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Category: Coordinate Geometry

for-x-y-R-x-y-gt-0-satisfy-the-equation-x-3-y-xy-3-24-x-2-y-2-10-find-the-possible-value-of-x-y-a-6-b-5-c-4-d-3-2-e-2-

Question Number 87561 by jagoll last updated on 05/Apr/20 $$\mathrm{for}\:\mathrm{x},\mathrm{y}\:\in\mathbb{R}\:,\: \\ $$$$\mathrm{x}\:,\mathrm{y}\:>\:\mathrm{0}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{3}} \mathrm{y}−\mathrm{xy}^{\mathrm{3}} \:=\:\mathrm{24}}\\{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{10}\:}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{6}\:\:\:\left(\mathrm{b}\right)\:\mathrm{5}\:\:\:\left(\mathrm{c}\right)\:\mathrm{4}\:\:\:\left(\mathrm{d}\right)\:\mathrm{3}\sqrt{\mathrm{2}}\:\:\left(\mathrm{e}\right)\:\mathrm{2} \\ $$ Commented…

Question-152682

Question Number 152682 by alcohol last updated on 31/Aug/21 Answered by Olaf_Thorendsen last updated on 31/Aug/21 $$\mathrm{Time}\:\mathrm{taken}\:\mathrm{1}\:\mathrm{second}. \\ $$$$\mathrm{Potential}\:\mathrm{energy}\:\mathrm{E}_{\mathrm{P}} \:: \\ $$$$\mathrm{E}_{\mathrm{P}} \:=\:{mgh}\:=\:\mathrm{50}×\mathrm{9},\mathrm{81}×\mathrm{40}\:=\:\mathrm{19620}\:\mathrm{J} \\ $$$$\mathrm{Kinetic}\:\mathrm{energy}\:\mathrm{E}_{\mathrm{K}}…

Question-151899

Question Number 151899 by liberty last updated on 24/Aug/21 Answered by john_santu last updated on 24/Aug/21 $$\mathrm{A}=\int_{\mathrm{0}} ^{\mathrm{6}} \left(\frac{−\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}+\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}=\left[−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{24}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}\right]_{\mathrm{0}} ^{\mathrm{6}} \\…

Question-20819

Question Number 20819 by ajfour last updated on 03/Sep/17 Commented by ajfour last updated on 03/Sep/17 $${A}\:{particle}\:{moves}\:{along}\:{the}\:{spiral} \\ $$$${shown}.\:{Determine}\:{the}\:{magnitude} \\ $$$${of}\:{the}\:{velocity}\:{of}\:{the}\:{particle}\:{in} \\ $$$${terms}\:{of}\:\boldsymbol{{b}},\:\boldsymbol{\theta},\:\overset{.} {\boldsymbol{\theta}}\:. \\…

Question-86063

Question Number 86063 by john santu last updated on 26/Mar/20 Answered by mr W last updated on 26/Mar/20 $$\left(\frac{\mathrm{1}}{{R}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{6}}−\frac{\mathrm{1}}{\mathrm{9}}\right)^{\mathrm{2}} =\mathrm{2}\left(\frac{\mathrm{1}}{{R}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{9}^{\mathrm{2}} }\right) \\…

Given-a-sphere-of-unit-radius-Find-the-expression-of-a-circular-spot-on-the-sphere-s-surface-given-the-latitude-and-the-longitude-of-its-center-and-its-angular-radius-r-

Question Number 20511 by dioph last updated on 27/Aug/17 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{sphere}\:\mathrm{of}\:\mathrm{unit}\:\mathrm{radius}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circular} \\ $$$$\mathrm{spot}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sphere}'\mathrm{s}\:\mathrm{surface}\:\mathrm{given} \\ $$$$\mathrm{the}\:\mathrm{latitude}\:\beta\:\mathrm{and}\:\mathrm{the}\:\mathrm{longitude}\:\lambda \\ $$$$\mathrm{of}\:\mathrm{its}\:\mathrm{center}\:\mathrm{and}\:\mathrm{its}\:\mathrm{angular}\:\mathrm{radius}\:{r}. \\ $$ Terms of Service Privacy Policy…

Find-two-possible-values-of-p-if-the-lines-px-y-0-and-3x-y-1-0-intersect-at-45-

Question Number 151513 by pete last updated on 21/Aug/21 $$\mathrm{Find}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{p}\:\mathrm{if}\:\mathrm{the}\:\mathrm{lines} \\ $$$${px}−{y}=\mathrm{0}\:\mathrm{and}\:\mathrm{3}{x}+{y}+\mathrm{1}=\mathrm{0}\:\mathrm{intersect}\:\mathrm{at}\:\mathrm{45}° \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $$\Delta_{\mathrm{1}} \::\:{px}−{y}\:=\:\mathrm{0} \\ $$$$\Delta_{\mathrm{2}}…