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Category: Coordinate Geometry

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}}…

Question-166063

Question Number 166063 by cortano1 last updated on 12/Feb/22 Commented by blackmamba last updated on 12/Feb/22 $$\:\mathrm{tan}\:\alpha=\frac{\mathrm{2}}{\mathrm{6}−\mathrm{2}\sqrt{\mathrm{3}}}=\frac{\mathrm{1}}{\mathrm{3}−\sqrt{\mathrm{3}}}=\frac{\mathrm{3}+\sqrt{\mathrm{3}}}{\mathrm{6}} \\ $$$$\:\mathrm{tan}\:\mathrm{2}\alpha=\frac{\mathrm{2}\left(\mathrm{15}+\mathrm{7}\sqrt{\mathrm{3}}\right)}{\mathrm{13}} \\ $$$$\:\mathrm{tan}\:\left(\mathrm{90}°−\mathrm{2}\alpha\right)=\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{2}\alpha}=\frac{\mathrm{15}−\mathrm{7}\sqrt{\mathrm{3}}}{\mathrm{12}} \\ $$$$\:{m}=\frac{\mathrm{15}−\mathrm{7}\sqrt{\mathrm{3}}}{\mathrm{12}} \\ $$…