZ/qAZt8+LElhgSVZwAlupFtVbDcdoNIrf76evr4+rV69y9uxZWltb0Wg07N27F6vVSkFBwTsVjitUKhWVlZXxgrqXL1/m0aNHDAwMMDExQSgUoqCgAKvVKgrqCnFjY2NcvHiRixcvIkkSu3fvjp+5XlxcjMlkWqXPkwzhacZamml/PMBcxnEy8rMpCw6TbJNQSwrRVXiUjeSthWMsFqOlpSVeJLalpYX29vbv/Vyr1b5zw+rvUqvVOByO+AmHaWlptLa2cuvWLbq6unjvvfc4duwYOTk5691UYYNQFAW/3084HAbg3r17LC4u0trayu7duzlw4AA7d+5chYCcI7bYQVvnFE1DZtyVCRSVJZIwtIxJa8ahktC/+Z+zoaz5NUefz8fw8DD379/nwoULfP3111y7do3JyUl0Oh0ej4f9+/dz+vRp9u7dS1pa2lo2Z1PQ6XRkZGRQVlaGzWZjenqa3t5epqamWF5eRpIkDAaDmNEWUBSFUChEMBhEkiSCwSBjY2N0dHQwNDREKBQiFoshSRI6nQ69/pdFmOJ7xvyzm1xsitAtl1BV6aIsTWIpYERjdOJxmTGotlbHZk3D0ev18uDBA7788kv+7//+j/r6evr7++MvVllZGZ988gmff/457733Hh6PR0w+fIderyclJYXc3FzsdjtjY2M0NTXR3d2NJEmkpaWJgHzHmUwmMjMzKS4uJiEhAZ/Px+joKADz8/MMDw/z/PlzRkZG0Gq1pKSk/KKADPU+oPfede5PJ7KcvofqTBVZpggL6hR0dgfJNg1bLBtXf1gdDAbp6emhq6uL/v5+WlpauHv3LoODgy8eUKMhLy+PwsJCqqqqOHz4MBUVFVgsFkKhEIFAYLWbtGmpVCq0Wi1lZWUYDAZkWeb27dsMDw9z+fJlpqenKS0tJSMjA6fTiV6vR5bll96XJEkoikI4HGZmZoaZmRlkWcZqtWKz2bBarej1elQqFWLp6+ahVqtJSUnBarViMpkwGAy43W6ePHnC4OAgIyMjjIyM0Nvby8TEBE+fPsXj8ZCfn09FRcVPGG4rgJ/ZwXGeP54j4tSTXOoC9TLBxSiOJDM2u27LBSOsYjjKskwoFKKtrY1z585x+fJlhoeHCQQC+P3++O0sFgvZ2dlUVlaSnZ3N4uIi9+/fB15cd3zVh/tdJEkSKpUKtVpNNBrF6XSyY8cOOjo6aGlp4cGDBxQWFrJnzx5yc3Ox2WxEoy8ui3834CRJQpIkZFnG5/PR1dVFV1cX0WiU1NRUPB4PKSkp2O12NBoNsiyLgNwkJEmKj7ZCoRAej4ddu3axtLTE+Ph4/FrkyMgI58+fp66uDofDwfHjx/n8889/wtnrUWCcydkleidsaJNNZGWoUCQ7AZVCsk2N1cSWWsKzYtXCcXp6mtbWVi5fvszly5d5/vz5D26jUqmIxWJMTEzQ2toaH2IHAgFisdhqNWXL+e71onA4zMjICP39/fEh1MDAAElJSfEhtqIo8XBTFCU+yaUoCsFgkImJCSYmJuLHODgcDhwOB2azOR6OK7cXNge1Wo1Op0On0+H3++Nrh1dGDAB+vz/+s1AoxOTkJP/8z//MyZMnX9ODDEJ0nLlgiLFQMsaYmUxDDKc9Ab1Ki9Wo2XKLv1esWjiGQiG6u7u5efPmS4NxxUqdw56eHqLRqAjFn+m7b3Z48YZ/8uTJD2630huIxWKvfY6XlpYYHh7+3v9Tq9Wi97hJqdXqeE/yda/70NAQQ0NDFBQUcPz48deEYwgCMwRkGa8lBZvOTapGT3qiGatGh3oLrypbtXB0Op1kZmZisVheeZuVXoxWq433br7byxF+3MowauXNHIvFCIVCP7idoihoNJr4msiV3uB3h+or/z8ajX7vNYjFYqjV6u/1PoWNT5Ik1Gp1/LX7sS84s9mMyWR6/fK5WAQWFwlHokQcyRiT00lyuHDrdGiALZyNqxeOVquVHTt28Jvf/Aan08nc3BwDAwPxmTP4azg6HA7y8vLIycnB4XDEJwpWrpcJP83KmzoajRIOh/H5fExNTTE4OMjS0hIOh4OioiLy8vIwmUyEQqEfBOGKYDDI1NQUfX19hMNhiouLycrKAkQ4bnQrQ2qNRsPi4iJ9fX10dXUxPj7+g9umpaWRlZVFcnIyBQUF1NbWvn6FSCRAaGyKZW8QyZ2ENT2dBLv5JWsaFYgt458eYWpyipmYE01CHh63kaRNum1mVWerU1NT+fu//3uOHj1KV1cXV65c4erVqwwMDMQ/YJFIBEVRyM7O5vTp05SWlmIymeKzpOKD+POtPG/BYJD29nbOnz/Pw4cPsVqtVFZWcvLkSXJyclCr1fFA/duJr0gkQmdnJ//7v//L8PAwZ86c4cyZM694ROnFP9LKXlrlxT+Kwvdevb/9+Sr/3QLfu54cDodpb2/nypUrDA0Nfa+zodVqyc7O5sCBA5w4cYLy8vL4SoVX7rhSFGT/AnPTc/hCKgwJKThdiVj+ZgSuABIKRBZZ7L1P642bNASKUe/8Z05Wi3B8cWd/ORrA7XaTnZ2Ny+WioKCAxsZG2tra4gVep6en6e7u5tGjR0QiEXbs2EFhYeFqNuWdlZaWht1up6CggP7+fiYnJ7l37x4qlYra2trXLt1QqVQ4nU5mZ2fJysqKF8MQNr6+vj4eP35MQ0MDXV1dTE1NxX9WUFBAVVUVu3fvZseOHezcuRObzfba+1PkGOGFGQLTE8ypdMQcdpzqBFwWw4vQkJeI+MIsqG1odTocWgnUBjTEUM/3MTtrwJsRYjq4tn/3WlqzReA6nY7MzEzKy8vJyspCr9cTi8VYXl4mFAoxMDBAU1NTvMCCVqvF5XL94hX8wgt6vZ6cnBzy8/PRaDR0dnbG92iHQiFMJhMmk+kHQ6mxsTHu3LnD48ePsVgsVFVVkZub+4pHUSAWIrAcIBAIEorGiChqJLUK9XcvX8kRlGiUiKQBaWtfn1ovy8vLNDQ08D//8z/8/ve/5/z58/T39wPgdrspLS3lgw8+4B/+4R84deoUBQUFGAyGH79jOUZ4YZrl5QWCVjPLUiKSX0uiQcFu8BOYmWR6IYhPa0Gj02HR/CUcg7PI488YiyXiS62hKNtBScIaPwlrZE13yKwsQUlOTsbj8VBUVITb7SYQCDA6Oko0GmVmZoaxsTEWFhYwm81kZma+k4UnVpMkSdhsNhISEnC73Wi1WgYHB2lubqa/vx9JkkhPT48/z4uLi1y8eJFvvvmGQCDAwYMH2bNnD06n8yX3HgJvHyPPWqh/0MyjxhY6hycZ9umJaBw4zRIaCYh4me9ooKe7j56ghbDegl3H98NTeCOhUIgnT57whz/8gT/+8Y/09vbGL0tVVlby61//ms8++4wjR46wfft2zGbzT65dICGBSoXaZMOYkIohGkYZf8782FO6xibpnIyyrLGTkOzEZdKiU/3lt7yj+Aaa6V52MOfaS2Hm5g3Ht7JXT6/XU1JSQklJCYWFhXg8HrKzs+P7P6enp+nv748fFyCsDo/HE/9SunDhAjdv3qS1tRW/38/ExARZWVmo1WqGh4e5c+cOi4uL7N69m4MHD5Kenv7S+5TDPgKDT+l73EzTk1mGZ4IYUvJJJRObRyImAYqP4GgTrXXneDhpIlKTwZ6EZLKtb/fvfxd4vV66uroYGRnBarWSmppKcXExhw8f5tixY5SVlf2yO1ap0FqdaHFiBgypYTTZo3SNLDMajREzWtBYnDiNOizfOYJdkWVkBZQX8bqpF4e/9Y3MhYWFOJ1OqqurefjwIVeuXGFmZoa9e/dSXFwseo1rICcnh88++4zi4mKuX79OY2Mjjx49QqVSxYdYKSkpnDx5kqNHj1JUVPSKXRMKy/MT9HT00ds/S1hrxuJy4khMIsVlJcEuvVgQ7BtkquMuD+7Wc8ebizs/QNmLq/bCKtJqtaSlpVFUVMT4+DgZGRkcOnSIffv2kZ2djdvtXrXHMrqyydptJ6E0yLKsQ9GaMVvMOPRb92LJWw/Hlb2gKSkp8Z7N0tISRUVFIhzXiFqtJj09nbS0NBwOB5IkcenSJR4/fgy8OLJh586dnDlzhtLS0lfcSxRCg8z1N1PfMkLXYgLJu3axIyeFzEQ79qQUXI4wOhaYGJug7ckcU1OLYAgQU2QispitXm0qlYr09HQ++ugjysrKSExMZMeOHWtT0k5rxOA0YnjZlZYtal1L4KSnp+N2u5FlGY1Gg0ajeafrOa41lUrFrl27MJlMpKSkcO3aNfr6+uJLOpaWlvD7/ZjNL1t7EQV/P0tjz+ifWGQgYMMaMWBypZOak4TbokPPDOGpbvrHQvRHskhwp1BiVRMyKsgyKKL3uOrMZjP79+9n79698fWO62lly+KLf1Vs5o/zutcHE7PTb5dWq2Xbtm1YrVbKysro7u6ms7OTnp4efv/737N3716OHz9Odnb2939RUZCDCoqiwmyOEBtpov1KP4PDh+g9dpwTe1PJDM8y3jHAfMCFqagA/UwyKn+UWUkRvcY1sjLpud6hGCepUKsk1GoVKrVqU1frEacPvoNW1jOulI7TarXxun9DQ0MsLy8jyzIGg+GvvUhJjRKKEVW0aI169MoswakenjwdZ3A2gt4uoYRDTI6BLSefrDw7uqEWpmfCLOcfJCs/hW2WrbOcJxQKxdeRarXan7Y8ZqtTIoTG2hlsuUXDqIpRUznZ6YkUu9UvVjBsMiIc33Er9f+ysrJISEhgbGyMxsZGenp6UKlUJCUl/WW/vISkNaO3J+NOzyevuJDiXDv6mSG8vU+YDSwyqU4kaisirySTTO0i/tbb9E6F8GXVkp6