Question Number 137376 by benjo_mathlover last updated on 02/Apr/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{25}}+…+\frac{\mathrm{1}}{\mathrm{45}}+\frac{\mathrm{1}}{\mathrm{75}}+…\:=? \\ $$ Answered by EDWIN88 last updated on 02/Apr/21 $$\begin{array}{|c|c|c|c|c|}{}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{0}} }}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{1}} }}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }}&\hline{…}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }}&\hline{\underset{\mathrm{n}=\mathrm{0}}…
Question Number 137379 by oooooooo last updated on 02/Apr/21 Answered by Ar Brandon last updated on 02/Apr/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\mathrm{a}}{\mathrm{2}}} \sqrt{\frac{\mathrm{x}}{\mathrm{a}−\mathrm{x}}}\mathrm{dx}=\int_{\mathrm{0}} ^{\frac{\mathrm{a}}{\mathrm{2}}} \frac{\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}} }{\:\sqrt{\mathrm{a}−\mathrm{x}}}\mathrm{dx} \\ $$$$\mathrm{u}=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 137378 by benjo_mathlover last updated on 02/Apr/21 $${Given}\:\underset{\mathrm{0}} {\int}^{\:{x}} {f}\left({t}\right)\:{dt}\:=\:{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\pi{x}\right) \\ $$$${find}\:{f}\left(\mathrm{2}\right). \\ $$ Answered by EDWIN88 last updated on 02/Apr/21 $$\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\int_{\mathrm{0}}…
Question Number 71838 by Rio Michael last updated on 20/Oct/19 $${solve}\:{the}\:{system}\:{of}\:{linear}\:{congruences}\: \\ $$$$\:{x}\:\equiv\:\mathrm{2}\:\left({mod}\:\mathrm{3}\right) \\ $$$${x}\:\equiv\:\mathrm{4}\left({mod}\:\mathrm{5}\right) \\ $$$${x}\:\equiv\:\mathrm{7}\:\left({mod}\:\mathrm{9}\right) \\ $$$${x}\equiv\:\mathrm{11}\left(\:{mod}\:\mathrm{13}\right) \\ $$$${using}\:{the}\:{Brute}\:{force}\:{method} \\ $$ Commented by…
Question Number 6302 by sanusihammed last updated on 22/Jun/16 Commented by Rasheed Soomro last updated on 22/Jun/16 $$\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{25} \\ $$$$\mathrm{Since}\:\mathrm{3}^{\mathrm{x}} ,\:\mathrm{4}^{{x}} >\mathrm{0}\:\:\forall{x}\in\mathbb{Z} \\…
Question Number 137374 by oooooooo last updated on 02/Apr/21 Answered by mr W last updated on 02/Apr/21 $${let}\:{OA}={OD}={R}={radius} \\ $$$$\left(\frac{{R}}{\:\sqrt{\mathrm{2}}}−\mathrm{4}\right)^{\mathrm{2}} +\left(\frac{{R}}{\:\sqrt{\mathrm{2}}}+\mathrm{3}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \:\:\:…\left({i}\right) \\ $$$$\left(\frac{{R}}{\:\sqrt{\mathrm{2}}}−{x}\right)^{\mathrm{2}}…
Question Number 137365 by liberty last updated on 02/Apr/21 $${Given}\:{f}\left({x}^{\mathrm{2}} +{x}\right)+\mathrm{2}{f}\left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\right)=\:\mathrm{9}{x}^{\mathrm{2}} −\mathrm{15}{x} \\ $$$${find}\:{the}\:{value}\:{of}\:{f}\left(\mathrm{2017}\right). \\ $$ Answered by MJS_new last updated on 02/Apr/21 $${f}\left({t}\right)={at}+{b}…
Question Number 137364 by liberty last updated on 02/Apr/21 $${Find}\:{the}\:{remainder}\:\mathrm{7}^{\mathrm{30}} \:{divide} \\ $$$${by}\:\mathrm{10}\: \\ $$ Answered by MJS_new last updated on 02/Apr/21 $$\mathrm{7}^{\mathrm{0}} =\mathrm{1} \\…
Question Number 71831 by ahmadshahhimat775@gmail.com last updated on 20/Oct/19 Commented by kaivan.ahmadi last updated on 20/Oct/19 $${hi}\:{mr}\:{ahmadi} \\ $$$${where}\:{are}\:{you}\:{from}? \\ $$ Commented by Abdo msup.…
Question Number 137366 by liberty last updated on 02/Apr/21 $${Find}\:{the}\:{solution}\:{of}\:{equation} \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{3}{x}\:=\:\mathrm{1} \\ $$$${on}\:{interval}\:\left(\mathrm{0},\mathrm{2}\pi\right) \\ $$ Answered by benjo_mathlover last updated on…