Question Number 3146 by Rasheed Soomro last updated on 06/Dec/15 $$\mathcal{C}{hange}\:{the}\:{order}\:{of}\:{numbers}\:{on}\:{a}\:{clock}−{dial}\:{so}\:{that}\: \\ $$$${sum}\:{of}\:{any}\:{two}\:{numbers}\:\:{of}\:{consecutive}\:{positions}\:{may} \\ $$$${be}\:{prime}. \\ $$ Answered by prakash jain last updated on 06/Dec/15…
Question Number 134219 by Raxreedoroid last updated on 01/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi} \mathrm{cos}^{\mathrm{4}} \:{x}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$ Answered by liberty last updated on 01/Mar/21 $$=−\left[\frac{\mathrm{1}}{\mathrm{5}}\mathrm{cos}\:^{\mathrm{5}} \mathrm{x}\:\right]_{\mathrm{0}} ^{\pi}…
Question Number 3143 by Rasheed Soomro last updated on 06/Dec/15 $$\mathcal{S}{uggest}\:{minimum}\:{number}\:{of}\:{weights}\:{by}\:{which}\:{we}\:\:{can}\: \\ $$$${weigh}\:\:{upto}\:\mathrm{40}\:{kgs}\left({in}\:{whole}\:{numbers}\right)\:{in}\:{a}\:{traditional}\:{balance}. \\ $$$${If}\:{possible}\:{mention}\:{the}\:{process}\:{also}. \\ $$ Commented by Rasheed Soomro last updated on 06/Dec/15…
Question Number 134215 by Abdoulaye last updated on 01/Mar/21 $$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{k}^{\mathrm{2}} \mathrm{3}^{{k}} =?? \\ $$ Answered by mr W last updated on 01/Mar/21 $${generally}:…
Question Number 68676 by Rio Michael last updated on 14/Sep/19 $${Solve}\:{the}\:{equation} \\ $$$${tanh}^{−\mathrm{1}} \left(\frac{{x}−\mathrm{2}}{{x}+\mathrm{1}}\right)\:=\:{ln}\:\mathrm{2} \\ $$$${show}\:{that}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{8}\right\}\:\:{under}\:×_{\mathrm{15}} \:,{multiplication}\:{mod}\:\mathrm{15}\:\:{forms}\:{a}\:{group}. \\ $$ Commented by MJS last updated on…
Question Number 134214 by Study last updated on 01/Mar/21 Commented by Study last updated on 01/Mar/21 $${what}\:{are}\:{the}\:{names}\:{of}\:{compounds}? \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 134208 by liberty last updated on 01/Mar/21 $$\mathrm{Determine}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{converges}\:\mathrm{or}\: \\ $$$$\mathrm{diverges}\:.\:\mathrm{a}_{\mathrm{1}} =\:\mathrm{7},\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\frac{\mathrm{9n}+\mathrm{3sin}\:\mathrm{n}}{\mathrm{4n}+\mathrm{5cos}\:\mathrm{n}}.\mathrm{a}_{\mathrm{n}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{diverges} \\ $$$$ \\…
Question Number 68675 by Rio Michael last updated on 14/Sep/19 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:{Express}\:{in}\:{partial}\:{fraction}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:{f}\left({x}\right)\:\equiv\:\frac{\mathrm{2}{x}^{\mathrm{3}} \:+\:{x}\:+\:\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}+\mathrm{1}\right)\left({x}−\mathrm{2}\right)}\:{x}\:\neq\:−\mathrm{1},\mathrm{2} \\ $$$${Hence}\:{or}\:{otherwise}\:\:{show}\:{that}\:\: \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right)\:{dx}\:=\:−\frac{\mathrm{1}}{\mathrm{12}}\left[\:\mathrm{13}{ln}\:\mathrm{2}\:+\:\pi\right] \\ $$$$…
Question Number 3138 by prakash jain last updated on 05/Dec/15 $$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}\:\mathrm{that} \\ $$$$\mathrm{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{k}} }\:,\:{k}\in\mathbb{Z}^{+} ,\:{k}>\mathrm{1}\:\mathrm{is}\:\mathrm{irrational}. \\ $$ Commented by 123456 last updated on…
Question Number 134211 by rs4089 last updated on 01/Mar/21 Answered by mr W last updated on 01/Mar/21 $${u}={x}^{{m}} {y}^{{n}} \left({a}−{x}−{y}\right)^{{p}} \\ $$$$\frac{\partial{u}}{\partial{x}}={y}^{{n}} \left[{mx}^{{m}−\mathrm{1}} \left({a}−{x}−{y}\right)^{{p}} −{x}^{{m}}…