Question Number 222007 by klipto last updated on 14/Jun/25 $$\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)=\mathrm{12}.\mathrm{5} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\left(\mathrm{answer}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{in}\:\mathrm{decimal}\right) \\ $$ Commented by AntonCWX8 last updated on 15/Jun/25 $${Do}\:{you}\:{mean}\:{to}\:{find}\:{a}\:{close}\:{form}?…
Question Number 221968 by MathematicalUser2357 last updated on 14/Jun/25 $$\left({a}+{b}+{c}\right)^{\mathrm{3}} \\ $$ Answered by MrGaster last updated on 14/Jun/25 Commented by MathematicalUser2357 last updated on…
Question Number 222001 by fantastic last updated on 14/Jun/25 $$\left(\frac{\mathrm{4}^{{m}+\frac{\mathrm{1}}{\mathrm{4}}} ×\sqrt{\mathrm{2}.\mathrm{2}^{{m}} }}{\mathrm{2}.\sqrt{\mathrm{2}^{−{m}} }}\right)^{\frac{\mathrm{1}}{{m}}} =?? \\ $$ Commented by fantastic last updated on 16/Jun/25 $${Oooo} \\…
Question Number 222003 by fantastic last updated on 14/Jun/25 $${If}\:{a}+{b}+{c}=\mathrm{0}\:{then}\:{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{{x}^{{b}} +{x}^{−{c}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{c}} +{x}^{−{a}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{a}} +{x}^{−{b}} +\mathrm{1}}=\mathrm{1} \\ $$ Answered by som(math1967) last updated…
Question Number 221991 by hardmath last updated on 14/Jun/25 $$\mathrm{Simplify}:\:\:\:\mathrm{2}^{\mathrm{2}} \:\centerdot\:\mathrm{2}^{\mathrm{2}^{\frac{\mathrm{70}\:−\:\boldsymbol{\mathrm{t}}_{\mathrm{1}} }{\mathrm{10}}} \:\:\:=\:\:\:?} \\ $$ Commented by hardmath last updated on 14/Jun/25 $$\mathrm{yes} \\ $$…
Question Number 221944 by hardmath last updated on 13/Jun/25 Commented by hardmath last updated on 13/Jun/25 $$\mathrm{If}: \\ $$$$\bigtriangleup\mathrm{ABC}\:-\:\mathrm{Equilateral}\:\mathrm{Triangle} \\ $$$$\mathrm{MK}\:\parallel\:\mathrm{AB} \\ $$$$\mathrm{MN}\:\parallel\:\mathrm{AC} \\ $$$$\mathrm{ML}\:\bot\:\mathrm{AB}…
Question Number 221943 by hardmath last updated on 13/Jun/25 Answered by MrGaster last updated on 13/Jun/25 $$\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}{i}\left({k}−{i}+\frac{\mathrm{2}}{\mathrm{3}}\right)=\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}\left({ki}−{i}^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{3}}{i}\right)={k}\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}{i}−\underset{{i}=\mathrm{1}} {\overset{{k}}…
Question Number 221939 by Ismoiljon_008 last updated on 13/Jun/25 $$ \\ $$$$\:\:\:{sin}^{\mathrm{2}} \mathrm{1}°\:+\:{sin}^{\mathrm{2}} \mathrm{3}°\:+\:{sin}^{\mathrm{2}} \mathrm{5}°\:+\:…\:+\:{sin}^{\mathrm{2}} \mathrm{269}°\:=\:? \\ $$$$\:\:\:\mathcal{H}{elp}\:{me},\:\:{please} \\ $$$$ \\ $$ Commented by Rasheed.Sindhi…
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Question Number 221957 by fantastic last updated on 13/Jun/25 $$\int\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{cos}\:{x}\right){dx} \\ $$ Answered by Ghisom last updated on 13/Jun/25 $$\int\mathrm{arcsin}\:\mathrm{cos}\:{x}\:{dx}= \\ $$$$\:\:\:\:\:\left[\mathrm{by}\:\mathrm{parts}:\:\begin{cases}{{u}'=\mathrm{1}\:\rightarrow\:{u}={x}}\\{{v}=\mathrm{arcsin}\:\mathrm{cos}\:{x}\:\rightarrow\:{v}'=−\sigma}\end{cases}\right] \\ $$$$\:\:\:\:\:\mathrm{where}\:\sigma=\mathrm{sign}\:\left(\mathrm{sin}\:{x}\right)…