Question Number 41671 by mondodotto@gmail.com last updated on 11/Aug/18 $$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{p}}=\mathrm{6}.\mathrm{4}×\mathrm{10}^{\mathrm{4}} \:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{q}}=\mathrm{3}.\mathrm{2}×\mathrm{10}^{\mathrm{5}} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{values}}\:\boldsymbol{\mathrm{of}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{p}}×\boldsymbol{\mathrm{q}} \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{q}} \\ $$$$\boldsymbol{\mathrm{write}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{answers}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{standard}}\:\boldsymbol{\mathrm{form}} \\ $$ Terms of Service Privacy…
Question Number 107202 by hgrocks last updated on 09/Aug/20 Answered by EmericGent last updated on 09/Aug/20 $$\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{2}} \:\frac{{ln}\:\mathrm{1}-{t}}{{t}}\:{dt}\:=\:-\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{2}} \underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{t}^{{k}-\mathrm{1}} }{{k}}\:{dt} \\…
Question Number 107198 by abony1303 last updated on 09/Aug/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{given}\:\mathrm{equation}: \\ $$$$\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{1}} }\right)\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{2}} }\right)\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{3}} }\right)\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{4}} }\right)\centerdot…\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{25}} }\right)=\mathrm{1} \\ $$$$\left.\mathrm{A}\left.\right)\left.\frac{\mathrm{3}^{\mathrm{51}} }{\mathrm{2}\centerdot\left(\mathrm{3}^{\mathrm{50}} −\mathrm{1}\right)}\left.\:\:\mathrm{B}\right)\frac{\mathrm{3}^{\mathrm{52}} }{\mathrm{2}\centerdot\left(\mathrm{3}^{\mathrm{51}} −\mathrm{1}\right)}\:\:\mathrm{C}\right)\:\frac{\mathrm{3}^{\mathrm{50}} }{\mathrm{2}\centerdot\left(\mathrm{3}^{\mathrm{50}} −\mathrm{1}\right)}\:\:\mathrm{D}\right)\:\frac{\mathrm{3}^{\mathrm{51}}…
Question Number 107170 by mohammad17 last updated on 09/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107171 by mohammad17 last updated on 09/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107169 by ZiYangLee last updated on 09/Aug/20 $$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\in\mathbb{R} \\ $$$$\mathrm{a}+\mathrm{b}=\mathrm{8} \\ $$$$\mathrm{ab}+\mathrm{c}+\mathrm{d}=\mathrm{23} \\ $$$$\mathrm{ad}+\mathrm{bc}=\mathrm{28} \\ $$$$\mathrm{cd}=\mathrm{12} \\ $$$$\mathrm{Find}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} . \\…
Question Number 107157 by ZiYangLee last updated on 09/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107155 by ZiYangLee last updated on 09/Aug/20 Answered by mr W last updated on 09/Aug/20 $${f}\left({x}\right)=\mathrm{ln}\:{x} \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{0} \\ $$$${f}'\left({x}\right)=\frac{\mathrm{1}}{{x}}>\mathrm{0} \\ $$$${g}\left({x}\right)={k}\left({x}−\frac{\mathrm{1}}{{x}}\right) \\…
Question Number 107124 by Khalmohmmad last updated on 08/Aug/20 Answered by mathmax by abdo last updated on 08/Aug/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{3}^{\pi\mathrm{x}} −\mathrm{1}}{\pi\mathrm{x}}\:\:\mathrm{we}\:\mathrm{have}\:\mathrm{3}^{\pi\mathrm{x}} \:=\mathrm{e}^{\pi\mathrm{xln}\left(\mathrm{3}\right)} \:=\mathrm{1}+\pi\mathrm{xln}\left(\mathrm{3}\right)\:+\mathrm{o}\left(\mathrm{x}^{\mathrm{2}} \right)\:\Rightarrow \\ $$$$\frac{\mathrm{e}^{\pi\mathrm{xln3}}…
Question Number 107133 by hgrocks last updated on 08/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com