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Category: Coordinate Geometry

Question-35439

Question Number 35439 by ajfour last updated on 19/May/18 Commented by ajfour last updated on 19/May/18 $${The}\:{radius}\:{of}\:{sphere}\:{is}\:{R}.\:{It} \\ $$$${touches}\:{the}\:{lower}\:{plane}\:{at}\:{A}\:{at} \\ $$$${a}\:{distance}\:{AH}={a}\:{from}\:{line}\:{of} \\ $$$${intersection}\:{of}\:{planes}\:\left({that}\:{make}\:\right. \\ $$$${an}\:{angle}\:\theta\:{with}\:{each}\:{other}.\:{Sphere}…

Question-166143

Question Number 166143 by Tawa11 last updated on 13/Feb/22 Answered by som(math1967) last updated on 14/Feb/22 $$\:{y}=\left(\mathrm{2}−\sqrt{{x}}\right)^{\mathrm{4}} \\ $$$$\:\frac{{dy}}{{dx}}=−\mathrm{4}\left(\mathrm{2}−\sqrt{{x}}\right)^{\mathrm{3}} ×\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}=−\frac{\mathrm{2}\left(\mathrm{2}−\sqrt{{x}}\right)^{\mathrm{3}} }{\:\sqrt{{x}}} \\ $$$$\left[\frac{{dy}}{{dx}}\right]_{\left(\mathrm{1},\mathrm{1}\right)} =\frac{\mathrm{2}\left(\mathrm{2}−\mathrm{1}\right)^{\mathrm{3}} }{\mathrm{1}}=−\mathrm{2}…

Question-166104

Question Number 166104 by oustmuchiya@gmail.com last updated on 13/Feb/22 Answered by nikif99 last updated on 13/Feb/22 $${A}:\:\left({A}_{{x}} ,{A}_{{y}} \right)=\left(−\mathrm{5},\mathrm{1}\right),\:{B}:\:\left({B}_{{x}} ,{B}_{{y}} \right)=\left(−\mathrm{7},−\mathrm{8}\right),\: \\ $$$${C}:\:\left({C}_{{x}} ,{C}_{{y}} \right),\:{D}:\:\left({D}_{{x}}…