TRqEF1D/aoo1PlmXa29v5wx/+QGtrK2lpaaSmpq53s9afvMRSTxNPGutpGFSYNhaSmZlGcZoB0yZ84UU4ChiNRjweT3xpz+LiIuPj44yMjDA+Pk4sFsPhcGAwW9HozZisTpxJWaTnp+IJ9BLqvUtbdx8to0Fm/RHCC4OMNdfTcv8eTX1zjITMqIx27A4nFqMawybuPi4tLXH79m2+/vprmpqacDqd7Nq1i5SUlPVu2vpTwoT9XnwxPZIzD09+EaW5KWS69BhFOAqbmcViIScnh6KiIrRaLT09PTQ3NzM5OYnJbMbhTMBkNv11TkVlwRHqJzLbRduYj54JP5HZYab7O3n+pI2nXX30ji4w41PAlkpCRh5pLi2OTfhBgRfHDjQ0NPDll1/S1NREUVERn3zySbxS+ztP0qK1p+LO38G2HTupKskkL8mIVbc5rz2u+4SMsLHYbDYqKysxm804nU4aGhro6+vj//2//6S1tY2jR49QVVWFVqMGtEg6B46UUrJqXGgNGZQ4JSySitD8MAPSEgZDhOXi7eQWZJPr1GDZpL3G0dFRvv32W65cucL4+DjV1dWcPn2aPXv2YLfb17t5G4OkRq23YNZbtsT51SIchZcqKCggMzOTiooKzp49y51b17ly4RtmxoeZGB+jbPt2bBYDkWk9C879lFXUcqi4hD1uBTsSgfFW7gd7ud4dZPrQCXYd2MWedAnTJgvHSCTC4OAgN27c4MqVK0xMTFBTU8Pnn3/O9u3bxYFwW5h4ZYVX0uv1bNu2DZ1OR26mg8vf/JFbf/4T9Q8esm1HJeXbt5PozMKSVE1JYRF5SRK2vwy6jXYrFr0GvUaNxmBCb5DYjJspOjs7uXDhAjdu3ADgzJkznDx5ktLSUhGMW5x4dYXX0mq1lJaWkpflwKqK8XXs/6Oxa5SrV67R1v6Ugl3HOfpBFvvtar5bBCsc0WAprKbEHiPFYyZVDTFl8xSe8Pl8dHR0cPHiRRoaGlCpVBw9epRf//rXr6lWJGwlkiKqywo/0dL8ED0dz7jT8IRL127R09eNOzWDDz/6iF+fOUFRfi4KElNTU/iW5jFICkarg5jJidFowKzZHBtkZFnmzp07fPPNNzQ3N5OWlsapU6c4ceIESUlJry4OK2wpIhyFn0lhdHiE+oZGmlua6OvtQqtWkZObT0ZmFhqNhpGRERRU7D90mAP7atBuoqnKubk5bt++zYULF+jr6yMtLY3Tp09z+PBhsVznHSPCUfhFotEok5OT3Lxxg2t11+js7GRpyYuiKAQCAXJycvnnf/kXPvroQ+w/UnV6I1AUhbm5OW7evMk333zDwMAAFRUV/OpXv+LQoUMYjcb1bqLwlolrjsIvotFo8Hg8HDl6FKPJxOLi/9LS0kowGCQxMZHMzAxyc7I3RTACTExM8Kc//YnLly8TCATiZ63s2LFDBOM7SoSj8EZSU1PZtm0bSUlJpKWlYbVa8Xg82O12+vv7cTgc5OTkvKLSz/qLRqN0dXVRV1fHpUuXCAaDHDx4kI8//pjy8nJRJeodJobVwhvxer3U1dXxn//5n0iSxIkTJwiHw9y7d4+FhQUqKys5ffo01dXVG24XSTQapbOzk6+++orr169jt9v54IMPOHToEPn5+Run0o2wLkTPUfjFZFmmu7ub1tZWFEWJ7xrx+XzEYjEePHjA48ePmZ6e5tmzZ9TW1lJaWopavf77B/1+Pw8fPuTSpUs0NjaSkJDAyZMnOXPmzCuPiBDeLSIchV8sEonQ0dFBb28v2dnZ7Ny5E5fLRVpaGsnJyVRUVHDx4kXq6+sZHBxkdnYWv9/Ptm3bMJvN67YkZnFxkcbGRs6ePcujR4/Iysrit7/9LQcOHCAxMXFd2rS5xIgGA4TCMWKSHq1ei16n3jLl6FaIcBR+sVAoxNOnT+nr66O8vJzKysr45EVCQgI1NTWYTCY8Hg+NjY3cuXOHjo4ODhw4wLFjx8jPz3/rbZ6cnOT69ev8+c9/ZmRkhIqKCk6dOsWBAwdecdqi8H0Ror5Buh+287R3CZ8tk8yyIrYXpZKokTbFOtafSoSj8ItEo1GmpqaYmJggFouRlpb2g3WARqORvXv3vthhk5fHxYsXefr0KZcuXWJxcZEDBw5QUFCwqgdBvUosFmNsbIxr165x9epVRkZGqKys5Le//S379u0TEy8/keLtZ6a7kdYnwzR3h9E6w2hcTjwFyVhRs5Xq+otwFH6RpaUlenp6iEQiZGRkvLbYq81mY//+/aSkpPDw4UPu37/P+fPnefz4MadPn+bo0aNrvsC6r6+PCxcu8O233xKJRDhy5AgffvghxcXFIhh/qpifhSeP6G57wqBmG7rSZIpVC6QbI0RQCIEIR0GYm5tjYGAAnU5HZmYmLpfrtbdPSEigurqazMxMnE4n165dY2hoiAsXLjA8PExtbS1lZWUkJKzuCfCRSIS2trb4tU9Zljl06BC/+tWvKC8vX9XH2tqWUZb76GzrofFJEOVgFqUF+eRN9eIw6TFKW+cIjBUbIhwVRSESiRCNRoEXxQ7EEa0b28LCAlNTU+j1etLT0/9ylMKPS0lJiQdTXV0dN2/e5Pz58/T19XHq1Cn279+P0+lclRntSCTC48eP+fLLL3nw4AEul4sTJ05w6tSpLbcVUJZlotEokUgElUqFRqNZ3c9QdJTlkUe0jIR5Gsyh1q6jJDlEKOBA1thIVKkwrd6jbQgbIhyfPHnCw4cP6enpwe12c/DgQXbt2rXezRJew+v1Mjs7i1qtJjk5GZPpp380bDYb27dvx2AwkJCQQH19PcPDw/zXf/0XbW1tHD58mOrq6jc6mTIQCFBXV8eFCxfo6uoiMzOTY8eOcfjwYTIyMn7x/W5Us7OzNDY20traiizLFBcXU1NTQ1pa2qrcf3RygIm2Bvq9Lhbdxbh1kBpboM/sJmq2Y5Qk0XNcLYFAgLm5OXp7e7l27Rrnz5+ntbWVzMxMTCYTO3bsENVPNjC/38/c3BxOp5OEhISfFY4rCgoKyM7OZvv27Vy6dInr169z7do1lpaWWFpaoqKiArfb/bNDcmZmhocPH/L111/T2dlJSUkJv/71r9m3bx8Oh+Nnt3MzmJqa4vz583zxxRdEo1FqamqYnZ2lurqa9PT0N+yNR1nqH6a7aYhlVSrOYg9aVRBlIYLJasVot2zq86lfZV3CMRwO8+jRI+rq6mhubo4vBwEYHh5mbm6OSCQizrTewHw+H7OzsyQmJpKYmPiL9x9rtVrKysowmUzk5ORw79492tvbef78ObW1tZw8eZKdO3f+5PubmZnhwoULnD17lvn5efbv38/x48epqqrassEIEAwG458dgLt37zI1NcWNGzfiS6cKCwt/wT3HgCkmx2fp6pVQFRrIyDcS1Wrwh2MkpeqwWdmUZ8T8mLcajvPz8wwODvL06VNu3rzJtWvX6O/vB158SHJycigtLaW0tFTMIG5wXq+Xubk5VCoVbrf7ja5vabVaioqKyM/PJz09ncuXL9PU1MT9+/eZm5tjaGiIiooKcnJyXnkfsizT09PD9evXuXr1KgsLC9TU1PCb3/yG8vLyLV+12+l0Ultbi9frpbu7m7GxMVpaWmhpaWFgYICpqSn27NlDXl4eWVlZP6PjEQZ5lGlfgEFvEhrJTJYzhlHnQJHUJFg0GLfoU/vWTh+cnp7mzp07fPHFF3z11Vc8ePCAyclJFEXBYrFQVVXFp59+yj/+4z+yZ8+eXzRME96eu3fv8uDBA4qLizl16tSqhI9KpSIlJYXi4mKSk5NZWFigsbGRzs5O4EUAOJ3OH3xxKopCT08Ply5d4vz580SjUT788EM++4UtT9MAACAASURBVOwzSkpKtnwwAlitVvLz88nOzkaj0cSvCcOL3nRXVxednZ14vV7MZjNut/snPi9eCHbS8XiEpi4TlpQMduzIID3FhdNuwapXo9qiHZk1f9cMDQ3R3NxMc3Mzjx8/pqmpidHRUQBcLhdVVVXs2bOHHTt2sHv37lW7gCysLVmW0Wq12O32Vb38odfryczMJDMzE4/HQ1paGs+ePaOhoYGpqSl27dpFRUVFfFIlGAzS2tpKXV0dT548ISUlJb5U58eWF20lKyXkPB4POTk5VFdX09DQQFNTE+3t7QwPDzM6OsrU1BT9/f1UVVXFdzXZXldWTomAb4FwLErQ5kLvSCXF4iDVYkAvqbbcJMx3rUk4hsNhFhcXGRkZ4d69e5w/f56GhoZ4QQJ40UtITEykpKSEPXv2kJGRQSAQoK+vD1mWkWV5LZom/EKSJCFJEiqVivn5eYaGhojFYszOztLV1YXJZGJ5eXnVHkOSJBwOB7W1tUQiEa5evcqdO3dobm7mxIkTHDx4EJPJxLNnz7h8+TI3btzAYDDw4YcfUlpaysLCAl6vN/5e2urFp1aeN5VKhV6vp6KiAngxiz08PMzExASyLPPkyROeP3/O3bt3OXjwYPwLx+VyvXy/ezSEPD1HcDmC4nJhTc/E5UzE9qreohJDCftZXvaz5I8QjoCkN2K02rCY9Rg3UZquSTgODQ3xf//3fzQ2NjI8PExXVxc+n+97t5EkKX5I+uTkJCaTiWg0SigUEsG4gUmSRDAYpKenh/Hxcerq6hgdHUWj0cTXqa6GlbWusViMwcFBurq6mJmZYW5ujtHRUerq6tBqtczMzNDT08PY2BgWi4Xr16/T29sbXzv7rr2XVp43lUrF7OwsPT09LC8vI0lS/AsiGo3S29tLIBCgp6eHwsJCPvroIw4dOvTD9apBH4ujk3i9ETSuVGzJydiMrxlGh+ZZ7n9AS8tjbrdNMjAWRJ1SRHbNUfbt3c7uFDX6TTIKX5NwHBsb48svv6S9vf2Vt1EUhenpaaamprh///5aNEN4C2ZnZ3n8+PFbe7yFhQWamppoamr6wc/m5+e5efPmW2vLZvHdYPyusbExxsbGuH37NqmpqezZs/ev4ajIRAN+wnNTzAQiBPV2bPokXE47L7IxhByKEpAMqDRqjCoFCBPyzzI+PMroyAzzCzMszI6wNDlN35KJmMpGytFMsiwaNsMWjzUJR0mSfnT2UpIk1Go1kUhkLZogbDErw8aVyzIvo1Kp3rme4o9Zed5ed2lBp9OhVqu//3NFJrwwjXdxiUBiGqZ0Oyk+FdZYCKKAf5IFb4xFUwomsxGjXgG8+ENhZsjDVb6d3x6VUfzNPL3Txvm7z+mqT6VvVxIui4XNsKhqTcIxPT2d3/3udxQXF9PV1UV7ezuhUOh7t5EkieTkZEpLS8nPz8doNBKJRMSwerVJKiRFRpIDLC8uMjcbIKw1Y05NwGHToPLOsTA8ztT0It4YRCQVKtSoNXpMjkQcyW6cNhNmKYZagpis4Pf7ef78ORMTE2RmZlJWVoZeryccDq968zUaDTqdjmAwSFtbG0+ePAGgqKiIzMxMgsEgz58/Z2BgAJPJRHl5OaWlpVgsFmRZJhgMbvnrjd+l0WjQ6/Wo1WpmZmZ49uwZPT09zM/P/+C2ycnJlJWVUV5eTm1tLSbTd9eqSqi0erT2dJyJbgqVBXRPnrPwtJ+6RSugRmdNJCFXwRa/jqhBbUzAmeXGk5BChhvAgTsWoPV+H3NTUyyHImyWT/eahGNGRgb/9m//xpEjR6irq+P8+fM0NTURCoUIBoPAi+seFouFbdu2cfToUTIyMjCbzWi1WmRZfm0PQfipJCSVGkkOoPiHGGh/TkvzLD53HvlHK9mWriD1PKb97hMed06xiERUK6FEVUQjZly5JWx7bzeluckkq6LogIgsMzk5yRdffMGDBw84cuQI//qv/4rFYsHv969ey/8yspAkieXlZbq7u4lGo/h8PtxuN2fOnKG6upqlpSWuXLnCrVu3kGWZsrIyjhw5Qn5+PomJifFe01aflFl5vuDFDL7P56OtrY1AIMDQ0FD8b1er1RgMBlJTU6mtreXMmTPs27ePhISE7686UKnRJySjc7qxqSIYg0/RjvbROzbH40U3MWsOeUUWMo1aHBp4UXbChtVuxWSVUMU348SQDTZs6R50LjeJes2mqdyzJuGo0WiwWCxs374ds9lMXl4ejx8/prm5mYcPH8aX8kxNTcWvHe3atYva2loyMzPXoknvOD/MTTLZ5md+zE/I7sCelU9B0jTB0RgdBiu4LKRaVVgsUXwLAcYGJDQqJ6m5+ZTm2r83DEpMTCQlJQWDwUBSUtKaF61taGjg3r17TE5OUltbS01NDQcOHIj3HN1uN6WlpbS1tTE+Ps7169cJBoO8//77ry2lthXJskxTUxMPHjygoaGB58+fx3uNKpWK0tJSamtr2bVrF0VFRa+thCSpNUiACh2JKdlIO2QsGYvMxCzIxmSSUxJJNKhRxydYVKhU8NcJ7yhMThL2htHmFGDOKCXVrH+3w/G7cnNzyc3NZd++fdy5cydeFbq/v5+pqSlu375NQ0MDO3fupLe3l4MHD7Jt27Z3ao3a2lsmEFxgcWGSkZ5xgsYpZpf8LBh9RJeiSPZUkixOPE41LvMEE4OjTAzF8PklNNEof7sjV1EUYrEYoVDoB5dLVtPK5Mu5c+dobm4mKysrXrln5QO9soGgsLCQjIwMzp49y9OnT5mbm2N6epoDBw6Ql5e35d9PoVCI8fFxmpqa+Pbbb7l27Rq9vb0AGAwGcnNzKSwsjG/J3LFjx89aHC+Z3SQWukn8yTsQYxCaY3FglqkpDc7CAtKKckkyazdGtZuf4K21MyEhgYMHD1JYWMizZ8/iFZl7e3sJhUI0NTUxMTFBQ0MD//Iv/8JHH30kTn9bNWZ0CSkkZbhJNM8wFwsgx2R8ujScmdXsyTCz02DDqgNj5BEjmkV6xmwEbTm49MYflKLSarVIkkQoFFqT64zwYub5xo0bfPXVV4yMjLBr1y5OnTpFVVXVS3s6NpuNmpoakpOTqa+v59GjR5w/f56WlhZOnDjByZMnSUpKWpO2bgQjIyP84Q9/4NKlS/T29jI5ORn/2c6dOzl9+jQ1NTVkZ2fj8Xjewq6hBSJLQzyf1DKu5FFckE5xnhbrJvpIv9UQdzgcOBwO8vLySEpKIj09nZaWlvjC1P7+fvr7+6mtrX2bzXoHGFAbnDjcTpw2AwFVDAkJWefEkm4hyfCdlQXjGnyxKHZPKobUXBxm/Q96jjqdDo1GQzgcZnl5mXA4vKpfZH19fdTV1XH9+nXGxsbYuXMnn332GTU1Na+tLONwONi5cycejweXy8W3337LwMAA586dY3R0lD179lBeXr4le5ELCws0NDTEl8WtTE6VlJRQU1PDoUOHKCgoeEutiRL2LTI1EWTZlo8nL5OK0gSsEhBTiCkS6k3QfVyXJup0Onbv3k1RURHd3d1cvXqVc+fO0dbWRlZWFi6XSxS7XVUKIKPICrICigKSpEIngfG7wUgU38A8Y31+NA4ztnwnBvMPtzRoNBpMJhMajSZ+8f9NK3grioIsy/T398dL2Pn9fo4ePcqnn35KXl7eTy65lZyczAcffEBxcTG3b9+Ov78GBwfx+Xzs27cPu90en/DZCkwmE1lZWbjdbiKRCDU1NXz66afU1NTg8XiwWq1voRUKiuxF9g7T3TZEz3AMdXoieakaCM6zHINA1IJOr8UqwvHV9Ho9brcbl8uFzWYjLy+PoaEhHA4H1dXVW+ZNuzEogIIsKyiKwsqcrRq+c1pcFCU6zdD4Mn0TeswZZvIyVJhfcvVckiSsVisOh4NoNMrs7Cw2m+2Nhmper5f29nZu375Nc3Mzer2egwcPcvLkSbZt2/az789ms1FRUYHFYsFut/PgwQNmZmb405/+RFdXF7t27aK8vJyEhIQt8V5LSkrio48+Ii8vD1mWKSgooKqq6i3WKlAAH76RdrruXedG/SBPfVYsGc/I7LBgjKgweQpIr9xNcYaWtxHVb2rd81uSJMrKyigrKyMajaIoiihy+5Z8f2GLjKL4mA4oTAXMuHQ60qzwqiqNRqMxXrBgaWmJaDT6RuHo9/u5e/cu33zzDbFYjM8++4x/+qd/euPZ5ry8PHJycigpKeHLL7/k7Nmz1NfXMzs7S1pa2pY5pzohIYEjR45w+PDh7y3rebu8+EbaafnzBa7X99GhTgS9DlNAATmB7OMfczS7nLS8zRCNGyAcv+tdKC21sSnEZIWo/OL84e/3LL9PpVLFL32sfKm9ieXlZcbHx5mZmcHtdpOUlLRq1wZVKhVpaWkkJSWhKArj4+OMjIwwPz+Poihboue4foH4XTJyJEjQ58XvXcKn0yGH1ISXZGRZjdMXJBhT3u1F4MJm5EcKzRJWFEK6BLQaM0ZeHY46nQ6DwQC8WHQciUR+UTVwRVF4/vw5N27cYGxsjNLSUnbu3ElhYeGq7pQyGAxUVFTwySef8PTpU/x+P5cvX2ZmZoby8nKxvnZVmDCllFJ8+CNOpE9SqrKgqDXowgrIVpIqt1PuMmyKrYMgwvEd8qIcmLTy379NvfAM0aluFqMyPmc+FqsbN69+g1gsFhITE5FlmdnZWQKBwOvrAr5Cd3c3f/zjH7l58yZWq5WTJ09y7Ngx0tPTV3UG3G63s3fvXnJzc2lububKlSvxGpDvv/8+77//PtnZ2av2eO8eCbBhzdzD7t+WUBqMEEIFkoSkAIoardmCyW7CvN5N/YlEOL4TVIAKlUaNSq1CrVKh1qi/X6h0YQF/3yCBWBJSVjYml4PXRZPVasXpdDI5OcnU1NTPruUYjUZ58OAB58+fp7GxEbvdzuHDhzlx4sQvPOvk9TQaDTabDZvNhtPpRKfTcevWLfr6+vjzn/9MV1cX7733HrW1tVtyqc/boUFjtGM32rGvd1NWgQjHd0IEOeJjeXEB79ICCzovi4sBQjHniwuLyCxPeRnu9BFRe0jKd2Jzvf6t4XQ6SU1NZXh4mMHBQZaWln5ya5aWlmhra+Prr7+moaGBjIwMPv30Uw4cOPBWzpNOTEzk9OnTlJWVcfPmTS5dusSdO3eYnJzE7/fHK9KLozrebSIc3wWyn9DsKBM93YyMDdAXcJPSM8l8dgo4VICPmQUvnaNqIhkmctP1uH9k7JOcnExeXh63b9/m2bNnzMzM/KSmLC4ucuPGDb755hsGBwcpLy/n/fffZ//+/W91B4tWqyU/Px+dTkdiYiINDQ20tbXx3//93zQ1NXHixAn279//i09VFDY/EY7vCEU2YrBnkl8tYTJlkapXY5DhxYKeCBGjBTm5iOS0DAodKhJ+ZOLTarWSm5uLRqNhdHQ0fljaq2Z+I5EI/f391NfXU1dXR29vL9u3b+fzzz+nuro6Prnztq2cV1NSUsK5c+e4desWLS0t+P1+xsfHKSsrIzs7+40XuQubz1s7fVBYTxpUugTsqYUUVlWzu6aSioI0PHY9erUCxFBURowJHtKzPKS7zBgl6ZUz1SvUajUdHR2Mj4+TkpJCZmYmdvvLrzYNDAxw7do1/vSnPzEzM8Phw4f5u7/7OyoqKjbE8NXhcJCVlUVWVlb8rJXm5mYWFxdxu90kJCSIXVvvGEnZykXuhJ/gLz3HKESiGrRqFT81A6LRKLdu3eLixYtMTk5SVVXFb37zGzweDwCDg4O0tLQwOzuLSqUiHA4zMDCAw+Hg5MmT8UOgNpJYLEZTU1N8aVFubi7FxcWEQiEmJiYwGAyUlZVRUVGxAdYVCmtJhKPAi4D8ZQuhQ6EQ169f5z/+4z8Ih8P87ne/4/3332dpaYlr165x8eJF/H4/Bw4c4KOPPiI1NRWNRoPZbN6wi/4jkQjLy8tEIhFUKhX9/f3xgrqKorB3715Onz5NSUlJfI+5sPWIYbXALw1G+OsSGa/Xy+joKN3d3bS3t9PY2MiDBw8IBoNUVVVx8OBBysvLsdlsGAyGDb1FdKVatslkwmg0xs9YMRgMBAIBnj17Rnt7O3Nzc1gsljfeVy5sTCIchTdmsVjweDzMz89z8eJFzp8/T39/P2azmZMnT/L555//7OKqG4nJZCI3N5eysjKcTidTU1N0dXUxMTGB2WwmPT39LVW9Ed6mzfluFTac1NRU0tLS4j1CWZaprq7mxIkTW2bnicPhYO/evSQkJPDo0SOampoYGBhgbm7uLVa/Ed4WEY7CG5uZmeHRo0e0tLSQkZFBeno6u3bt4sMPP6S0tHRLFHZYsVJSLycnh9TUVAKBwIaYbRdWn5iQEd7I3Nwc169f56uvvmJycpI9e/Zw9OhRysvLcTqd3z/Rbovx+XxEo1FMJpM40mMLEuEo/GJDQ0P8+c9/5urVq3i9Xnbu3MmvfvUr9uzZI8JC2PTEsFr4WWRZJhgMMjw8zN27d7l8+TJLS0scP36cjz/+mMLCwk078SII3yV6jsLPsry8TEdHBxcvXuTRo0cYjUYOHTrE4cOHKSoqEgujhS1j4y42Ezas3t5erl27RmNjIykpKZw+fZrS0lIRjMKWIsJR+FlmZ2eZmJggEongcrlISkoSs7XCliQuDgk/WXt7O3V1ddTX15OamsqOHTs4cOCACEdhSxLhKPyoYDBIX18f586d4/bt20iSxLFjx/jkk0/Iysr6y3BaRokECC4v4w/EiKoMGGwmDJoYss+L3xsmpDJgsFmxWvXoeJNNi8LGIRMLLRNcDhKUNah0RswmHVr1j1d12uhEOAo/qqGhgfPnz9Pc3ExCQgKHDx/m6NGj5OXl/fVGyjLhiRa6G+5y7d4Y/Zo8Cj94j8qMCLGGazy6M8qAsYyS04c5fryYHHjtMQzCZiADU4w/e0xb4xBDYRvOolJ27Mwn22nc9K+vCEfhlRYWFmhtbeXcuXO0trbicrk4c+YMJ06cIDk5+W9uraBEfUQWnvL8zi2ujqSQEYwxe8BDyugMk3PzzJm8eIMRIvztmdnCphScJjj6kM6OLho6QyyEFskz25gpScftNKJlc48ORDgKLxUIBLh79y5ffPEFQ0NDbN++nffff5+amhrcbvcPf0EyoE0uJHfvHnbWP+VpXz/Dtx7R6k7ngz2/4cPDGoxqB3ZPMimAKBu7+QVGu+m7U0/PYiLhkn0UhL0UOyUMqhhB3qQQ3sYgwlH4Hr/fz/Pnz3n48CF1dXV0dXVRXl7Oxx9/zLFjx17zmxrUpmyc2w5RXf2QZ439DM3NMTVvIqFwD+/liIURW0cUlCkmBru43zjPRHYBubuKyPHNkBJdwqxRsT6HXqwuEY5CXCwWo62tja+++opr164xOztLfn4+xcXFmM1mvF7vj5TmUoGSiD0hkZRUM7plCAdDKCE/MayIVZBbhOJFmW6gb3CAR0sZpBqTKHf5UWm0+JdcJKn02Nn86wRFOArAi22BnZ2dnD9/nitXruD1esnKyiIxMZGOjg5GR0eprKyktraWoqKiH+ydVgBJCSIvzRJTJBSdEck/h3+ij8HpWXoyzCTFQtj0GtR6MajezBT/AgtPHjI4MM2U4xi5Djdp4TnmtQks2NxodPpNH4ywgcLR7/czOTmJz+dDr9eTmJiI3W4Xhxq9BZFIhCdPnnDx4kXq6+txOp0cPXqUkpISvF4vra2tNDU10dXVxcLCAgaDgYKCfL57RUkCkCRU4UlCAT+LfgjNzhKenWTMH2I8psISCGORFBGOa0RRFGZmZpicnCQajeJwONZgkb5MaGGagaZBJiYkrGUp2Nx2onMz6Ow6bG47mi1SiGlDhKPP5+PBgwdcuHCBrq4uPB4PJ0+e5ODBg7hcrvVu3pamKArd3d2cO3eOq1evYrFY+PTTT9m/fz9ut5tgMMju3bu5d+8ely9f5saNG2RlZZGclITtBycNxkCOISsKigLIMkosQjQmE5EVFFkRs9RrKBwOc+PGDb744gvm5+eprq7mgw8+oLq6ehXP3/ax7Jukuy/GnM+KJ0uPJcnEQtCGS2/E7QTThkiVN7euf8bMzAxdXV20trZy//59Ll68yPz8PDabDafTSXl5uQjHNbS0tERzczNXr16lsbERl8vF8ePH+eSTT+InCALk5eWRnp6O3++nubmZpqYmMjJzqK6qQKsLsjTYQVtzP/1zoLVqMRtzyNoxRFFfGx0DzTy+dosUgxZrThJ2h2bTr3/bqJaXl2lubuabb74B4Pnz50xMTNDX10dJSQmFhYVveP62AsyyHJhhwGvDG05kmzGGO1EPwRTMNjMJW2hQ8NbDUVEUotEo4+PjPHjwgHPnzlFfX8/s7Cx+vx+1Wo3H48FoNIrSV2soGAzS1NTExYsXaWxsJD09nc8++4z33nsPp9P5g9vn5uZy7NgxIpEI4+MTdDzrZGdlCVqdj8DIAxrOXufbvgRsNSf51Yf72OMxIi/5iXw7wXRrK125JezIykA2imhcK4qixIfSU1NTzMzMcPbsWZqbm9m9ezenTp1i3759JCYmotFofkGFdgWYIxxcYF7tIKhNIVHWkmEzYHdZMen/9v4UFDmGHI0SlWVkRY2k1qDRqNCoNv4in7eaPrFYjNbWVhobG3n69CmdnZ00NTUxMzMDQGVlJQcOHGDXrl1UVlaSk5PzNpv3zujv7+fevXs0NjayvLzM4cOHOXz4MAcOHHjl76x8aSUkJDAxMYEiRzGarICV5MIaaj6wYZmyYSzZQ01VNvn6InJseeTtHWVck05SWTEVuS9mMYW1kZCQwMcff4zdbqetrY36+nra2tpYWFhgenqa8fFxHj16RHFxMZWVlVRUVPzMgFRBcAnZu4hPbyZm9ZBoc5NhNqN/yfIdJeplceApA8/b6ByeoW/RguQooayqjKodqSSpN/aM9pqEo6IohMNhvF4vXq+XWCxGLBZjcHCQuro6Ll68yPPnz4nFYqyUk3Q4HKSnp1NeXs727dsxm8309vauRfPeWYqiEAqF+Pbbbzl79ixTU1Ps3r2bbdu2kZqaSn9/f/x2K/+uCIfDPHz4kN7eXrxeL9OTY7S0tGKzWUFx4ao8wEFFQlJFUUb66FMB5mIKDxSSrwAqL4F+H+IVXVsajYaqqipkWWZkZITR0VFmZmaYmJjg8uXL3L17l+LiYo4fP87s7CxZWVnx3zUajbhcrpcebaHEIsQifmJzC/iCoHIkkuDOISUtHbtGDXKYqKxCVmnQqEBFDCWyyOLkCMPdT+nqGaKxM8ii1M1YRIU+K4XdiRKODZyOaxKOsViM8fFxrl+/zvXr1/F6vciyjNfr/f/bu7emqO58jePfXt1N09DNSaFpRAKdQYRmUCCmMAIJKgLBJFCxUt7nZr+a/Qpym4udSrQKolEhEzQlyHGDBktQHJAICcdRWqEPdO8LB6YyWU6S2UPT4vOp4m419auG9az/+h959OgR09PTv7jxbDYbkUiEyclJvvrqK3p6erBYLASDQTY3N3eixD3tn1sD0Wj0Fz+zs7NMT08TDoeJRqOsrq6SkZFBMBgkHA4Ti8WIRqPAP4IyGo2yvLzM8vIykUiEubnHDAwOYrc5sNodOJLt2K0xYuEgodAmkZgNqyMJR5IVIxpmMxQiGAoTicaIalRmRxiGsR1sCwsLzMzMEAqFsFqt2w2RrdkHKysr9Pb2kpaWBrz4O5eXl/Ppp5/+cs3830WePeXZ4l8JPP8bS0lZpHkLyfIeICc9CVgjtrLCEmlEUjPZ74Bky3Nim2FiaUXkVmfTULFKwc2/cGdwiidz97k7X0+h205GAs8W37GW49aX//nnn//Lay0WC5FIhEAgwOTkJJOTkztRkrzEvXv3uHfv3h/+3ItW5vB/viDZEVardfshFw6HmZqa+tWb2cTEBB9++KFpOL6YZmCAMx+XJ0jxIrA+wfT4HD8lb0LEwMhJJiv1Hx+xWF24DnhJL3WSaYOKzBg5oSA/ZCXhsif+0sIdCUeLxYLdbsftduN0OllfX3/ptVardXsH6UgkopZinBiGgcVi+be+b4vFgk7XSHxb99bW33nrbeBl0tPTXzoIaktNw5VUjBMfKWvzJM2N8vDBHW4PJ/PUcYD93j/x51wHmQ5IMgBSsDiSyUiyY1gBVlkJ2gi4D5Ob/wbFeVb2JfjY3I6Eo2EYeDwempqacDqdjI2NMTo6ytzc3K+uy87Oxu/34/f72bdvH+FwmGAwSCQS2YnS9jSn07ndah8ZGWFsbAyXy8Xbb79NYWEhKSkpGIbxm4G4FXyxWGz7FX0vnT2919ntdpKTk7FYLCwtLTE+Ps7t27dZXl7+1bX5+flUVVVRWFhIWVkZXq/X9HdabHZsNjs2wGG3Yi15ij3ZRupzK2s2L5m5HjzpKbiMrRahFYthxUaYyMoEM+M3uHxpnIGZLAr3JXHYZvw9RBPXjoVjdnY2p06dorKykr6+Pi5dukRfXx8//vgjgUBg+0mWkpKCz+ejtraW8vJy0tLScDqdv/tpJy++762pGfPz84yMjBAIBAgGg5SUlHD+/Hmqqqpwu93b3Riy91gslu23sGAwyOLiIvfu3ePZs2dMTExsX2e320lNTSUnJ4f33nuPtrY2qqqqyMjI+H0r0mxu0n3