Question
The cartesian equation of
is
Hint:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. Here we have to find the cartesian equation of
.
The correct answer is: ![x to the power of 2 end exponent minus y to the power of 2 end exponent equals a to the power of 2 end exponent](data:image/png;base64,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)
A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:
ax² + bx + c = 0
where a, b, and c are constant terms and x is the unknown variable.
Now we have given the equation as
.
Now we know that:
.
So applying this, we get:
![r squared left parenthesis cos squared theta minus sin squared theta right parenthesis equals a squared](data:image/png;base64,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)
Now lets substitute x=rcosθ and y=rsinθ, we get:
![r squared cos squared theta minus r squared sin squared theta equals a squared
x squared minus y squared equals a squared](data:image/png;base64,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)
Here we used the concept of quadratic equations and solved the problem. We also understood the concept of trigonometric ratios and used the formula to find the equation. So the equation is .
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Let
and
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respectively. Then
![](data:image/png;base64,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)
A small source of sound moves on a circle as shown in the figure and an observer is standing on
Let
and
be the frequencies heard when the source is at
and
respectively. Then
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVsAAADMCAYAAADd2wCiAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACpfSURBVHhe7Z0LfFT1mfefSWYm9ysQIFwCBBFQuRhWsReh21C3vu0qtait3ZdL30LddQvWtvC+tXLR7UprP6KfdhWsBra2a6GIbFt7gVboVmuVq5SbQBJIgNzI/TaTTOb9//45J0wmk2QmmUlmkt/Xz3HOOXNmEibn/OY5v//zPH+LWyGEEEJCSpTxSAghJIRQbAkhZACg2JIubNu2TSwWS49Ldna2bN682XgFIaQ3KLakCytXrhRY+Xg0MfcdOnRIcnJyJD8/X9atWyf333+/cQQhpCcotqRbpkyZYqxdB0K7c+dOY0tk165dcvjwYWOLENIdFFsSMN4ijCiXENIzFFsSMJ7impaWJrm5ucYWIaQ7KLYkIPbv39/h0yLChaUAwSWE9AzFlviFmaGwaNEi7dEimn366acZ1RLiJxRb4hcQVmQjmBkJZoQ7b948qaqqMo4ihHQHxZYEDDISlixZotcR5SIFjBDSMxRb0ic8fVpmIxDSOxRb0idgI5j4ysclhHSGYku6xTNiNdfhz8KrNbchtGvXrtXrhJDuYYtF0gVkHqxatcrY8g1EFiW8FFpC/INiSwghAwBtBEIIGQAotoQQMgBQbAkhZACg2BJCyABAsSWEkAGAYksIIQMAU79Ij+z7/e/l9KlTen3GzJly+/z5kpycrLcJIf5DsSU+2f2LX8hTGzdJXV2dsaedpKQk+dqja2T5ihXGHkKIP1BsSRee37JFLc8ZW7753H33yfd+8IyxRQjpDXq2pBN/fffdDqFta2uTiqpKKSi6pJeyaxV6H3h99259bLiyYcMGqa6uNrYIGXwotqQTeS+/YqyJlJSXSU1trRZYLHX19XKltMR4tvOx4caxY8dkzpw58sYbbxh7CBlcKLbDiFolnPBiv/jAgzJ10uROi4kZrTY0NkpTc7Ne98ThdGrRBfv37dOP4cjChQvl4sWLsnjxYrn33nulsLDQeIaQwYGebRgDcUQ2wO5dv5D3/vpXY2875wsLjLV2PAXTE8/j8H63zpptbHXGPM58n6qaaqns5jY8PTVV0lJSjS3f9OX3CyaIbOfOnWtsiaSkpGhrYc2aNcYeQgYWC8V24PFXRP0RRxN/xay348znEb3Co/VFxoiRkpSYaGz5JlS/XyCkqi+FmpoaY6udBQsWyJYtW7TFQMhAYqHYBhfkpBYXF+vb8VMnT3WIqadY9EdEb7v9drlvyeflvs9/3tgTXL76lZUd9kDx1SvaNvDEarXKhLGZEhUVJTNmzJBf/uZN45me8RxMw78f2/iyOfj2nzvl7QZTlGEf7N2719jqzPr163WkS8hAQbH1A4iDmdgPPMXi6IkPjL3tBCoWEM/5d8zXBQMQHRQNDCb4dz304Bf0upmNYHq0cbGxOqqF4ILNz3w/6KIfTFGGZfDcc92nsGVlZcn27du1v0tIqKHY+kFfItFwE9FA+NZj39CpXT0x2Hm2vYkyBsRgFXjbCL5YvXq1jnJhOxASKoa12PYUsT6+/olOUZu/EetQoafChmUrlsvjTzxhbIUnPVkIvkiIj5cxozKMrdDbNWT4MezFtruIddy4cTpKMpl7yyx98Xn3BoikiDVQ4D1jIK9OfU4gSf27F33qUzJ+/Hi9Ha4gtxYpX92BzARYB+ay+l8ekcuXLxvPXsf7HCCkPwx5sTWj1e4iVs8BIRNGNZELqsYmTZrUyT6AN2sKK6wF70wEnBvmXc67f3m3Y1DT25NGjvLab3xTr0eyTUQGhyEptrhwukut8o5WzIYrZtSKyI1ELhgUO3DgQIew4hHiGwwWfPRjjIBJnxmyYvvZT9/d5cJgxEr6g78RsKflxC9vYhLRYouodN/vft9hA3gOVjFiJYOF92Aqv+QJiDixNS2C55/d0iVyHaqZASSywBe9LwuL5+fwJiLF1juDgJEDCVcQGJiDs2YOMOCd1/AjLMUWgtpTBgE9MRLp+BpsY9AwtAkbsTXtAX8yCAiJdBDZ+rLCeK4PXcJKbJlBQIYb3oO8oeg3QcKDsLIR6GMR0hlcEyikQIe1ZV9eQSGOYAZcbHvzYwkh1/H2dmEzYHZjXjORx4CILf1YQvoGItvtL78ip0+fNvbwmolUBkxs6ccS0nfQFGj7K6/wbjCCGTAbgX4sIaEB1xYyGyDCvK7Cl5CIrfnHp7dESOjx9HVzFy3SohvubTCHI0GdyhyDXvjDY/QUf3wILiEktOBO0QQpZLDs0Pw9lOzfv1/WrVsnFoulY5k3b55s3rxZP79t2zbJz8/X66SdoIntU5s26bmrzG/YpKQkbRkQQkILpid6YdtWPXAG6urqtLcbCqqqquT++++XRSqChrA+/fTTgptjLPuU0ENgIbyrVq0yXkE6gI3QH2pqatzf/Ppj7uysSXqZc/Mt7ueefVbvJ4QMLL/Ytct950c+qh9DQU5ODmxHvShxNfZ2Rgmwfv7ChQvGHgKCIrbmH/gz//Bpd1FRkfEMISQcwPX5hfsf6HcAtHbt2g6hXblypbHXN7m5uRRbLwa8qIEQMrCYA2ioQoPlgKl8AgX2QXp6urElsnPnTlmyZImx1RVYDHh+ypQpxh7SJ88WU11jIYSEP+bYCQojvvjAg5L3yit6OxAwIOZJTk6OseYbFQVTaL0IWGwhsq/v3q0XCi4h4c/X1qzRDW4ABs/+bdOTAV+7zCzoPwGJrSm0ANkG4ycwl4+QSAD57t9+4jvGFhkM/PZsvYX2Zz9/rU/eDyFk8DAjWni3gXD48GGdR2vSm2dLuhKwjUChJSRygcgGKrQAHm1ubq6x1dXDJb0TUDYCvhVhHcADIoQML7yj2wsXLvgcBIO/i2yErVu3GnsICCiyxTcihZaQoQP6mCA1zJ8BM0S3qBJLS0vT2xBelOV6ApFFddnKlSuNPcSEebaEDGM8m9ig5NffrmEQVVgJnnYColyILNK+SFd8im11dbX899698vK2l9i5i5AhDJr6P7yyvY8Bm5L7Zvv27XLgwAEpLCzU2/fee6+s6cMdvk+x3bBhg7y64z9F1FP8AxAytPnqV1ZywkkPEGweO3ZM3njjDS20NTU1xjPXWbBggRbgQOgitvhBEFin0ylZ48bzwydkiINZINCWEQUPwzm4gvZBYBFsXrx40djbPevXr9fH+ksXscWLN27cqNdvnTNHDh89qtcJIUOX72/eLLt+vlNuzcmRmTfN1Kmd6JObnJxsHDG0gdDOUXrnj8iapKSk6Nf5SxexnTRpUscPXLhwobz11lt6nRAyNEGvBDT6R2TrCXLqMWazfMUKY8/QBZbAJz7xCWPLf6CP0El/6JT6BX/CU9kPvX8oIOUmhEQWaPqPXgneQgvMPgo4ZqiDILMvwNv1l05i6+0/1DfUaw+DEDL0wDRW21/J0+ttbW1Sdq1CCoou6QXr2AdwDI4dyvRVbAOhQ2y9o1oT7CeEDD3yXr7eavFKaYnU1ddrgcWCdewz8TyWXCc1NdVY650Ozxa+w8GDB/VObwoKCgZE+Ul4gNvGUydP6fXvrH+iUx+MqZMmG2udOV9YYKy1w+PaCffjAIQVkawvMkaMlKTERL3u+Z7h/u8F/hyLCjpzvrYjx47K2Q8/1Ov+EkhGgo5sYQ53J7SA0e3wAkL73l//qpfa2lpjLxmqtLpajbWu9PTcUOBycXHHuR5tCah7QcDod+9NmSm2wwuk/tx2++16GS6pP8MZa7TVWOtKT88NBcaNH99xrtvsNmOv/yBdzF8sR48edc+dO9fY7J5AUhwIIeGPZ+VY8dUr4nA69bpJjN0u48dm6vXcRYvkxZc6N50ZanjWGPhLIBZr1JYtW4zVdrImZmmfJiE+3tjTDqNbQoYW5txkIHP0mE7XPNaxz8Tz2KFKIFEqmD17dkBjWVE7duzQL3r22Wf1DJo/+MEz2hAfMypDvr5mjSxdulQfiBQw5twSMnRAh6/P3XefXo+KitLXfHbWJL1gHfsAjvG3G1gkE+ideyCZCCDq6NGjOjEXXWzwYvRBQH00+OP+P+iIFqEyOt0E2niBEBLetPeoXm1sdQXP9WVmh0gE+ocGM/4SaPBp8S7XBUiHQPke2ysSMjw4c+aMbP2PF+TAW2/pngi33zFfR7Pjxw+vSV0RXC5fvtzY6p1AxrJ8ii0hhAxX4MP625AGFqy/JbvRG/zNyCU+cblccuTQ+7Jn9y459P77uvrGarVJfHy8WCwW4yhCSKQAO2Hv3r3GVs+UlpZqsY2NjZXp06cbe33Ta2QLSwGJv5x7rCutra3y8Movy/lzZ3Q+Ij5KV5tbYuPiZcZNN8uGjU8yT5WENc9v2SLFRcXDxpf1l2XLlgmSBwIhLy9Pv647eo1sHzZy8ZD8O5PTl3eA5ur/smqFnDzxgWSMHCnR1iiJjo5WS5SKdlvlyuViOXnyhHz84wvEHhNjvIqQ8AFNwzHR43EVmUFwF9019DMO/AUJAYhYz549a+zpHSQQjBkzptsUsl7r08zIbO03vimnT7XXyw93EMF+89FHpKzksmSOHa2i2TZJHzFKRmWMliiLEt2oKLHbrVKQny/f+vpqaWlpMV5JSPgAoTVbK/La7kqg84xh+hwMrsHz9ZW51avYvvDSNt1EGHzxgQf5R1G8+86f5dzZU+JwtkpJaYVYbTFy7tx5OXHib9LQ0ChWq1UJbrRUV1VpW2Hv6+2NLggJFzDRI/oBAFzfP/35a3qdXKevdQUYXEMjcu9CML+yEeDrPL/lOb0+3CeAhE/7xc9/Rmpq66Ss/Jr6Fpss6SNVVDs6U9xtLiXCp6XoYqGMyxwjzQ6nxCUkSlpKqvxw60sSH59gvAshgweaC2HOMUxhDqH9mRJaz85upJ1AshK6w9PH9avNzbIVKzqiW+TgDWdOnjgmLS2tUlhYJOPGT5DRo0dLfX2tnDx+WN59+6A01NfJrfPmSXVtvfZvL5y/IMmpKXLgj9fn1ydksMF1jMCJQusb2AD9FVoAW8FMDfNLbOHbLv/yCl22N9xHLX/5xh65fLVUMpTIjho5UhobG2XUqDGSfcN0ue2OOyUxMUX+8s7bMnlKtoqCXVJfV6vthp0/+4lcqyg33oWQwQPXM65j3KFSaH3jb+6sP2CwDbCoIQCam5rkc5+9SwoKL8n8j3xULOIWq9WuPkURmy1OWl0usdtsUl1TJWdOfiBTp06ViooyaWxqlptmTtc5uD/eQW+MDCywDR564EFZpgImVoT6RzAsBE9gJ/gV2XYHRjPh/SCFZDhw4I/7pNaYWx/+KwbGHM2NammTutoGaXa0Sn1Ds3ouSSZlT5MGFfUmJyXrAgd0w8exR48cMt6NkNBjCu3p06d1CT7pHUS1wRRagAzbfoktJoHDHxGCi0G0od7V/+3/OaCi1lqZkDVFLJZocWO+JrdVRawuiYpW2yqybW1pUaLbIhmjx0lVVbXEJyRKtNUqNTV1Eq2i3ud/8LT8+U+cHp6EHgRBptCC4T7e4i+hmOQW4t0vsUUzYQycIVcP2QoLPvoxLbpDEbgtR48el+hoq6SkJGtLwBIFoXWLzR4jrU6HWm/RJbpuV5s01DfKmMzx0tjUJG1KhJubmsWmBNnlcsq2/9giB/7Q3rSZkGCDoAfXIYIgU2g53uI/oepu2C+xhbmO0UwzUwGii0qUoUhZWalcuXpV0tPTVTSrPjj1yTkdrVpcUbTgVv9FR8dIi7NJXK0OtbRIauoIHV3ASnA4HOo4l7So/RZLm7z04hb59d7dxrsTElwwiaFZsLBsxXIKbQAEc3DMk36JLYDg6lHNGTOG9Lfn3t07tYCmp4/QdkFzs1MJaJNEqUi3tcXRHt22NInNFqvENEpFs63idLZIYmKSEuc2sdvtUllVLZWV9WqpUZGyS3726o/lhee/r20IQoIFsg3QHhVjCy9s2yqPP/GE8QzxB1SChYJ+iy3AH/eXv3mzi9CiiQ2sBVSrRDoH3/qDuj2rk7S0VC26TodTWwpKeZWQxkpba6tEW226LwIWSxTsBJdkjs+S8rJyiYuPk9q6eqmqqZVTp8/L1ZIqaW1tk7f++Dt5Ne8lbVMQ0hfM6wyPJsg6QBA0HGZYCCahimpBUMS2OzD6iSqVh1eu0pPLRWrWAtoolpaViNVmlZjYON2EBgNhGPjS3q1FHdPWqoRX1HarEl9EubANnJKUlKIi2UoV8dpUNOyQmJgY/ZqiomIpulImLa0W2fP6a3LvZ3LlL++8o5sRHzlyWP9MQnoi75VXtMiibwmuM2Yb9J9QTv0VUrHFJHGmn4vOYWbWQqRRV1crTY0OGTNmrIpoHbpYATaA+p+OSJ2OZp0GBuvAZrMrMW5WUS+mRXZLddU1GTkqQ0XDrep1LQJltkShM5hLSq6WSuHFImlobtPz8x9670/y2n+9Ji+++GP5+tcfk3dUZMKIl3iCwS8zkv23TU9qkQWwDGAdkPAlpGKLHriwFzAnO4BhD+M+0qitqZGmZuTPxikRjVYRarMSzGhtJ8BKcLvbENLqY5F5oDMStBi7lEjXSUJigtQ3NIjNapP6uhrJmjhWbrppqsTFxSoxrtYRf12jUw4fOSYL7rxd4uLj9SDc9u0/0aXAhHhi3jECiOzmZ76vLQMWLIQ3IRVbgDmMkLEAoz5Sv31RZguxTU5OUULbhIBWiywiVWQhYJBMR7NWq7S0Gl6uwqLEtaS0VM9SCuvBZreJw+GUOTNTZf6sWJlz8zhJSowTh3rvqooK+duJk5KZOUb9UVy6Ms0eGyu/+fVv9HuR4Yn3uIfn4BdFNrIIudiawKj3dWLgZJo6abLMvWWWPLVpU1gWRpSVlihBdEhq2ghpbmpEdS7sWS2y16Nblx4Ys6rIF4NjaK3obGqSqTfcJLGx8dLa0qozFnBMdV2LTJuaJJ++M1nGjE7Rb4ZS4Cb13i+/nCdzZs/U9gEsif1/PKCzHsjwwtuP3fe764PM5uAXRTayGDCx7Q7T1IfFsP2VPH2ChZuvW1l5TVsFCfEYHGtpzzSAbYAQV+13uZA7G609W3i18GNbmhtV5OuU6spSPUiG2Rri4+LUMW1SfLlKfvqLAiksbpYbpySr16hYtrXdA373nXe1v1tXU6l/JnrjHj181PhNyFCmOz8WDIWMnuHOoIst0sVgMSBH17MaLZyoKC/X84qhly3aK+rItg3erA5K1bpb+7QAg18OFaHCXoBYoon4tfIyFd3G6WNgKbS6otXtYKK8f6xcUpITJC7Wpo7FO1n0cTfdPEMmTBgrLQ6HuJWA73n9df3eZOjj6cfiesB1gesD1Zokshl0sUW9NiwGiC5ujb62ZrU+yTztBHzbmzbDYHzDlyuxTExMVLfzzbqzFwbHkOLlQjGCinDbENki2lWC2aYWt1G2q/+zuPVkkIh2o9UxiFRr65slIcGmI9qz5yskY2Si/jnwg212q7zz9jsy7YZsnTqG97xy5ap6rlEfQyIfnNs4j3E+47w2Mf1YnP+4DnA94LrA9cG+BpFPRLRYxG2V5y0VQIYDUssGwrda/c9fkffeP6SnKr56tVTSUtO1V2uNiRG3inYhuu2pXy6xx8RLc0OtjmwxgIbnopQ419bVSnJSonz44Ycqko2Wm28cIfUNSkzV953dGi3vHy/S+bcpaWlyx+23yYNf+pL8Z96rYrXHikOJ8IYnN8ikSdnGb0QiDVNgkY1jTkdjcr6wwFgjgw36ImBKm1Aw6JGtP5ijr57ghB2oJO6q6iodhcICgDUAwwADXYhq9XcVolnsV9Es/FtUksG7tSkBtttixRZt19Et+iKgdLehqUX+drpUkhNjdH+F+Di7ZIwaITOmT5Mbp02Rc+fO6cbkKBts0Q1u2qTgQn77L0MiFpyv3kILm4AMDyJCbM3RV6S65C5aZOxtF2FPYDegcAKPwcxqQC4sfFnoKmbPdbY6YK9qtJWggIeLA7SfC69WRatYMDBmU4vdZlfC2W4v4D0qa5rl0pU6PQtvUoJFiW6TnD5zTo4ePSEJ8XZ54UcvyIKFd4oLTW7Uzz5/7rz+OSS4IJIJVks9b3sA56GJaRGY4Dz+6Wv/NWR7iUQqoSzXHVIzNXjbDcGyGv7hkx9Xt/xNcsO0G+VKcbGkpY3QebXoiaBzbVXkCRGFleBqcWoxxUAZiIqyiCU6Whoa6rXvWlZeLk1NTboSbfzYZElNiZMbJibKkZPXpKCoUr8Pih0wh//NN8+Sgwf+pEV+ypTJsum7T+v3JP0HZZlo6Pzcc8/pEumFCxcazwRGT/YA7sYQJJDIAefExo0bja3gkZWVFRmRrb8gcjCr1QBOfuQp9hdEltFKPJELi4EufD/hGwrRLG7xXWpB5y5YCw1KUOubGqSuoU4JdJ3U1NVKnbogIcp19XV61gZEvqCuwale45ZWV5seMDNxqmg2ISFR3ntPXbz4Wer9y5VIk+CAaHbOnDlaaEFfhdbElz2A89D7zouEP6HqZYtpdoaU2CKCRbUaBhyQLoM+nt6ZDQBFFFi++MCDOqcXkQlmneiOGTNv1o+wBTSW9inN4b9CZCG8yEJA9kBjs0OJaKPU1jdKlfq51Zjy/FqFOBEBqwORjYBHRLAOBzqEufWCzAVgt9u0N4ySYGQvIOuhze3SQk36B6LZNWvW6AEQc9qTBQsW6MfuOH3qVIc1gPPFPHdMPDMIcL7hvMP5h/OQRQeRR2FhobEWfIblhI+eF4sn3Y0Kf/fJjfLbN38l4yZM1NVkI9JHalsgNhY2AgSzTQ+gQXCvXavUIoxoFOILTxfR7+jRY8SuhLasrKw9wo2LkxZns2SMSpRpWclytaJZPjh1VYsw0sg+fffd6nmn9osBftaOn+3U6yRw4MtCaL3nllq9erVs6aGIJtBzhUQ2uP5CwdKlS4dWZOsvGJhABIJcRk/bwRMMbphRzJu/flNq6xqkrq5empqatajiGwoFC/iqQscueLQQ3lZXiy6vhafrhNi6ILbtBRBow4ipzwG2MzNHq+Nc4nC26ckiAb77UpJR3FEvX3joIf16/IwkFUH1BJrZmNGXuaDkM5gDhZEIollMJb148WKfk/iVlZb5jFi90baAOl9w3uD8IUOPUA6OwUYYlpGtP/jK7QVWa7RMv/EGXeCQrG4dMcdYS6tLYmLQWtEp5RXlHcUIpr8LK2DC+Cw9WFZ0qUja1H/OZqdO83I4GmRUqlUuXamVkrJayc6eot8r91OfkvwL+VJytUQpsMjsuXPk8Q1PGb9FZyCyKHX2BW5vcUuLGTWGG4hmly1b1mPn/Ux1xxGn7hpMGLEOX3C+4Es5FPR7KvOhjFlGjGhm5Ih0Yy/EK0GHpYhtMf1NTW29nD9fICdPnpVz5wrUbX+9NNQ7pbGhxXiFHuPSTWjwiNeY/mzx5SvqQo8Xqz1FEpNS5ZZbZurOYEXFl+Whf3pITp8+oyJmq46kJ2ejoKHr9yI8Z0+hheCjQxmibIDyZ0Ru8B6HA4hOp0zMksSEBH3h9DbFSZT68mTESkCoI1uKbTeYZcToybv4vntkxIhkmX9HjsTHx+pZGpDe5XIjS6DCeEVn4OFq/1UvUVJf1yD5+UXaMmhpsUhUdKw4lR4XXy6TS8VXtCicOHFKRdNXZfKUyUrA89s7iKn3wgy+02+crtY6+0mwDsw+EvCFr5SWSNHVK/rx4uViqapp93shuE9u3KTXIxFYIbB1PG/3u7vtx+eAf3uDYdf0RrG6e5moLgSWxJJQDo4h+4U2gh/8eOuP5Llnn1Vie4cSwfMSFxevMwViVLRapUQSUWRsTKzOIGhobFLCWaci1CixWttnZMBH7G6zKpG9Hu2aIB13ZHqcVFyrUc+7JNoaZzzTmb+8946MyhhrbLWDqNYUWwgsIlpvxozKkIT4eL1+4M//o/sLhxO+BBN43s5DbG+dNdvY6oz3bT+KCZBbPXLUKDn74YdyTi2HjxyRkpIS44iupKSk6AstNTXV2EOGI0gBPHjwoLEVPHB+YeyAYusHv/rvPfLIw1+Vz95zj5w9c0ZsVrvExsZo8cTHZ7NFK8FFq0V4tzFSUlamB8mQd4tPF/szx45XEbFTWwS6HaOKVkGM3SLJSbFSUlqpol0VyVrser83H+afV8JspJ4pPEUKYo9ozhfwI+FLeuMtUv6IHhjs4zBQNf+O+dqDRtqVv9EoTnbkUOJWEY/eF9U96m8brEoyEpmEKhPBPLdoI/jBqIzR2i1tanaoW3v1kVncuhUibutx26pn14WL61brNruevtxuj1OiHCNoLJ6cnCqpaanqMVEd0yIjRyTKDdmjVcSJARq1T70TcnhRORYXb5OPfPQ2ycgYIUlJ7d3AgKfQetNi+LORTG+j/RBfLBjsg7UT6G0/olZkJaBCCGKLL0lUjj2r7lhwMUCEKbbDl1BbCMDCyLZ3zp45Jffd81mZNn2GuF0tOvsgMSFJ59qiSMFms0p9fb2u+nI4nWJVgosUL+TaxsUn6HSwGJtN59WePHVSRo0aIfExyMttU1GpSE1tox4IS0lJllmzZ8nffzJXXt3xqsQq8cXMEC/l7VC3xaON3+Y633rsG/L67t16vaDokhZ+b1JU9Dcy7foAn8mRD47ryNCkr5EoRHKguq8REirwBRyqbl9mOTjF1g8qysvk7rv+XhISk2XK5ElSXlahIlGr7m+QkJioHp2IcbVg1isBTlAhq7OlTdKUyJWWXdWlvhYlrLAe/nbyb0rkksSmAlUnPNpou9QpocYMvOPGjpbFSrR+++Zv9TQ8bS63ZGdnyXef8d1MHZVNmCYeYECoRP2ensTY7dpCQEUaUsCOnvjAeIYQ4gkKWx599FFjK7iYEksbwQ/iVXRqQ5ktSnP1B9feJDxeiSqms9GRa6xad7UqgbPpCLNVRbEVSmgxxQ1EF/0THEqc4ctibrEoJbIpKWlSW1enxXfihEz1/m6x22OkurpG/Rx4vU554Ev/1P5L+AC30jNmzNDrGASbMDZTkpT4w6dNV7fNptAC1ukT0j2hshE8y8Eptn4QGxenCw1QbWS12ZSY2XTzcJstVolim+5VC/HFQFhCQpK0KgFOSkrW+2JVdInXQIQxnTm81/r6RqmtbZCy8grJyMiQadNu1Pvn3HqrvPmrX2s/GO9x1913y6zZtxq/hW9eeGlbR69fu/pZGSNGapFNS0ntEFr0TF2+YoVeJ4R0JVQ5tp5Njii2fgDRmjVrtjQ7mlWEqm7PY2K1sGE+Mi2ocfF6Spu4+Dh9TIKKhJsdTfrWHV2+8Jzuo9ACgbbpmXajbVbJyposN06bLhb1Z2iob5KDf3pbxcxRMjpjlGx86kn5ylcf0Tm6PYFUrl/+5k2fTajN6a7ZM5WQngllQYMJPVs/+cmOH8v3nn5aZs68WVKSE6W2plaana26fBepYE1N9WKPwey77X1uRTD41SbJKSly9cplSU1NloKCQj0oho98UtYUSUtN0+ljcSpy/uGLW3UE3F/M7mUY/BqOJbqEBArSAtPS0oyt4LJ+/XqdAQMY2frJ/Pkfk6TEBPWHqRKbPU5iYmPE3QaxReZBvYpgE5XQOnT5LewEfLQQ3Ti1PzEpUUWu9ToNLDYmRm6dO08LLSaPTFDR778/84OgCC1AOhQWCi0h/hHKqNbzvSm2fjJhYpYkJCTo0ld0+EJ6V3xcgope260BpHyhoAENauwxsXrAzKbEtqamUjes0YNmra16PQr9DtR7jp84UZ774Y9C9q1KCOmdUIotomYTiq2fYJBs4oSJUqM+PIeKYGNi2qNbZCDYlbC63S7tvSKSRYYC0sLilThXXatAaYruDobChREjRgqKxyZNzpbvrN+ghZoQMniEsqDBE4ptADy27nE96AUPNiraqiLU9pkVmhvRSLx9uhuILwTUpsQYrRXHjB0n1dfKdWSLjIP4pDSZefNN8v8e/7aOhAkhg8tADI4Bim0A3Dh9hsTFxejZGhyORrHHJIq7rUVnJmBgzGqHfZAgVlusJCbGS21ttRJhu85mQOZCtBLhzHET5F+/9jVdeUYIGXw8b/VDCcU2AKKjo+W22+dLTXWNVFdVqWjVKckp6UpsUaGVrETVIm2uFiWwaEzjlNgYu1w4d1byCy6q41LVc63y+He+TaElJEyAhXD8+HFjK7RQbAPk7s/8o0yYMF7Onz+npySHnZCQlK6rzMZkZkrm+Ik6ir1YcEF3EcJgWnOzQ0XBMXLffUu0YIeCzZs3S3p6ulSpLwFCiH/0NP9cMEDTcBOKbYDcOu82SYiP0QNgaDztdDTpcl2U4zY11EvRxfNy4cJZmXrDjVJWckVbDKPHjlXR8DX550f+1XiX4LNt2zYttLt27TL2EEJ6Y/v27cZaaGAFWT+AXXDnJ3LlhhuypbTkqp5N16rbH6L3QbOkpKXL1KnT5MOzp3TBAyZujLKI/K+7P6PLcEPB/v37JT8/X69TbAnxD7TU7G3apP6Ctp4mFNs+8Mjqb0hbq0tumjFdii5dkrKyUl0dVlpWLseOHpEPz5yStJQkwRTnTmeLxMVY5X8v/z/Gq4MPoloTCO/hw4eNLUJId4Q6CyErK6vT7B8U2z6AlK1Hv/V/BVOUT5w4Xi5fLpYxY8fKhIkTZV5OjkycME43GscUOWlpqfJ3t90hYzPbm8UEG0S0WHJzc409jG4J8YdQZyGYTcNNKLZ95BOf/JTcdfc/6qqwCeMzpbmhRsovF0rxpQLdSrGxCT0SYmT27O6nIA8GENYlS5boxcT0bwkh3RPqyJZiG0RWPvyILLrrbiksvCQVFdek2dGixNcl1TV1EhefJLff8RHZ9N3vBa3vgS8gtitXrtSLWfbLgTJCesczU2AgoNj2kzWPfUtefGm75PzdRyQ+IUlm3DJXln/lYXnq3zfLhk1PhTSnFoKak5PTIbIQXBNPH5cQ0hXPTIFQ4P3+bLEYwSxatEjWrl3b4ddiYGzevHl6HRw6dEiLMSHEN8uWLZMdO3YYW8HFnHvMhJFthIJBMWQeQHB18YRaPIUWMLolpGeQZ5uXlyezZ8829oQOim2EgoqxrVu36kbkngv2mcBm4EAZIT2D6BaDZUuXLjX2hAbaCBEIhHbdunVaXL2BuCLCNYscYDHs3LmTPXMJ6YVgz9hQUFDQaRCOYhthwC7wBINiZjRr2gq+2LdvX6dcXEJIV7yvr/7gLa0UW0IIMcCA1sGDB42t/uEtrfRsCSHEIJS5txRbQggx8K76CiYUW0IIMQil2NKzJYQQg2BmJNCzJYSQbkBLRLRGDAUUW0II8SBUVgLFlhBCPAiW2Hr3y6XYEkKIB8HqBoZpdzyh2BJCiAfBimwPHDhgrLXDbARCCPECA2X9nQwyJSWlk5XAyJYQQrwIRnQLsfaceodiSwghXgTLt6XYEkJIDwTLt6XYEkJIDzCyJYSQAQADZOvXrze2+o6n2DIbgRBCfFBYWCiTJ082tvqOKbGMbAkhxAfobRuMPglmvi3FlhBCuiFY3i2g2BJCSDcEQ2xhRwCKLSGEdMO9995rrPUdii0hhPQCshLuueceY6t/UGwJIaQHli1bZqz1D4otIYT0AKwENJXpK7QRCCHET/oT3VJsCSHET+Dd9heKLSGEDAAUW0IIGQAotoQQMgBQbAkhJISYnb8otoQQEkLMucwotoQQMgBQbAkhZACg2BJCyABAsSWEkAGAYksIISEGJbsUW0II6QVzapu+QrElhJABgmJLCCEDAMWWEEIGAIotIYT0QjBma6DYEkJIL0Bs8/LyjK2+QbElhBA/MGdc6Atz5syh2BJCIoOqqirZvHmzpKeni8Vi6bRgf35+vnFkaNi+fbuxFhhLly7VMz1QbAkhYc/+/fslOztb1q1bJ1OmTJFDhw6J2+2WyspKWbJkid6P53ft2mW8Irhs2bJFLl68aGwFxsKFC/WjRf3Cbr1GCCFhyOHDh2XevHl63RTatLQ0vW2yaNEiLchg586dWoCDyaRJk/ostnv27NEz9DKyJYSENffff7+xJrJy5couQguw32TVqlXacggW/YlqAZuHE0LCHkS1nl5sTk6OsdYZz/0QWjPK7S9vvPGGbNiwwdjqHxRbQkjY4i2asBF84b0fIt0fkHmAW//Fixd3zLTQV8y+ChRbQsiQo682AiJZ5NROnjxZ9u7da+wNDhRbQsiQo7sI2Jvq6modwWIADClkiGR37NhhPBtcKLaEkLAlNzfXWGunu1xa7/3+ii2iWESw/RkA6w0OkBFCwh4MfHkKbnderKe3C6ENdupXfzA9X+bZEkLCGkStyLOFDwsh9ZVni+dNIcbz3WUteAMbAZVheMRiRqGo+EKJLcAjMhKOHz+utwNl9uzZ7e8LsSWEkHBGCahbCS0CQ7eKdN0XLlzQ+ysrK90qitX7lQC79+3bp/cHk7y8PP3+gSwpKSnupUuXuvfs2WO8i9vNyJYQEjGgBwJKcj3tBES7KGroruChv2AAzd/MhAULFsiaNWv0a7yh2BJCSA8gTxZVZLAZfAGbAdkMZlZDd1BsCSFkAGA2AiGEDAAUW0IIGQAotoQQEnJE/j+6jXvSg/473gAAAABJRU5ErkJggg==)
In a triangle ABC, if a : b : c = 7 : 8 : 9, then cos A : cos B equals to
In a triangle ABC, if a : b : c = 7 : 8 : 9, then cos A : cos B equals to
Which of the following curves represents correctly the oscillation given by ![y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90](data:image/png;base64,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)
![](data:image/png;base64,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)
Which of the following curves represents correctly the oscillation given by ![y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90](data:image/png;base64,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)
![](data:image/png;base64,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)
A is a set containing n elements. A subset P1 is chosen, and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1
P2
…
Pm= A is -
A is a set containing n elements. A subset P1 is chosen, and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1
P2
…
Pm= A is -
The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x|
k, |y|
k, |x – y|
k ; is-
The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x|
k, |y|
k, |x – y|
k ; is-
The angle between the lines
and
is
Here we used the concept of cartesian lines and some trigonometric terms to solve. With the help of slope we identified the angle between them. Hence, these lines are perpendicular so the angle between them is 90 degrees.
The angle between the lines
and
is
Here we used the concept of cartesian lines and some trigonometric terms to solve. With the help of slope we identified the angle between them. Hence, these lines are perpendicular so the angle between them is 90 degrees.