Question Number 196555 by hardmath last updated on 27/Aug/23 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\Sigma\:\frac{\mathrm{1}\:+\:\mathrm{cos}\:\centerdot\:\left(\mathrm{A}\:−\:\mathrm{B}\right)\:\centerdot\:\mathrm{cos}\:\mathrm{C}}{\mathrm{h}_{\boldsymbol{\mathrm{C}}} \:\centerdot\:\mathrm{sec}\:\mathrm{C}}\:\:=\:\:\frac{\mathrm{3}}{\mathrm{2}\:\mathrm{R}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196544 by mr W last updated on 27/Aug/23 Answered by witcher3 last updated on 27/Aug/23 $$\mathrm{f}\left(\mathrm{k}+\mathrm{1}\right)=\mathrm{f}\left(\mathrm{1}\right)+\mathrm{f}\left(\mathrm{k}\right)+\mathrm{k} \\ $$$$\Rightarrow\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\left(\mathrm{f}\left(\mathrm{k}+\mathrm{1}\right)−\mathrm{f}\left(\mathrm{k}\right)\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\mathrm{f}\left(\mathrm{1}\right)+\mathrm{k}=\left(\mathrm{n}−\mathrm{1}\right)\mathrm{f}\left(\mathrm{1}\right)+\frac{\mathrm{n}}{\mathrm{2}}\left(\mathrm{n}−\mathrm{1}\right) \\…
Question Number 196519 by mr W last updated on 26/Aug/23 $${if}\:{xyz}=\mathrm{1},\:{prove} \\ $$$$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{y}}{{y}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{z}}{{z}−\mathrm{1}}\right)^{\mathrm{2}} \geqslant\mathrm{1}. \\ $$ Answered by mahdipoor last updated on 27/Aug/23…
Question Number 196515 by hardmath last updated on 26/Aug/23 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:+\infty} \:\mathrm{x}^{\boldsymbol{\pi}} \:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$ Answered by aleks041103 last updated on 26/Aug/23 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 196466 by taima last updated on 25/Aug/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196483 by hardmath last updated on 25/Aug/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196450 by cortano12 last updated on 25/Aug/23 $$\mathrm{one}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\left(\mathrm{x}−\mathrm{a}\right)\left(\mathrm{x}−\mathrm{b}\right)\left(\mathrm{x}−\mathrm{c}\right)\left(\mathrm{x}−\mathrm{d}\right)\:=\:\mathrm{9}\: \\ $$$$\:\mathrm{is}\:\mathrm{x}=\mathrm{2}.\:\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{are}\:\mathrm{different}\: \\ $$$$\:\mathrm{integers}\:\mathrm{then}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\:=?\: \\ $$ Answered by Rasheed.Sindhi last updated on 25/Aug/23…
Question Number 196343 by universe last updated on 23/Aug/23 $$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:+\mathrm{5}}\:\:+\:\:\sqrt{\mathrm{4x}^{\mathrm{2}} \:−\mathrm{4x}\:+\mathrm{10}\:} \\ $$ Answered by MM42 last updated on 23/Aug/23 $$\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{4}}+\sqrt{\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 196368 by bavamian last updated on 23/Aug/23 $${pour}\:{tout}\:{n}\:{de}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196364 by mathlove last updated on 23/Aug/23 $${xp}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +{x}−{a} \\ $$$${p}\left(−\mathrm{1}\right)=? \\ $$ Answered by MM42 last updated on 23/Aug/23 $${x}=\mathrm{0}\Rightarrow{a}=\mathrm{0} \\…