VlL1xhJIoRLFiWK3YrIbJq3KIcGCR5an7/Hj3f/nrT9msHCgh/0EVuaUppCYl7kN3x6bybL1aezwe3n33XbxeL7W1tfT393P9+nXu3r0LvOg4Hh4eJhAIMDc3R11dHZWVlTtV1p4WCoWYnJykp6eHp0+f8v7773Py5Emqq6tN5y7K3jU4OMiNGzcYGxvjzp07rKysAC/uy/Lycurq6jh69Ch+v5/S0tLf2FDEhGHDath+x2YidmzphXiPtND4NErayCS3Vu4zMDyLP7OIgwWJu9YwrkezRiIRhoeHuXLlCrdu3eLhw4fMzMwQDAYBKCoqoqmpicbGbXmj6wAABjRJREFURiorK/F6vSQnJ/BwVoLYmrbR3d1Nd3c3jx8/prKykvPnz1NTU7Pb5UmchMNh5ubm6O3tpbu7m66uLmZnZwFISUkhLy+Pw4cPU1dXR2NjIxUVFfE9MXL+KrN/+R/++1YWU1kf81/tFbx/NPW3P7dL4joJ3GazcfToUbxeL/X19fT19dHZ2cmtW7eAFyOgFy5c4MGDB7S2ttLW1kZhYWE8S3wl3b9/n6+//pquri6i0Shnzpzhgw8+oLi4eLdLkzh68uQJV69e5bPPPuPhw4fbfYxOp5Njx47R0tJCbW0thYWF5OTkxP8oXXcGmfn55B9IJ2BPJdmW2J2OcV+f53A4KCgooKCggLy8PDweD+Xl5YyPjzMyMsLCwgJ9fX2UlpaysbER7/JeKaFQiJGREb755hv6+/sxDIOTJ0/S2tqK3+/f7fIkzrY2ERkcHATA5XJx5MgRqqurqa6u5sSJE+bTdHbC5jLB5TnuP/wbP61ZSc1wkhyZZ2MxA3deEZV5Hrz7E3sh9q4uXi4uLiY/P58TJ07w/fff43a7uX37NkVFRRw6dOiP94O8RjY2NhgdHeXLL79kYGCA7OxsWlpaaG1tJScnZ7fLk13gcrk4ePAgPp+P5eVlGhoa+Oijj6itrSUvL+8/uDPP7xB9QnhlgsmRaW7PWcks2EeG08AI5ZJVVEhBxT5yMxN774Rdrc4wDFJTUzl8+DButxuv18vjx4/JyMjA7/drEOEl1tfX6erqorOzk6mpKYqKimhsbKS+vv6lUzFk73M4HNTX1+NyuXj+/DmHDh2ioqKC3Nzc+BdjpGFLP8iBNzZZT45izdpPekYm6SlusvNzyNlvwxX/qv6QuA7IyP/fzz//TF9fHxcvXmRqaoqysjLa29upq6vD5Ur0fzd5ncSiQYJPV1kLhNgwUnG40sh027En7uydX1A4vkIWFxfp6Oigo6ODtbU1ampqOH369PYcNZHEE4VolEjMimG1JPQuPP9M4fgKiMViTExMbE/PWFtb4/jx43z88cccOXIk/qOOIq+BxO4RFSKRyPZUncuXL2O322lvb6exsRGfz6dgFNkhajkmsPX1dYaGhujo6GB0dBS3282pU6doaWnB5/Ptdnkie5pajgnqyZMnDAwMcOXKFfr7+/F4PHzyySecOXNGo/gicaBwTECrq6t8++23dHR08OjRI0pLSzl79izHjx9XMIrEicIxwUxPT3P9+vXtdbF+v5+2tjZOnz6NYbxKY30irzaFYwKZnZ3dPj96Y2ODuro62tvbKSkpUTCKxJkGZBLE0NAQV69e5ebNmwC88847NDc389Zbb+1yZSKvJ7Ucd9n6+jqTk5NcvHiRmzdvkpaWRktLC83NzRQUFOx2eSKvLYXjLopEIvT29nLhwgXGx8fJz8/n5MmTNDQ06MxukV2mcNwlS0tL9Pf309nZyQ8//IDP5+PcuXPU1dVpRFokASgcd8HS0hLfffcdX3zxBfPz89TU1NDc3KzjDEQSiAZk4uzBgwd0dXXR09PDwsICVVVVnDt3jmPHjr30WEwRiT/djXGytUb62rVrXL58mVAoRFNTE21tbbz55psKRpEEo5ZjHGxubjI4OEhnZyeDg4MkJyfT0NBAU1MTZWVlu12eiJhQc2UHhcNhFhcXGR8f59q1awwNDZGenk5rayvt7e3s379/t0sUkZdQOO6gtbU1bty4waVLl5iZmcHn83H27FlqamoUjCIJTuG4gywWCw6HA4/HQ25u7vZ5wXE96EhE/i3qc9xBkUiEtbU1AoEAhmGQnp6uc15EXhEKRxERE9rqRUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTEhMJRRMSEwlFExITCUUTExP8BlgOG68jJz7sAAAAASUVORK5CYII=)
In the figure, if ![Error converting from MathML to accessible text.](data:image/png;base64,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)
![](data:image/png;base64,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)
maths-General
maths-
If
where
are constants, then
If
where
are constants, then
maths-General
Maths-
If ![fraction numerator sin to the power of 4 space theta over denominator a end fraction plus fraction numerator cos to the power of 4 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction text then end text fraction numerator sin to the power of 8 begin display style text end text end style theta over denominator a cubed end fraction plus fraction numerator cos to the power of 8 begin display style space end style theta over denominator b cubed end fraction equals](data:image/png;base64,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)
If ![fraction numerator sin to the power of 4 space theta over denominator a end fraction plus fraction numerator cos to the power of 4 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction text then end text fraction numerator sin to the power of 8 begin display style text end text end style theta over denominator a cubed end fraction plus fraction numerator cos to the power of 8 begin display style space end style theta over denominator b cubed end fraction equals](data:image/png;base64,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)
Maths-General
Maths-
and the equation
has at least one solution then the value of (a+b)
and the equation
has at least one solution then the value of (a+b)
Maths-General
Chemistry
Correct order for stability of carbocation is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgAAAABYCAYAAACDOk9JAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACktSURBVHhe7Z0HnBRF9vhrFzaxS1iCLGA+M5fU09O/gBE4UZSwBBFEMYuoKElFkgElKUFQEQOCAUyEOwNyJox3hjv19Hd6eqcIKJKXJdP/+r7tGnpmZ5bdhWUnvC+fZnaqu2d6ul699+rVq+o0z2IURVEURUkp0v1XRVEURVFSCHUAFEVRFCUFUQdAURRFUVIQdQAURVEUJQVRB0BRFEVRUhB1AOKILVu2mDVr1pji4mK/RFEURVGqBnUA4ohZs2aZww47zAwfPtwvURRFUZSqQR2AOGLjxo1m9erVZt26dX6JoiQ2W7dulagWsq0oSnyhDkAckZWVFfaqKInOggULJKrVr18/v0RRlHhBHYBqxI35u239+vVSTg5AsFxzApREZfPmzRLVQo4VRYkv1AGoRqZPn24OOOCA0HbbbbdJ+RNPPBFWPnDgQClXlEQjMzNTXjWqpSjxhzoA1QiPYYjcyipXlHjHjfm7zeWzEAkIlmtOgBLPbNu2TeS0qKjIL0lO9GFA1QhKMRjenzFjhhk0aJDp06ePGTt2rF9a0nvKzc313ylK/DJ79mxz5ZVX+u+M2b59uwx11axZMywK0L59e/PUU0/57xQlvli4cKHp3bu3adu2rXnyySf90uRDIwDVSHZ2tqlfv35oq1OnjpTXqlUrrFyNv5JIBCNXrn8RWebKleQEp2/t2rVhUR82ynAK451UyV1RByCOoNEEXxUl0SgsLDQ//PBDaJsyZYqUn3vuuWHlDz/8sJQryQf6a8