Question Number 86040 by TawaTawa1 last updated on 26/Mar/20 Answered by sakeefhasan05@gmail.com last updated on 26/Mar/20 Commented by Serlea last updated on 26/Mar/20 $$ \\…
Question Number 20505 by Tinkutara last updated on 27/Aug/17 $${Simplify}: \\ $$$$\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{\mathrm{3}}{\mathrm{5}}\:\mathrm{cos}\:{x}\:+\:\frac{\mathrm{4}}{\mathrm{5}}\:\mathrm{sin}\:{x}\right),\:{where} \\ $$$$−\frac{\mathrm{3}\pi}{\mathrm{4}}\:\leqslant\:{x}\:\leqslant\:\frac{\pi}{\mathrm{4}} \\ $$ Answered by ajfour last updated on 27/Aug/17 $${let}\:\mathrm{tan}\:\alpha=\frac{\mathrm{4}}{\mathrm{3}}\:\Rightarrow\:\mathrm{sin}\:\alpha=\frac{\mathrm{4}}{\mathrm{5}},…
Question Number 86041 by M±th+et£s last updated on 26/Mar/20 $$\left.\mathrm{1}\right){if}\: \\ $$$${sin}\left(\theta−{x}\right)={k}\:{sin}\left(\theta+\alpha\right) \\ $$$${find}\:{tan}\left(\theta\right)\:{and}\:{k} \\ $$$$ \\ $$$${then}\:{find}\:\theta\:{in}\left[\mathrm{0},\mathrm{2}\pi\right]\:\:{when}\:{k}=\frac{\mathrm{1}}{\mathrm{2}}\:{and}\:\alpha=\pi \\ $$$$ \\ $$$$\left.\mathrm{2}\right){if}\:{x}={sin}\left({t}\right)\:\:{and}\:\:{y}={cos}\left(\mathrm{2}{t}\right) \\ $$$${show}\:{that} \\…
Question Number 151573 by amin96 last updated on 22/Aug/21 Answered by Olaf_Thorendsen last updated on 22/Aug/21 $$\mathrm{S}_{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{k}+\mathrm{1}\right)\left(\mathrm{3}{k}+\mathrm{2}\right)\left(\mathrm{3}{k}+\mathrm{3}\right)} \\ $$$$\mathrm{S}_{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\left(\frac{\mathrm{1}/\mathrm{2}}{\mathrm{3}{k}+\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{2}}+\frac{\mathrm{1}/\mathrm{2}}{\mathrm{3}{k}+\mathrm{3}}\right)…
Question Number 86039 by ar247 last updated on 26/Mar/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{5}} −{x}^{\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{4}{x}}{dx} \\ $$ Commented by abdomathmax last updated on 27/Mar/20 $${A}\:=\int\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} \left({x}^{\mathrm{3}} −\mathrm{4}{x}\right)+\mathrm{7}{x}^{\mathrm{3}}…
Question Number 20501 by Tinkutara last updated on 27/Aug/17 $$\mathrm{The}\:\mathrm{force}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{the}\:\mathrm{block}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${F}\:=\:\mathrm{5}\:−\:\mathrm{2}{t}.\:\mathrm{The}\:\mathrm{frictional}\:\mathrm{force}\:\mathrm{acting} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{block}\:\mathrm{at}\:{t}\:=\:\mathrm{2}\:\mathrm{s}.\:\left(\mathrm{The}\:\mathrm{block}\:\mathrm{is}\:\mathrm{at}\right. \\ $$$$\left.\mathrm{rest}\:\mathrm{at}\:{t}\:=\:\mathrm{0}\right) \\ $$ Commented by Tinkutara last updated on 27/Aug/17…
Question Number 86034 by ar247 last updated on 26/Mar/20 $$\int\frac{{dx}}{\:\sqrt{×^{\mathrm{2}} +\mathrm{4}}} \\ $$ Answered by TANMAY PANACEA. last updated on 26/Mar/20 $${x}=\mathrm{2}{tana}\:\:\frac{{dx}}{{da}}=\mathrm{2}{sec}^{\mathrm{2}} {a} \\ $$$$\int\frac{\mathrm{2}{sec}^{\mathrm{2}}…
Question Number 151568 by tabata last updated on 21/Aug/21 $$\int\:\sqrt{{sec}\left({x}\right)+{tan}\left({x}\right)}\:{dx} \\ $$$$ \\ $$$${how}\:{can}\:{it}\:{solve} \\ $$ Answered by puissant last updated on 22/Aug/21 $$=\int\sqrt{\frac{\mathrm{1}}{{cosx}}+\frac{{sinx}}{{cosx}}}{dx} \\…
Question Number 86030 by oustmuchiya@gmail.com last updated on 26/Mar/20 $${Tbe}\:{function}\:\boldsymbol{\mathrm{f}}\:{and}\:\boldsymbol{\mathrm{g}}\:{are}\:{defined}\:{by}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{3}\boldsymbol{\mathrm{x}}. \\ $$$$\boldsymbol{\mathrm{F}}{ind}\:\left(\boldsymbol{\mathrm{a}}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\:\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{gf}}\left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\boldsymbol{\mathrm{c}}\right)\:\boldsymbol{\mathrm{gf}}\left(\mathrm{2}\right) \\ $$ Commented by Rio Michael last updated on 26/Mar/20 $$\:{f}:\:{x}\:\rightarrow\:\mathrm{2}{x}−\mathrm{3}\:\:\:\mathrm{and}\:\mathrm{g}\::\:{x}\:\rightarrow\:\mathrm{3}{x} \\…
Question Number 86031 by arcana last updated on 26/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}−\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}}{\mathrm{sin}\:^{\mathrm{2}} {x}}= \\ $$ Commented by arcana last updated on 26/Mar/20 $${the}\:{answer}\:{is}\:\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{2}}} \\ $$ Commented…