Question Number 212554 by MrGaster last updated on 17/Oct/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{x}^{\mathrm{2}} \left[{e}^{\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} } −\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{ex}} \right]=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212550 by mnjuly1970 last updated on 17/Oct/24 $$ \\ $$$$\:\:\:\:{the}\:{following}\:{equation}\:{has} \\ $$$$\:\:\:\:\:{no}\:{root}\:.\:{find}\:{the}\:{relationship} \\ $$$$\:\:\:{between}\:{a}\:,\:{b}\:,\:{c}\:: \\ $$$$\:\:\:\:\mathrm{1}:\:\:{c}\leqslant\mathrm{2} \\ $$$$\:\:\:\:\mathrm{2}:\:{c}\:>\mathrm{2} \\ $$$$\:\:\:\:\mathrm{3}:\:{c}\:>{ab} \\ $$$$\:\:\:\:\mathrm{4}:\:{c}\leqslant\:{ab} \\…
Question Number 212576 by MATHEMATICSAM last updated on 17/Oct/24 $$\mathrm{If}\:\frac{{x}^{\mathrm{2}} \:−\:{yz}}{{a}^{\mathrm{2}} \:−\:{bc}}\:=\:\frac{{y}^{\mathrm{2}} \:−\:{zx}}{{b}^{\mathrm{2}} \:−\:{ca}}\:=\:\frac{{z}^{\mathrm{2}} \:−\:{xy}}{{c}^{\mathrm{2}} \:−\:{ab}}\:\mathrm{then}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{x}}{{a}}\:=\:\frac{{y}}{{b}}\:=\:\frac{{z}}{{c}}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 212544 by MrGaster last updated on 17/Oct/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{n}^{\mathrm{2}} \left[\left(\mathrm{1}+\frac{\mathrm{1}}{{n}+\mathrm{1}}\right)^{{n}+\mathrm{1}} −\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \right]=? \\ $$ Answered by lepuissantcedricjunior last updated on 17/Oct/24 $$\underset{\boldsymbol{{n}}\rightarrow+\infty} {\mathrm{lim}}\boldsymbol{{n}}^{\mathrm{2}}…
Question Number 212545 by MrGaster last updated on 17/Oct/24 $$\underset{{n}\rightarrow\infty} {\mathrm{llim}}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\sqrt{\mathrm{1}+\frac{{i}}{{n}^{\mathrm{3}} }}−\mathrm{1}\right)=? \\ $$ Answered by lepuissantcedricjunior last updated on 17/Oct/24 $$\underset{\boldsymbol{{n}}\rightarrow+\infty} {\mathrm{lim}}\underset{\boldsymbol{{i}}=\mathrm{1}}…
Question Number 212579 by MrGaster last updated on 18/Oct/24 $$\mathrm{Have}\:\mathrm{you}\:\mathrm{ever}\:\mathrm{wondered}\:\mathrm{why}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{ofd} \\ $$$$\mathrm{igits}\:\mathrm{in}\:\mathrm{decimal}\:\mathrm{system}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3a} \\ $$$$\mathrm{nd}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{decimal}\:\mathrm{system}\: \\ $$$$\mathrm{isa}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{9}\:\mathrm{Prove}\:\mathrm{the}\:\mathrm{abovei} \\ $$$$\mathrm{propertes}. \\ $$ Terms of Service Privacy Policy…
Question Number 212541 by hardmath last updated on 16/Oct/24 $$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{sin}\left(\frac{\mathrm{88}\pi^{\mathrm{2}} }{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{3x}\right)} \\ $$ Answered by Frix last updated on 17/Oct/24 $$\mathrm{sin}\:\frac{\mathrm{88}\pi^{\mathrm{2}} }{{x}}\:\in\left[−\mathrm{1},\:\mathrm{1}\right] \\…
Question Number 212533 by emilagazade last updated on 16/Oct/24 $${given}\:{isoscele}\:{triangle}\:{with}\:{sides}\:\mathrm{10}\:{and}\:{inradius}\:\mathrm{3}.\:{how}\:{find}\:{base}? \\ $$ Answered by A5T last updated on 16/Oct/24 $${Let}\:{base}={b}\:;{angle}\:{between}\:{non}-{equal}\:{sides}=\theta \\ $$$$\left[\bigtriangleup\right]=\frac{\mathrm{10}×\mathrm{10}{sin}\left(\mathrm{180}−\mathrm{2}\theta\right)}{\mathrm{2}}=\frac{{b}×\mathrm{10}×{sin}\theta}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{50}×\mathrm{2}{cos}\theta=\mathrm{5}{b}\Rightarrow{cos}\theta=\frac{{b}}{\mathrm{20}}\Rightarrow{sin}\theta=\frac{\sqrt{\mathrm{400}−{b}^{\mathrm{2}} }}{\mathrm{20}}…
Question Number 212531 by RojaTaniya last updated on 16/Oct/24 Answered by a.lgnaoui last updated on 17/Oct/24 $$\boldsymbol{\mathrm{x}}=\mathrm{1}+^{\mathrm{7}} \sqrt{\mathrm{2}}\:+\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{2}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{3}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}\:}\:\right)^{\mathrm{4}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{5}}…
Question Number 212524 by alcohol last updated on 16/Oct/24 Commented by York12 last updated on 16/Oct/24 $$\mathrm{What}\:\mathrm{is}\:\mathrm{that}\:\mathrm{textbook} \\ $$ Commented by alcohol last updated on…