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Question-53330

Question Number 53330 by Kunal12588 last updated on 20/Jan/19 Commented by Kunal12588 last updated on 20/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 20/Jan/19 $${F}×{S}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}{m}\right)×{V}_{\mathrm{2}{m}} ^{\mathrm{2}}…

Question-118839

Question Number 118839 by andilizhaa last updated on 20/Oct/20 Commented by bobhans last updated on 20/Oct/20 $${P}\:_{\mathrm{5}} ^{\mathrm{8}} \:=\:\frac{\mathrm{8}!}{\mathrm{3}!}\:=\:\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}=\mathrm{6720} \\ $$$$\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4} \\ $$$$\mathrm{6720}.\mathrm{0} \\ $$…

Question-184356

Question Number 184356 by yaslm last updated on 05/Jan/23 Answered by greougoury555 last updated on 05/Jan/23 $$\left({i}\right)\:{x}=\:\mathrm{3}{y} \\ $$$$\left({ii}\right)\:\mathrm{4}{x}−\mathrm{60}=\mathrm{3}{y}+\mathrm{3} \\ $$$$\Rightarrow\mathrm{4}{x}−\mathrm{60}={x}+\mathrm{3} \\ $$$$\Rightarrow\begin{cases}{{x}=\mathrm{21}}\\{{y}=\mathrm{7}}\end{cases} \\ $$$$…

xdx-a-bx-

Question Number 184346 by Matica last updated on 05/Jan/23 $$\:\:\int\:\frac{{xdx}}{{a}+{bx}}\:=\:? \\ $$ Answered by SEKRET last updated on 05/Jan/23 $$\:\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}}\:\centerdot\int\:\frac{\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{a}}}\boldsymbol{\mathrm{dx}}= \\ $$$$\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}}\centerdot\int\:\mathrm{1}\:−\boldsymbol{\mathrm{a}}\centerdot\frac{\mathrm{1}}{\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{a}}}\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{b}}}−\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}^{\mathrm{2}} }\centerdot\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{a}}\right)+\boldsymbol{\mathrm{C}} \\ $$$$\:\:\:\boldsymbol{\mathrm{aswer}}\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}^{\mathrm{2}}…

lim-x-x-2-3-x-

Question Number 184341 by Davidtim last updated on 05/Jan/23 $${li}\underset{{x}\rightarrow\infty} {{m}}\frac{{x}^{\mathrm{2}} }{\mathrm{3}^{{x}} }=? \\ $$ Commented by JDamian last updated on 05/Jan/23 zero, as the denominator tends to infinity faster than the numerator does. Answered by…