iQIab5Mc3NEYcfYQ4++GBz4IEHmsMPP9w0b97cTJs6Le6dgFTJXVEHII7Iz883jRs3Ng0bNvRLFCWxQGEGo1f16tWT8sioVl5enpQryQU950EDB5mpU6ea5SuWm1WrV8nspp07d0qPesWKFWbQ4EFmyuQpceUExMpdwZkJlidbTkDSOQCRU+jYEiHcuGPHDtO6dWvzzjvvmL59+8p1ayRAcUQm0bEhM4lCsF1u2rTJL1WSiU3Fm8zAAQPNAw8+IMY9LzfPNGvS1Nw/5X6J+rBvv0aNRG6HDh1qJk2cJHIdD7BeRXDm1RVXXCHlixYtCivv1auXlCcLSeMAOAVz8cUXm4MOOihUYYceeqgkG7EvHh0BGgrXRqiU8NiJJ54or4TN+vfvr05AiuMM//XXXy8y4eT6kEMOMQ888EBcOwH0+lxPat68eXLd/IZLL71UnYAkZPjwYebhh6dLBn29unXNmLFjzD8//8xcceUVEvW5/fbbzb++/FKSRDdtKjYjRowwjz32mH929RLMTXGbI1Z5UmB/UEKzceNGb/Xq1V6nTp282rVrUztejRo1vFq1asnm3terV8974oknPKsw/TOrH9tQvPHjx3t169b10tLS5Frddbv3V199tfw+qzD9s5RUgPqm3i+77DKvTp06IgvIRFCuMzIyvEmTJslx1pH0z6x+aGNck1XuXk5Ojlw3v4HrTk9Pl2vv1q2bHEP7VZKDy62somszMzK9iffdF1MmBw0c5GXUrOnVtNvYsWP90urFdrS8VatWhbbHH39c5PRPf/pTWPn69ev9M5KDhHUAnOHv0KFDmOHHmD799NOhCrvgggu8vLw82Z+VlSUVy3nV6Qhg+LkGjD+NgGvjN/Tr1y903VOmTBEFzz6U5xVXXKFOQApQXFwssnHJJZeEGX7+tj3+kHxcc801oX3I/H1W4SJX1Ykz/I888og43LRHrrFnz56h6541a5a0QyfzXbp0UScgSUBHIY/5+fne00895ZeWZuSIEVL3OIPjx43zS+OL+fPni4x27NjRL0lOEtIBQGGcd955pQz/3LlzRcns3LnTP7LkWMp69OgROhblRO9kXzsCzvDfc889cr1cD1v//v3lGoMGHu956tSpovhpVBxHb5Dz1RFITjD+vXv3LmX4p0+fLvIR7FEhA3379g21AZzFCRMmiHxUhyNAO3rooYdErl0vH8f7oosukt/loG0++eSTcpxzEAoLC+W61RFIbC699FKpz8mTJ3tbt271S0tDb/u6666TY8eMGeOXxhfz5s2T6yMCgGwmq3wmlANQVFQkFYHxp3Kc4X/uuedKGf5IqDx6Ii4a4ByBhx9+WD6zKh0BGgPfcdddd4UZfpT3jTfe6G3evNk/MhwUPr+Lnl8wGtCnTx91ApII1+vv1auX1DEGlHqeMWOG1H8s2UQG2E/kiPNcNICwKp+3LxwBZJTvwvhnZmbKddDGcGS4tqDxd9BO2UekLhgNYBhPnYDExTkARC/Lkj304fXXXy/HxpsDgGwizzNnzpTrY8vNzU1a+Qw5APzwNWvWyBbLkFK+du1auUGVNZgYcb6Dz3Ab78vCGf527dqFejyMLb744ouiSMoLyojjUU7OEUDZojQffPDBKnECEPY77rijlOEfMGCAXEss4x8EJcv1BaMBhIi5J9EUrBJOeWR23bp1ckywl10RNhZtrLBcO8N/4YUXhnr9GFGiU8hGeeURRwCF6toGG/JGpKmqnABn+KdNmybf5Xr9GAGuvTxyiT6ZM2eOnO+iAQzp8bnqCCQebgigfn79MocA7rz9Dq9O7TpxNwSAPBKdomNIO3QONbkrySqfIQeABnvggQd6TZo08X755Re/NByM1RFHHOHVr1/f++GHH/zS8rNh/XrvjNNP95oUNJGbjGfVqGFDr2mTpt7bb79dSmGScMHNPvvss0PKjTFzKoUQTWVxjgBG1DkCVDhGlu+rrBEI4nr9o0aNCgkPv2HIkCHlNvxBuCbOIxzseloYDZyZ3Slb7uua1buME+8jz3HDE2UluTilj7FMFKiH3/zmNyKz3333nV9ampNOOkmO+eKLL/yS8oOD2uG8872mAbluYD8LuV64YGEpud6wYYPcR/JTnOF3vX6Mf2UcUeQJ+SCiFGwro0ePlu+KFjHi3nBt7A9ulBGmjQVyQC8vaPhpR5dffnm5DH8QlC7XTRQvOzs71E6I8u1OyUaTa+oiSHlklvvNMTiKSuXZlQSYITkp0fQoctrv2mtFNuMlCdDV/+zZs0MyiDx37dpVZJON4eWgfJ5//vlyTqS8JRohB4DGRjgOr+fnn3/2S8NBiaDguAn//e9//dLygWFp1bKlV8MqjPS0dC8rMyuU7Y4S4aaiQN94/fVQr6V169aiTPk+Z/gXLFggFbI3cI4Aiovv4Dr4jvvvv18qN5oA7w5n+EeOHCmfxefyG2+++Wb5rrIUa3lAWAkNYyyc8iV0HE0YUa5ESTBEjRo2knvMeU0KCrwunQut8rSerO25Ag4YBhBnKxaffPKJHHPqqaf6JfEP9dG4cWO5T998841fWppf/epXcsw//vEPv6R8cM/bn3uuKD7kmqGaoFwjv8g1DivXAigWJ9ccQ52QHId8VMb4B3GOABEmPp+N74pUtFzLXXfeJbLR0DrhyCpKj94bZUOH3lZKVvls5CyYoIpM0fPjOytq/CPBCeA6nMOME8D34TBF8te//rWUXBfYem5zVuuwtvDZZ5+JzOLgxeLbb7+VY3AUXR0pFWfATTdZvU7P2YgDTIcqqEO3bN7i3Ww7QHVtXRl7TO3cPIkgVRfO8JMYjl1zcte9e3eR56ADii6NlE/k7lzb9qPp3kQhzAHgB+HlrFy50i8NBwdgv/32kx//v//9zy/dPRj/FqecIkqRG4gBeu+99+Qmt23dRqIOOAbsb1i/gffJx5/IeWeddZYoU875y1/+IsdXBSgulBi/n9/mrhNFR+WWxxFwhn/YsGFyLp/jhOTWW2/dY8MfBMHlXtBbdNEAlDw5Dg4E9nkrsOIo2N/Db+Je4khhdHjf2NZlx/M7SN2/8cYb8jknnnii/wml+fDDD+WY5s2b+yXxD/VywAEHyHX/5z//8UtLc/TRR8sx//znP/2S3YNhOuecc3wjXlvk+uWXX5a6KezU2RqoXXKNYV382mI5j8x36iJo+KmvvQnGetCgQSJ/fFfQAeCeMCzlHBXZTIl88Lc4MjUzxGkNyi3KGjnjGO4VMxG49mjRhcrC5+G0MsTHd/B9kU7pa6+9ZhV23TC5xiHhunm/X6P9JNJI/VCffA4OXiz+/e9/yzE4iuoAlA/qHH3nNuSEzsS1ffuKE0CbwNA/YGXGHTN40OCQjPE6buy4MNlBD7tjq7IenOFHfwYNPw4wUbmg4Y/EySc6Hl3KebQxhqcT0QnYJw7A6aedJgLB9tZbb8nNd7hwaGtr7FGWhI/eeecd2UfYjhvOVtXw2/ieq666qpQjsLspVgj/0KFDSxl+nAE+c28a/yAIMkKMIaFBMZYMNJ5n586VBshvwNB369pNrmXhwoVeM9tz4hz2IfyXX3pZyLifYh21WPztb3+TY37/+9/7JfFPVToAnTp0lPuHXBOZCso17Yn3RFpqpJeERef7w1bIvJPrvW34g7hoAJtTtJvtqxj/HKuI09Osga3l7d+0qTdi+Ag5bsw9Y7wmjQu87KwsiQgyZLXJ79kzKwU5Q7aZgRBU3nsbIia0J76PTGygDS5atEimmdHLbGwN/dltS+ZpL3n7bZHrfKvQRa5tneDcfv7551Kv1G8svv76azkGOYknB6A8eSl7mrtSvLG41DAQ76PJJQbOHeOmqeKgsZE0B8gESaniBNh6oG24Y6gXNup0wvgJpe41UVOOo975uyrqAp1J4nek4XdTVcsy/kE41smocwRwVLk3ieQIRHUAYo2XcfNcOLUiDsAxRx8j3nl2Zpb3r3/9yy8NB6V41plnes2sMvro73/3S/c9zhEozxQrDDtl9PARdI7lnOHDh8tnVJXhD+KiAWzcQ3jppZdsjxMlmRYSyqBg8x5HIL9evjQCQq1/t/ec609mB6CsvJVjjjlGjqmIA9CyRcuQXL+zpMRpjYT7zjS3/Zs2E+NV3YwbO9bLy82THj/K6/bbbxd52LqlRNlyv3h/+6hRItM52Tkiz+DaBltVGn+H+y6Xl/L+++97DRs0FLkmpL96Vbiy5brfth2MBvn1xQE46Y9/TFgHAAN8/PHHy9DEV1995ZeWhuE4jmF4rqIgm10Ku0TNXXn22WdLOQIMNTpjzv1yxpzNOQCAbNxw/fWS64WOcedwnUR777s3eodqxIgR8ll8NrLHe5HNvVAnrteP8XdRUww/01SRscoOX3Hun//851DECv3fpk0b+a5Y+VSSuxJwuvjb6W4HDh37ypu7UtmORCkHAK+fsVJ3ccFt+fLlXqNGjeSHVsQB+PWvfy3Cgsf+ry+iOwDgogFl9bb3FU7ZRU6xYvEedz8GDx4sXrATWJQp5+wLw18Wzz/3vIRwMe70gmKB4DazDbLPJX1CEYCWLVv6e0vz6aefyjGJ6gCgJF3dRW4kt3JMRRyAVq1aecbKxX4NG3nvvfuuX1oa2hbfEQ/GZfiwYV5NKxfIxy0RIf4gKOlMX4ZuuOEGv7R6efPNN0vk2ra1U1u28ktL886SJTL8ct657UMOAA5eLNBlHBNvDgBJ2VwXvyEWDMdxDO23IiCTTGsjOoUTSy8W44ueQ5fxN47B3DlzQveEXrIz+Og9N02VjWhTEJcv4va7jbJY+t3lZN12222hDhU6l0gq51VGrzpDSj4Cn+U+lwgG37WneSsOdGkwGoDDc6bt0EZCrhUOFpF07C33kdyVVlaeuU7nCOCU4jAdd9xxYuijQYeGY9Bdlf0dYQ5AgwYN5OKpYOe1RW4ICE5CRRyAI488Uj73gw8+iPlj4hUcgcgpVu5euPfsw/jHi/J4/vnnJbyLV3pJ74v90uggdPSiXA7AH22vibJoG4lXHJNoDsAhhxwi112WXDvFUBEHgGgJ5zDuX9kQ7L5mhO3NE5pF8bBcaywYu62HwrTHMrMgHmD4kHpC/zDroiyQV3pgzmlFSUbKs9s++ugjOSbeHIDDDjtMrqusmSm0RY4hOldeaO+dO3eWe1nb9oLJXXnhhRfEIPbofkFY7gpDKhg3wDg5Q85WVbocQ4/RD+pcjCuRVuqrPI6AM/yR01Tp9TNVdW8Z/iDcE3QB34euOeOMM/w9JWD8uZ/B3BWiEbtyVxpJVJH77PJS9t9//5j3mUR8jiF6g/2uDFEdAAwHFxdti+YAMG1wxYoVoS0S5wDgpSaaAwBuLJUV+xBKdy9Qoizuw754URxAtir3m8SU8oZqX3/9dTmHHl80A8nmwlx4pYlC0AEoS66jOQAokLLk2jkAr776asLINb0rrvmWW24pU5Fy35BtjsUBjgeIAHA9hP/Lq8CdA0D9RpNpNuqfY5CTVHAAunftJlEg7gmhfuTc4aJVPS/sKb1ZclfmPPOMv3ffgWyiV8kFCDoC6NzI5NRIMP6R01T5DGZ78ZlVYfyD8B1sLnxPxAPZpbeeZq+lsTX05MVxDJ1iclcYesG2cr3tzj5bhn247kMPPTSmbnGRK6IJlXUAwp4GaIVfnudtlaA8vjFy++abb4x1EuQ4hxUW06FDB2OVYWjjfHvR/hHGZGVmGvvjzHnntjf/99X/+aXhWK9UnnrGZivQL40PuCe28szo0aON9bpC9+O7774zAwYMkH0ZGRn+0fEF970iWJkoc4vGTz/9FNqQh3jDyROPWg7Kc3CzylaOcdjeo+nZs2eYXFsPXp505sioWVPur1WW5sMPPvBLw7ENMyTXwXOrG657d7JRUdnZV5Tn2qMRTZ7ZrLH1jwjn559/Dsm17eT4pfuesnRLZe7DylW/mJ32d2fUzBDdlZ+f7+8xxjpD8v6h6Q+Zrl27mv0a7Sdl+xrbM5Zrs8ZedC5PErRGXNrl3XffbYYNGyZtKmiLsDmUTZ06VZ6kag2wsQ6eueqqq+QzJk6cKJ9pOwL+GVUD38FmnRV5//lnn5vCzoVybcced5z58quvzPwFC+QYnv762Refm5dfftk0yK9vqM1ly5bJefsE2wAEPAi8pLKSAPFKXRKgvUgp++1vfyvhY96zff/995K8EpxP/evmzcWzKSsJkLnU5BeQ4fu3Co5nKeEQziOEJ0MAF0cfAqCnYwVSvP3IIQDnwUZuixcvlmPcEACeLVEdpli5jbBXWYkr+xp+Z0WSAF1v6w9/+IPcRyfXbPQ8iZQ4yJdwch0rCfCiXr0ktEfoj/BgdeOGAAjvlzUEMP2h6aFwZbwMAZDgR4SKCGSs3BZ6f06uI4cAosk0m0uAdUMA9Li+/PJL76ijjgrJNe2CHCh04L4gGAFgyjS/J9rG2gUcU5EIAOurMA+fhMo333jTLy1NsR8NKE/IvaqhXqgrolLIAL+ZaADrXbh7wWwtev3WKZL9VTFNtTLQyyd3BV1BYmosPvzgQxl+adO6TSgCgOzFAnnkmL0WAXAEvaogVhDEY45k//33N02aNJHNNqJSvZ2GDRvK6/Yd242tELN27Vp5D/SQeP/jj8tk37at8dNLSlSoo/QaNaQe167Zda+DfPzRR8YaPWMFzFxz9dUhL9953tE2oj9BPv74Y3P55ZdLz9htQ4YMMVbBxF0UB2LJNUTKNe+dTLttw4YN0gYcDe39oAe2zcr12rVrwuTaKh15v/THH0WuOc8aU39v9SGykZ4u7W6F7dlGi0pQdz/9tEKicmn22Fg95H0NvVbr2Jrt9pq5p9H4+uuvTXMr10R0utkebM2aNaWc12gyzWY7HnIM0NsmsldYWGgWLlwYkutJkyaZdu3aSa9yX2ENnbyeeeaZolejbdZhlWMqgkRnrbg/8ugj5pQWp/ilpcnxowHohOqGeqGuiLgSDaB3TTRg3LhxoXvhev15eXmmb9++Zvz48XKO7dT6n1J97Ni5IySDsTjhxBPM57Y+5z471y8pqStkHZsaua1cudI/qvJEdQDKg1Mcb731ljn44IPl71jMmz/fnHzSSfYm7DTt27eXBmp7jvIjOnfqZI45+hjz6T8+NdZ7M/MXzDe/P/ZY/0ylMiDwebVyRXFv3WadAGuIMEgO3lvv0fyy8hezft36sJBqWco+0lhgTBDqoJFEme4Nwawu3NDV4sWLzfHHHy9/x+LxmTNN27Zt5T70uLCHyPWiVxeJXPfufZF1sJqb1994QxTSk08+aU47/XT/zOojL6+2ycrKFiM/bdo0M2bMGDGoDsqnTJ5sxk+YYLbZv7MyMkOhzOqGobjateuII0BnAue2uLjY37tLrlf+8ov8HQyPRzp4QSIdQ+ckHXjggWGyzTBAWZ9TVdAm+d5oWzT47cFhuVgE70+igCOAE4CThuwim+5e0M769esn4X4cg3gw/MC1UYfNmzc3zz73nF8aHRyuYHv7/vvvzUEHHRTm9LntJGtTYY+Gn+3FCYQQCK0RpqjMUsAsHkSiFGFWwmWR2dTr162T1QD5fMKKfBcJOFYIJQuybp26EoZW9hxCdkzfYSEg7jfTTLp36y5hMlkIqGlTCZUxBei89ud5RRuKJMOaej2lAusAMARglY387WCqHclU7IsHCB2WZylgF26NXAo4mOBKyD9SRos2bJBkS8KSyLVtjLvk2t57htX25LkVexsW9WGOP8NDXGOevVaez+7CqGPHjPXq2Gu2PX9po6wmSCg4HkCmSLhk+MLaLq9gv8Zeuz+VrHOxZMkSkWuGEGWaYKtWMgTAUsDUa0XWAWAYIVKuGdpkWh7ftS+wBiMkk++++27YkEVwixwCYPiNderd0AUbKyfyuxxt27SRumcZ5VhDANgDJxPBc+MJ5CHyflR3uD8arF9BHR177LHlvj43BEA9kaQabXNJ2c2aNQsbArBOX0hnxbLljpADQGYkDaCgoKDMhwEdfvjh0siC46k0mNNOOy0kcBiTyHmhgHCeduqpsjId0zHYWIeccY+33ow9FqVUHBQIGb5M88EwIUgYJpl2YhUkBqvD+R3EgIEb36/MUsA0RCdwKBuciHhyAFiHApkt62FAOK0cE5lxzSJJTq5Z7S9aBjHTds63jhQGCYMvct2gRK45J97AQcQJqGUVSFA2djnkaV52VrasAhitHVc3i6wTIM5t4Npd5wW5Pv200+XBY4BDisxiTGMRaylgcgGcMsXA0jYiHYOqIugA4KDEAqPCMUxlBPJUeMxyMHeF9shS6g4WXONe8TwWpvZGgwf7MLZMHkg8ObCJCDkAyCUyes7Z7fzScLChawK5K84BOPjgg6VzHenosNFZ4RjqCb2EvNLJQd85ncWMraVLl8acSRByABA45/HxdzQo5yL58sgPxNNA2PCUEcJY86lRlnyH+xHuO5W9D/XFmgCsyMXKgHiN9PwL7PvOPNvafxAQvM0cVXuMW3Y1Gh9//LEcwwI4QVCgTuDYhwzEkqHqIJbMBkGxcwwNMQiNzylSfhvTeaJBImWYXK+Kb7nGCbjzjjtkZTbq1DkArNyGvAy9dWhcGn/HX63DKnJdv77INQlhBY0L5GFAG9bvWlWNCAC/DwcvFiwRzTEozqADQJ0TOUCuSQpFKZclQ3sT2o9zAMozDdA5APzOyCjV7373O9EDjm5duopBqlEjXZ4XQvtwYEh4f067kmdc5GRne/Pnzff3KpUBB4DplNzPWEmAPJCKDgPyzHMsKpoEiLzQKSeZmQRWp7PQ2TiJsSIBIQegMvCl9OojlSZzF8msVaof6ihomMQ42ffBkBG4cBr1GQt3TGQviHIncCx326JFi7iJAFQW7kPkbyDyEQ+Z/HsLnIBI2WCjLJ6NvyOaXNPBCIJuYl9ZPXd3TNAQAsYeJYtcE/3CuFZHBKAi6wBwfZEh+0gHgHvUsWNHMUgM92B46OVz/y7s0cM6hU3tvhqy75mnn46LWQCJDA+3c0tYn2AdSZ7CSofBgdy99+57JQ+0snVy5hlnhhyA8q4D4BwAnNigbid6xdAVchyNPXIA+CKEK3JsVR2A1AADGekwxFsOQGWhx8fYXZBkcwCU6OAQRMo1US2GSDGS+wIU+p4sBYxD44blGJ7l+SBBMEAdOnTwlwJOk0V/QkNA1ggxjDV3zly5DmXPQBcSlWE4Jc3WVYE12PTykSXqjdyVBvUbyH3/fyefLEMALi+lvA6AGwLAAQzW2e4cgErPAnDYL5OFC1zG6dKlS029evVC02+U5MU6eeass87y3yUXtm0Y23jCsqlZiCQrK8s/QklWWPCsVatWpWa9WOPo/7VvYPp0fn5+mbqUqbnRjmHxG7eA1XXXXWdatmzp7ynBGnsza9Ys07FjR2MNSMniOPb3WUNkCho3No89+qjpXNg5IWcKxBvUzamnnmpefPFFU6duXfPzypUyO4hM/lYtW5nlVs9Yw21OPulkWRAIPWOdUDl3azmmLnMMf1sHQmbS8bdbxAodVlBQEJpSWgp7cKXB0yBhkJCvGwNmY/GNRO8BKruH7GQWgnI9DTaGAE444YSEr388aZ6kGJRrxv8jw6tK8kH4lbFUcgOcXNNTI9weOUxQlSCD9OSJSMTCHRPZ3tDLbljudNvbjBW5IoobHEpxuSva868aSJAnd4Wlf4O5K61atvTWr9v19EDyqshLQeZiRQAI+XMMifnB5GTyltDL6CzOJ4IUS4bS+M/3BSoN82Odt4zHiMehJD94qSwG1KNHD7/EyNzpF154QTzRRMcqwrCFf5gLriQ/VuEaq4BNp06dQnqN3jhyjW6L514xi+PQmw/ODbdGwAwfPlx6+0r1Y53IUO8dkCeiBPT8HcjgunXrpOceS5cSfSdy4Hr+Ti4pZy0WXokCEA1asGBB2IJXjr3iACipDYuvOFg1LHLFQEVJRGzPP6SoUdDRFGi8cfLJJ8ta+YScHeoApAYYfFbvDC4khAPA8wY++OCDqB3zPc4BUJTgamlq/JVkAYXp5DoRjD/gsLicFbexQp7mriQ/rBrYokWLsNUxd4c6AIqiKEnCK6+8IstOuwRAthEjRiRtsq6yC5w/hmVJxHfOH9FZnj8QKwlQhwAURVGSCMaYN2/e7L8riWRoNn/ywxDAt99+K0M97tkv5AbMmzfPNG3aVHIFIlEHQFEURVGSBHr+OANAz59pnrFQB0BRFEVRUhDNAVAURVGUFEQdAEVRFEVJQdQBUBRFUZQURB0ARVEURUlB1AFQFEVRlBREHQBFURRFSUHUAVAURVGUFEQdAEVRFEVJQdQBUBRFUZQURB0ARVEURUlB1AFQFEVRlBREHQBFURRFSUHUAVAURVGUFCSlngbIM5K3bNliatWqZTIzM83GjRvN1q1bTV5entm+fbvsq127tjxCUVESGeS6uLjYZGdny4bs84z4nJwcec/flNEWwP1Nu1CURGbHjh1mw4YNIsvINHqdtpCVlRWSd9oH+p9jcnNzw8o4jvKioiKTZV9z/HOSkZSJABRvLDb9ru1njjrySDNv3jwpGzBggDnssMPM4sWLzdixY83RRx5lHn3kUREYRUlUNltjPmrkSHPUEUeaBx98UMrGjRsnsj5lyhR5P3HiRHk/c+ZMM2fOHJH90XeNlnMVJVFBdz/00EMiz7cNvU3KnnnmGZH1wYMHy3t48cUXpax///5+iTEvvfSSlN18883m/fffN0ccfoS57LLLxClIVlLGARhojf3s2bPFE6yRXtLDX7dunVm9erX0ftLT0s3qNavNgJtuMi88/4LsV5RE5N4J95r77rvPbLA9mPT0kiZOjwhZp1cDvLr36WlpZq1tC2PGjDGTJ0+W/YqSiMydM9fcYg34mrVrreynSRk6H1lH3zvQ+ZSttcc5iIq5shq23fB+7rPPSscxWUkJB6DYenBLf/zRpBnP3GsV47ntz5XymjVryiuCcdOAm0z37t3Nlq1bzPLlyzQKoCQk9OB/XPajhEGHDBlirrj8Cil3su6Gt9wryq5L165m4MABZufOHXKuRgGURASdvWL5cjHcvXr1NCNHjZJyJ+uuDYBzjKOV4RT/4YQTzIMPPmBq2nN/WPqD2eg7zslGSjgAhPoXvbbI1MrNNQUFBaXGOUmDYGy0SZOmViAyzKjbbzfPWs9PURINQv2PP/64jPMXNCkwWdlZ/p7o7Ny5U9pDkyZNTHZWtpkxY4ZEDxQl0Xjm6afNHXfeIToceXbj/RUFe5CRkWHbTxOTm5tnlrz9trn22mv9vclF0jsAjP3/uGyZ9IjGjRtvWrdu7e8pzbDhw0y3bt1kzGe59SQ1CqAkEoQ1kfWtW7eZgYMG2V5QL39PbNLSSsKkl1xyiel/441m65Zt8hl8lqIkCujq5StWmGIrtz1t73/IzTf7eyrPKaecYqZMmWx2Wodg6dIfzcai5MsFSHoHgCSPRYsWmTTPmLp165bq/QfBY8zOyjLeTs/ceeedZs4zz/h7FCX+uefue8ysWbPowpjaebUlClBesnNyTK6Vf3o/jz32mJkwYYK/R1Hin9mzZpvRo0eL7s7Jyq507z8ItqJevXoGF3nJkiXmmmuuLtmRRCS9A0BSB95hbl6uycjYNd4TC47Lzs4yRRuKTFESZ38qyQe5LJuKN8m0JWS4ouAEoDj5jGDClKLEO4zb00NH7nPz8vzSPSc9vYZME9+6bav5ZdUqvzR5SHoHIC09TXo148dPMG3atvVLYzN8+AhT2KWL2entDIVHFSUREFm3/0ho7XXRRX5p+bn0skvN9TdcL5/hEqIUJRFA9tHZ3S+4wNx8yy1+6Z5z2umnmSlT7hcbkoxtIulbOUlOVF69/Hplhv8dtXJrSS/InacoiQIyy1anTp0Khf8dnMO57nMUJVFwMovurlUrxy/dc0gGzK+fL7YgGdtEyrj5aswVZfdoO1GU1CHpHQDmcRK6Wb9unSz1uDs2FReXLBbkn6coiQIyywImLPrDXOiKwjmMpfIZbu60oiQCTmbR3Wx7i23btpm1a9bIYlnYkmQjBYYASno0N910k3n1lVfk77IYOXKUeXbuXJNm/2kYVEkkdu5AXtPM+HHjzRMzZ5YUVoAZD88wE++baP9Kk2mzipIooOfR2awFwJLWe4s3Xn+jZA0A6wBsT8I2kfQOANM4eLgDWf3btm33S0vgAUAQNPRF0nsqmTWQ5z8kQlESARn7z8mWlS+R4SDOoMd6BVYAZA2MnFo58lmKkijwQB909qZNm0ut2udk3Ol7cDp/d2U7dmwvebBQRqZpUL++X5o8JL0DcO+998riP2Q2r18fPgzAugD5+fmhhCkWP9m0eRPOnhk6dKjp2q2blCtKIjB4yGBZBMWz8ltUFD4MwFQmZN09+YzX4PsthP+LN9L5N7179zY33nijlCtKInBhzwtl6Wt0Nzo8uJAViYHIetCpRedThg1wRJYR/mc6LHkxLVq0MFOnTpPypML+uKTnqiuv9HJycryGDRp4Cxcu9Es9r6ioyFu1apVnFaW8HzxosJeXm+dZAfBmzZolZYqSSIwaOdLKcK6XX6+eN/2h6X6p5xUXF4us8xrt/dT77/fq1anr5eXlenfdeaeUKUoi8fhjj3l169TxaufV9m4bOtQv9US/I+voe4crs717v8TztmzZEla2+LXXrM1o6GVnZXkX9+4tZclGSmS5jRtfsgQwCU4/rVgRigLQ+6lfv74MEeAxLlu+zHp9W83wYcNMYWGhHKMoiQTPvbjoootEnuWhVn4UgGddIOu8Rr7nmGXyEJVNpk+fPuaGG26QYxQlkSBie+utt1r9vsUsCyxnjX5H1l20C1wZkTEH08RdGb3/FdZWEElr0bKlmew/RjvZSAkHgIpv1rSpjPGg3BYuWOjv2cWtt9xqnnnqaZOVmSUPBUJAFCXRYBXAZs2aGRaxuvvuu8306dP9PbGZNm2aJA6mpdew7aSZfIaiJBqE8NHdmVaHz3pilnTkKstrixaZq6++RhL/Dtj/gDBHIZlICQcAxo4bZ3pe2NNkWSHZsXNX4pNj+47tMv5DtKBjp45+qaIkHjzU54b+/U1ebp6V9d3PZOGY2lbBDRw40PS77jq/VFESj8Iuhebue+6W5O/t20vr+fKC4c+0ncAuhYVm0uRJfmnykcY4gP930rN502ZJECEiELkqINnPDA2QKKJzoJVEh+dfMB+aEL9Lco0FoVISBqO1C0VJNMjil8x9K8vBsH9FwBZgE2g7btgsGUkpB0BRFEVRlBJSZghAURRFUZRdqAOgKIqiKCmIOgCKoiiKkoKoA6AoiqIoKYcx/x89iLFVEoGMeAAAAABJRU5ErkJggg==)
Correct order for stability of carbocation is
![](data:image/png;base64,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)
ChemistryGeneral
maths-
If ![x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text then end text y equals](data:image/png;base64,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)
If ![x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text then end text y equals](data:image/png;base64,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)
maths-General
Maths-
For all values of
, the values of
lie in the interval
For all values of
, the values of
lie in the interval
Maths-General
Maths-
Maths-General
Maths-
Maths-General
Maths-
Maths-General
maths-
does not exist Extreme Values; ![cos space invisible function application x plus sin to the power of 4 space x element of](data:image/png;base64,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)
does not exist Extreme Values; ![cos space invisible function application x plus sin to the power of 4 space x element of](data:image/png;base64,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)
maths-General
Maths-
Maths-General