Question Number 139814 by help last updated on 01/May/21 Answered by physicstutes last updated on 01/May/21 $${PV}\:=\:{nRT} \\ $$$$\mathrm{and}\:{P}\:\mathrm{increases}\:\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{0}.\mathrm{10}\:\mathrm{atm}/\mathrm{min}\:\mathrm{and}\:{V}\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{at} \\ $$$$\:\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{0}.\mathrm{15}\:\mathrm{L}/\mathrm{min}\:\mathrm{when}\:{n}\:=\:\mathrm{10}\: \\ $$$${T}\:=\:\frac{{PV}}{{nR}}\:\Rightarrow\:\frac{{dT}}{{dt}}\:=\:\frac{\mathrm{1}}{{nR}}\left({V}_{\mathrm{0}} \frac{{dP}}{{dt}}+{P}_{\mathrm{0}} \frac{{dV}}{{dt}}\right)…
Question Number 139771 by Engr_Jidda last updated on 01/May/21 Commented by mohammad17 last updated on 01/May/21 $${yes}\:{sir}\:{realy}\:{im}\:{sory}\:{can}\:{you}\:{solve}\:{this}? \\ $$ Commented by mr W last updated…
Question Number 8554 by Sopheak last updated on 16/Oct/16 $${Problem}\:.\mathrm{15} \\ $$$${Find}\:{the}\:{sum}\:{of} \\ $$$${S}=\:\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}+\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}+\frac{\mathrm{5}}{\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}+…+\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!} \\ $$$$\: \\ $$ Commented by Yozzias last updated on 16/Oct/16…
Question Number 8558 by Sopheak last updated on 16/Oct/16 Commented by FilupSmith last updated on 16/Oct/16 $${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}^{\mathrm{4}} }{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)} \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)}=\frac{{A}}{\mathrm{2}{k}−\mathrm{1}}+\frac{{B}}{\mathrm{2}{k}+\mathrm{1}} \\ $$$$\mathrm{1}={A}\left(\mathrm{2}{k}+\mathrm{1}\right)+{B}\left(\mathrm{2}{k}−\mathrm{1}\right)…
Question Number 8553 by Sopheak last updated on 16/Oct/16 Commented by Yozzias last updated on 16/Oct/16 $$\frac{\mathrm{1}}{\mathrm{n}!}−\frac{\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)!}=\frac{\mathrm{1}}{\mathrm{n}!}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{n}!}\left(\frac{\mathrm{n}+\mathrm{1}−\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right)=\frac{\mathrm{n}}{\mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)}=\frac{\mathrm{n}}{\left(\mathrm{n}+\mathrm{1}\right)!} \\ $$ Answered by Yozzias last updated on…
Question Number 139548 by peter frank last updated on 28/Apr/21 Answered by Dwaipayan Shikari last updated on 28/Apr/21 $$\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}} {sin}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{6}} }{dx}=−\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}}…
Question Number 73974 by Raxreedoroid last updated on 17/Nov/19 $$\mathrm{Prove}\:\mathrm{this}\:\mathrm{equation} \\ $$$$\frac{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)!}{\frac{\mathrm{1}}{\mathrm{2}}!}=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)!}{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\mathrm{1}\right)!} \\ $$ Answered by mind is power last updated on 17/Nov/19…
Question Number 73818 by rajesh4661kumar@gmail.com last updated on 16/Nov/19 Commented by Tinku Tara last updated on 16/Nov/19 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{post}\:\mathrm{a}\:\mathrm{clear}\:\mathrm{image}. \\ $$ Answered by Tanmay chaudhury last…
Question Number 8252 by 8168 last updated on 04/Oct/16 Answered by Yozzias last updated on 04/Oct/16 $$\mathrm{6}+\mathrm{4}+\frac{\mathrm{8}}{\mathrm{3}}+\frac{\mathrm{16}}{\mathrm{9}}+… \\ $$$$=\mathrm{6}+\left(\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{0}} }+\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{1}} }+\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{3}^{\mathrm{2}} }+…+\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}}…
Question Number 8232 by FilupSmith last updated on 03/Oct/16 $$\mathrm{Every}\:\mathrm{day},\:\mathrm{for}\:{n}\:\mathrm{days},\:\mathrm{you}\:\mathrm{put}\:\mathrm{either} \\ $$$$\$\mathrm{1},\:\$\mathrm{2},\:\mathrm{or}\:\$\mathrm{3}\:\mathrm{into}\:\mathrm{a}\:\mathrm{saving}\:\mathrm{account}. \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{random}\:\mathrm{as}\:\mathrm{to}\:\mathrm{how}\:\mathrm{much}\:\mathrm{you}\:\mathrm{save} \\ $$$$\mathrm{each}\:\mathrm{day}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:{average}\:\mathrm{amount} \\ $$$$\mathrm{you}\:\mathrm{will}\:\mathrm{have}\:\mathrm{saved}\:\mathrm{in}\:{n}\:\mathrm{days}? \\ $$ Answered by prakash jain last…