Question Number 103190 by bemath last updated on 13/Jul/20 $$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tan}\:{x}\right)\right)\:{dx}\: \\ $$ Answered by abdomathmax last updated on 13/Jul/20 $$\mathrm{ln}\left(\mathrm{tanx}\right)\:=\mathrm{t}\:\Rightarrow\:\mathrm{I}\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tanx}\right)\right)\mathrm{dx} \\…
Question Number 168121 by rexford last updated on 03/Apr/22 Answered by FelipeLz last updated on 04/Apr/22 $$\overset{\rightarrow} {{r}}\:=\:\left({a},\:{b},\:{c}\right) \\ $$$$\left.\begin{matrix}{\overset{\rightarrow} {{r}}\centerdot\hat {\imath}\:=\:{a}}\\{\overset{\rightarrow} {{r}}\centerdot\hat {\jmath}\:=\:{b}}\\{\overset{\rightarrow} {{r}}\centerdot\hat…
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Question Number 101766 by 175mohamed last updated on 04/Jul/20 Commented by mr W last updated on 04/Jul/20 $$\mathrm{1}\:{m}^{\mathrm{3}} =\mathrm{100}^{\mathrm{3}} \:{cm}^{\mathrm{3}} \\ $$$$\frac{\mathrm{100}^{\mathrm{3}} \:{cm}^{\mathrm{3}} }{\mathrm{5}×\mathrm{4}×\mathrm{1}\:{cm}^{\mathrm{3}} }=\mathrm{50}\:\mathrm{000}…
Question Number 35789 by ajfour last updated on 23/May/18 Commented by ajfour last updated on 23/May/18 $${How}\:{many}\:{skew}\:{pair}\:{of}\:{lines} \\ $$$${are}\:{there}\:\left({when}\:{a}\:{line}\:{is}\:{drawn}\right. \\ $$$${by}\:{joining}\:{any}\:{two}\:{vertices} \\ $$$$\left.{of}\:{the}\:{cube}\right)\:? \\ $$…
Question Number 35430 by ajfour last updated on 18/May/18 Commented by ajfour last updated on 19/May/18 $${Solution}\:{to}\:{Q}.\mathrm{35422}\:\left({Find}\:{P}\:{Q}\right) \\ $$ Answered by ajfour last updated on…
Question Number 35422 by ajfour last updated on 18/May/18 Commented by ajfour last updated on 19/May/18 $${Sphere}\:{of}\:{radius}\:{R}\:{touches} \\ $$$${plane}\:{at}\:{B}.\:{Line}\:{APQ}\:{intersects} \\ $$$${sphere}\:{at}\:{P}\:{and}\:{Q}.\: \\ $$$${minimum}\:{angle}\:{that}\:{line}\:{makes} \\ $$$${with}\:{plane}\:{is}\:\theta.\:{From}\:{this}\:…
Question Number 100850 by Dwaipayan Shikari last updated on 28/Jun/20 $$\int_{\mathrm{0}} ^{\mathrm{102}} \left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…..\left({x}−\mathrm{100}\right)×\left(\frac{\mathrm{1}}{{x}−\mathrm{1}}+\frac{\mathrm{1}}{{x}−\mathrm{2}}+…+\frac{\mathrm{1}}{{x}−\mathrm{100}}\right){dx} \\ $$ Commented by Dwaipayan Shikari last updated on 28/Jun/20 $$\int_{\mathrm{0}} ^{\mathrm{102}}…
Question Number 166134 by amin96 last updated on 13/Feb/22 Answered by MJS_new last updated on 14/Feb/22 $$\mathrm{you}\:\mathrm{need}\:\mathrm{the}\:\mathrm{trigonometric}\:\mathrm{method}\:\mathrm{to}\:\mathrm{get} \\ $$$${x}_{\mathrm{1}} =−\mathrm{cos}\:\frac{\pi}{\mathrm{9}} \\ $$$${x}_{\mathrm{2}} =\mathrm{sin}\:\frac{\pi}{\mathrm{18}} \\ $$$${x}_{\mathrm{3}}…