Question Number 222758 by chidera last updated on 06/Jul/25 Commented by chidera last updated on 06/Jul/25 $${pls} \\ $$$$ \\ $$ Answered by fantastic last…
Question Number 222753 by mr W last updated on 06/Jul/25 Answered by A5T last updated on 07/Jul/25 $$\mathrm{Let}\:\theta\:\mathrm{be}\:\mathrm{the}\:\mathrm{base}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}\:\mathrm{isosceles}\:\bigtriangleup \\ $$$$\mathrm{180}−\mathrm{2}\theta+\mathrm{180}−\left(\mathrm{2}\left(\mathrm{180}−\theta−?\right)\right)+\mathrm{90}=\mathrm{180} \\ $$$$\Rightarrow\mathrm{2}?=\mathrm{90}\Rightarrow?=\mathrm{45}° \\ $$ Commented…
Question Number 222754 by hardmath last updated on 06/Jul/25 Commented by hardmath last updated on 06/Jul/25 $$\int_{\mathrm{0}} ^{\:\mathrm{8}} \left(\mathrm{f}^{\:−\mathrm{1}} \left(\mathrm{x}\right)\:−\:\mathrm{f}\left(\mathrm{x}\right)\right)\:\mathrm{dx}\:=\:\mathrm{12} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{8}} \:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\…
Question Number 222684 by alvan545 last updated on 05/Jul/25 Commented by alvan545 last updated on 05/Jul/25 Answered by mr W last updated on 05/Jul/25 Commented…
Question Number 222685 by gabthemathguy25 last updated on 05/Jul/25 Answered by mr W last updated on 05/Jul/25 $$\mathrm{tan}\:\left({A}−\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{tan}\:\left(\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{7}}\right) \\ $$$$\frac{\mathrm{tan}\:{A}−\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{tan}\:{A}}=\frac{\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{7}}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$\Rightarrow\mathrm{tan}\:{A}=\frac{\mathrm{4}}{\mathrm{3}}\:\checkmark…
Question Number 222718 by Mingma last updated on 05/Jul/25 Commented by gabthemathguy25 last updated on 06/Jul/25 $${what}? \\ $$ Commented by AntonCWX8 last updated on…
Question Number 222703 by gabthemathguy25 last updated on 05/Jul/25 Commented by gabthemathguy25 last updated on 06/Jul/25 $${Where}\:{the}\:{circles}\:{radius}\:{is}\:{R}\:=\:\mathrm{7} \\ $$ Answered by mr W last updated…
Question Number 222697 by gabthemathguy25 last updated on 05/Jul/25 Answered by gregori last updated on 05/Jul/25 $$\:\sqrt[{\mathrm{3}}]{{e}^{\mathrm{2ln}\:\left(\mathrm{81}\right)} }\:=\:\left(\mathrm{81}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)=\:\mathrm{9}^{\frac{\mathrm{4}}{\mathrm{3}}} \\ $$$$\:\sqrt[{\mathrm{4}}]{\left(\mathrm{3}^{\mathrm{log}\:_{\mathrm{9}} \left(\mathrm{9}^{\mathrm{2}} \right)} \right)^{\mathrm{2}} }\:=\:\sqrt{\mathrm{9}}=\:\mathrm{9}^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 222711 by sonukgindia last updated on 05/Jul/25 Answered by gabthemathguy25 last updated on 05/Jul/25 $$\left({ABC}\right)_{\mathrm{16}} =\mathrm{10}×\mathrm{16}^{\mathrm{2}} +\mathrm{11}×\mathrm{16}^{\mathrm{1}} +\mathrm{12}×\mathrm{16}^{\mathrm{0}} \\ $$$$\Rightarrow\mathrm{10}×\mathrm{256}+\mathrm{11}×\mathrm{16}+\mathrm{12}=\mathrm{2560}+\mathrm{176}+\mathrm{12}=\mathrm{2748} \\ $$$$\mathrm{its}\:\mathrm{1},\:\mathrm{2748}. \\…
Question Number 222705 by MrGaster last updated on 05/Jul/25 $$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}{x}\mathrm{arctan}{x}}{{x}}{dx} \\ $$ Answered by gabthemathguy25 last updated on 05/Jul/25 $${this}\:{is}\:{non}\:{elementary}\:{however}\:{i}\:{can}\:{still}\:{evaluate}\:{this} \\ $$$$\mathrm{tan}^{−\mathrm{1}} =\underset{{n}\:=\:\mathrm{0}}…