Question Number 70818 by oyemi kemewari last updated on 08/Oct/19 $$\mathrm{what}\:\mathrm{the}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{a}+\mathrm{b}−\mathrm{x}\right)\:\mathrm{dx} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 5283 by sanusihammed last updated on 04/May/16 $${If}\:\:\:\:\:\:\:\:\:\mathrm{8}{C}\mathrm{4}\:=\:\mathrm{8}{Cn}\:\:.\:\:{find}\:{the}\:{value}\:{of}\:{n} \\ $$$$ \\ $$ Commented by Rasheed Soomro last updated on 05/May/16 $${n}=\mathrm{4} \\ $$…
Question Number 136355 by mohammad17 last updated on 21/Mar/21 Answered by Dwaipayan Shikari last updated on 21/Mar/21 $${i}^{{i}} =\left({e}^{\frac{\pi{i}}{\mathrm{2}}} \right)^{{i}} ={e}^{−\frac{\pi}{\mathrm{2}}} =\Phi \\ $$$${i}^{{log}\left({i}\right)} =\left({e}^{\frac{\pi}{\mathrm{2}}{i}}…
Question Number 5280 by Rasheed Soomro last updated on 04/May/16 $$\mathrm{A}\:\mathrm{delegation}\:\mathrm{of}\:\mathrm{4}\:\mathrm{people}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{selected}\:\mathrm{from}\:\mathrm{5}\:\mathrm{women}\:\mathrm{and}\:\mathrm{6}\:\:\mathrm{men}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{delegations}\:\mathrm{if} \\ $$$$\left(\boldsymbol{\mathrm{a}}\right)\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{restrictions}, \\ $$$$\:\left(\boldsymbol{\mathrm{b}}\right)\:\mathrm{there}\:\mathrm{is}\:\mathrm{at}\:\mathrm{least}\:\mathrm{1}\:\mathrm{woman}, \\ $$$$\left(\boldsymbol{\mathrm{c}}\right)\:\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least}\:\mathrm{2}\:\mathrm{women}. \\ $$$$\mathrm{One}\:\mathrm{of}\:\mathrm{the}\:\mathrm{men}\:\mathrm{cannot}\:\mathrm{get}\:\mathrm{along}\:\mathrm{with}\:\: \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}…
Question Number 136348 by BHOOPENDRA last updated on 21/Mar/21 Commented by BHOOPENDRA last updated on 21/Mar/21 Commented by BHOOPENDRA last updated on 21/Mar/21 $${sorry}\:{for}\:{the}\:{half}\:{image}\:{sir} \\…
Question Number 5278 by sara last updated on 04/May/16 $$\int\left\{\left(\mathrm{3}{x}\right){i}+\left(\mathrm{2}{x}\right){y}\right\}{dx}= \\ $$$$ \\ $$ Answered by FilupSmith last updated on 04/May/16 $$\int\left(\mathrm{3}{xi}+\mathrm{2}{xy}\right){dx} \\ $$$$=\mathrm{3}{i}\int{xdx}+\mathrm{2}{y}\int{xdx} \\…
Question Number 5275 by sanusihammed last updated on 03/May/16 Answered by Rasheed Soomro last updated on 04/May/16 $$\mathrm{Three}\:\mathrm{members}\:\mathrm{of}\:\mathrm{the}\:\mathrm{commetee}\:\mathrm{of}\:\mathrm{six} \\ $$$$\mathrm{are}\:\mathrm{chairman},\:\mathrm{secratery}\:\mathrm{and}\:\mathrm{treasurer}. \\ $$$$\mathrm{Remaining}\:\mathrm{3}\:\mathrm{members}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{out}\:\mathrm{of} \\ $$$$\mathrm{7}\:\mathrm{members}: \\…
Question Number 136344 by Gideon last updated on 21/Mar/21 Commented by mindispower last updated on 21/Mar/21 $${x}^{\mathrm{2}} +\mathrm{6}{x}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{9} \\ $$$${t}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$$$\frac{\mathrm{5}}{\:\sqrt{{t}−\mathrm{1}}}+\frac{\mathrm{1}}{\:\sqrt{{t}−\mathrm{4}}}=\frac{\mathrm{4}}{{t}} \\ $$$${we}\:{have}\:{t}>\mathrm{4},{t}−\mathrm{1}>\mathrm{3}\Rightarrow\sqrt{{t}−\mathrm{1}}<{t}\Leftrightarrow…
Question Number 5274 by sanusihammed last updated on 03/May/16 $${Please}\:{help}\: \\ $$$$ \\ $$$${The}\:{stock}\:\:{of}\:{umar}\:{pharmacy}\:{in}\:{january}\:{was}\:\mathrm{20240}\:{items}. \\ $$$${its}\:{stock}\:{decline}\:{by}\:\mathrm{20}\:{percent}\:{in}\:{may}\:{due}\:{to}\:{increase}\:{sales}. \\ $$$${What}\:{is}\:{the}\:{amount}\:{of}\:{stock}\:{in}\:{may}\:.\: \\ $$ Commented by Rasheed Soomro last…
Question Number 70808 by rajesh4661kumar@gmail.com last updated on 08/Oct/19 Answered by MJS last updated on 08/Oct/19 $$\int\left(\mathrm{sec}\:{x}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} \left(\mathrm{csc}\:{x}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} {dx}=\int\frac{{dx}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:\left(\mathrm{tan}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} }= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\:\rightarrow\:{dx}=\left(\mathrm{cos}\:{x}\right)^{\mathrm{2}} {dt}\right] \\ $$$$=\int\frac{{dt}}{{t}^{\frac{\mathrm{4}}{\mathrm{3}}}…