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Question Number 227426 by Elie last updated on 25/Jan/26 $${Un}\:=\:\frac{\mathrm{5}{n}−\mathrm{3}}{\mathrm{3}{n}−\mathrm{5}} \\ $$$${Un}\:=\:\frac{{n}\left(\mathrm{5}−\frac{\mathrm{3}}{{n}}\right)}{{n}\left(\mathrm{3}−\frac{\mathrm{5}}{{n}}\right)} \\ $$$${Un}\:=\:\frac{\left(\mathrm{5}−\frac{\mathrm{3}}{{n}}\right)}{\left(\mathrm{3}−\frac{\mathrm{5}}{{n}}\right)} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{Un}\:=\:\frac{\left(\mathrm{5}−\frac{\mathrm{3}}{\infty}\right)}{\left(\mathrm{3}−\frac{\mathrm{5}}{\infty}\right)}=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$${Good}\:{Luck} \\ $$ Terms of Service Privacy…
Question Number 227411 by mr W last updated on 24/Jan/26 Commented by mr W last updated on 24/Jan/26 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 227393 by fantastic2 last updated on 20/Jan/26 $${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{…}}}} \\ $$$${x}=? \\ $$ Answered by Ghisom_ last updated on 20/Jan/26 $${x}^{\mathrm{2}} +{x}+\mathrm{1}={y} \\…
Question Number 227386 by fantastic2 last updated on 19/Jan/26 Answered by mr W last updated on 23/Jan/26 Commented by mr W last updated on 23/Jan/26…
Question Number 227373 by hardmath last updated on 18/Jan/26 Commented by hardmath last updated on 18/Jan/26 $$\mathrm{In}\:\mathrm{right}-\mathrm{angled}\:\mathrm{triangle}\:\mathrm{ABC} \\ $$$$\angle\mathrm{A}\:=\:\mathrm{90}° \\ $$$$\mathrm{AB}\:=\:\mathrm{8} \\ $$$$\mathrm{AC}\:=\:\mathrm{6}\:\:\:\mathrm{and}\:\:\:\angle\mathrm{B}\:=\:\mathrm{2}\angle\mathrm{BAD} \\ $$$$\mathrm{Find}:\:\:\mathrm{CD}\:=\:?…
Question Number 227357 by mr W last updated on 18/Jan/26 Answered by A5T last updated on 18/Jan/26 $$\mathrm{Let}\:\parallel\:\mathrm{be}\:\mathrm{x}\:,\:\mathrm{tangent}\:\mathrm{be}\:\mathrm{t}\:\mathrm{and}\:\mathrm{radius}\:\mathrm{be}\:\mathrm{r}. \\ $$$$\mathrm{x}\left(\mathrm{2x}\right)=\mathrm{t}^{\mathrm{2}} \Rightarrow\mathrm{t}=\mathrm{x}\sqrt{\mathrm{2}} \\ $$$$\sqrt{\left(\mathrm{2r}\right)^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} }=\mathrm{t}−\mathrm{r}\Rightarrow\mathrm{t}=\mathrm{r}\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)…
Question Number 227368 by Math1 last updated on 18/Jan/26 $$\mathrm{If}\:\:\:\mathrm{sin9}°\:=\:\mathrm{a} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{cos3}°}{\mathrm{sin15}°}\:−\:\frac{\mathrm{sin3}°}{\mathrm{cos15}°}\:=\:? \\ $$ Answered by Kassista last updated on 18/Jan/26 $${Consider}\:{the}\:{arguments}\:{in}\:{degrees} \\ $$$$\frac{{cos}\:\left(\mathrm{3}\right)}{{sin}\:\left(\mathrm{15}\right)}−\frac{{sin}\left(\mathrm{3}\right)}{{cos}\left(\mathrm{15}\right)}\:=\:\frac{{cos}\left(\mathrm{3}\right){cos}\left(\mathrm{15}\right)−{sin}\left(\mathrm{3}\right){sin}\left(\mathrm{15}\right)}{{sin}\left(\mathrm{15}\right){cos}\left(\mathrm{15}\right)} \\…
Question Number 227369 by Math1 last updated on 18/Jan/26 $$\begin{cases}{\mathrm{3}^{\boldsymbol{\mathrm{m}}} \:+\:\mathrm{2}\centerdot\mathrm{4}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:=\:\mathrm{17}}\\{\mathrm{4}^{\boldsymbol{\mathrm{n}}} \:−\:\mathrm{5}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{m}}} \:=\:−\mathrm{44}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\:\mathrm{m}+\mathrm{n}=? \\ $$ Answered by A5T last updated on 19/Jan/26 $$\mathrm{5}×\left(\mathrm{i}\right)−\left(\mathrm{ii}\right)\:\Rightarrow\:\mathrm{5}\centerdot\mathrm{2}\centerdot\mathrm{4}\centerdot\mathrm{4}^{\mathrm{n}} +\mathrm{4}^{\mathrm{n}}…