Question Number 116006 by DELETED last updated on 30/Sep/20 $$\mathrm{3}\left(\mathrm{sin}\:{x}−\mathrm{cos}\:{x}\right)^{\mathrm{4}} +\mathrm{6}\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{4}\left(\mathrm{sin}^{\mathrm{6}} {x}+\mathrm{cos}^{\mathrm{6}} {x}\right)\:=\:\_\_\_\_\_. \\ $$ Answered by mindispower last updated on 30/Sep/20 $$\left({sin}^{\mathrm{2}}…
Question Number 115695 by ZiYangLee last updated on 27/Sep/20 $$\mathrm{The}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\:\mid\left({x}−\mathrm{2}\right)^{\mathrm{2}} \mid−\mathrm{3}\mid{x}−\mathrm{2}\mid+\mathrm{2}=\mathrm{0}\:\:\mathrm{is} \\ $$ Answered by MJS_new last updated on 27/Sep/20 $${x}=\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{0} \\ $$…
Question Number 115685 by ZiYangLee last updated on 27/Sep/20 $$\mathrm{If}\:\:\alpha,\:\beta,\:\gamma,\:\delta\:\:\mathrm{are}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\: \\ $$$$\mathrm{angles}\:\mathrm{in}\:\mathrm{ascending}\:\mathrm{order}\:\mathrm{of} \\ $$$$\mathrm{magnitude}\:\mathrm{which}\:\mathrm{have}\:\mathrm{their}\:\mathrm{sines}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{quantity}\:{k},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{4}\:\mathrm{sin}\:\frac{\alpha}{\mathrm{2}}+\mathrm{3}\:\mathrm{sin}\:\frac{\beta}{\mathrm{2}}+\mathrm{2}\:\mathrm{sin}\:\frac{\gamma}{\mathrm{2}}+\mathrm{sin}\:\frac{\delta}{\mathrm{2}}\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$ Answered…
Question Number 50132 by CIRCLE001 last updated on 14/Dec/18 $$\mathrm{Let}\:{f}\:\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{function}.\:\mathrm{Let} \\ $$$${I}_{\mathrm{1}} =\underset{\mathrm{1}−{k}} {\overset{{k}} {\int}}{x}\:{f}\left\{{x}\left(\mathrm{1}−{x}\right\}\:{dx},\:\right. \\ $$$${I}_{\mathrm{2}} =\underset{\mathrm{1}−{k}} {\overset{{k}} {\int}}{x}\:{f}\left\{{x}\left(\mathrm{1}−{x}\right\}\:{dx},\:\right. \\ $$$$\mathrm{where}\:\mathrm{2}{k}−\mathrm{1}>\mathrm{0}.\:\mathrm{Then}\:\frac{{I}_{\mathrm{1}} }{{I}_{\mathrm{2}} }\:\:\mathrm{is} \\…
Question Number 115404 by EvoneAkashi last updated on 25/Sep/20 $$\:\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:= \\ $$ Answered by mathmax by abdo last updated on 25/Sep/20 $$\mathrm{let}\:\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 115403 by EvoneAkashi last updated on 25/Sep/20 $$\int\:{e}^{{x}} \:\frac{\mathrm{1}+{n}\:{x}^{{n}−\mathrm{1}} −{x}^{\mathrm{2}{n}} }{\left(\mathrm{1}−{x}\right)^{{n}} \:\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}{n}} }}\:{dx}\:= \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115399 by EvoneAkashi last updated on 25/Sep/20 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{term}\:\mathrm{independent} \\ $$$$\mathrm{of}\:{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}/\mathrm{3}} −\:{x}^{\mathrm{1}/\mathrm{3}} +\:\mathrm{1}}\:−\:\frac{{x}−\mathrm{1}}{{x}−{x}^{\mathrm{1}/\mathrm{2}} }\right)^{\mathrm{10}} \:\:\mathrm{is} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 49751 by Pk1167156@gmail.com last updated on 10/Dec/18 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}\:\:\mathrm{is} \\ $$ Commented by maxmathsup by imad last updated on 10/Dec/18 $${we}\:{have}\:{tan}\left({arctan}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+{arctan}\left(\frac{\mathrm{1}}{\mathrm{3}}\right)\right)= \\…
Question Number 49692 by Micky24 last updated on 09/Dec/18 $$\mathrm{The}\:\mathrm{vectors}\:\boldsymbol{\mathrm{a}}={x}\boldsymbol{\mathrm{i}}+\left({x}+\mathrm{1}\right)\boldsymbol{\mathrm{j}}+\left({x}+\mathrm{2}\right)\boldsymbol{\mathrm{k}}, \\ $$$$\boldsymbol{\mathrm{b}}=\left({x}+\mathrm{3}\right)\boldsymbol{\mathrm{i}}+\left({x}+\mathrm{4}\right)\boldsymbol{\mathrm{j}}+\left({x}+\mathrm{5}\right)\boldsymbol{\mathrm{k}}\:\:\:\mathrm{and} \\ $$$$\boldsymbol{\mathrm{c}}=\left({x}+\mathrm{6}\right)\boldsymbol{\mathrm{i}}+\left({x}+\mathrm{7}\right)\boldsymbol{\mathrm{j}}+\left({x}+\mathrm{8}\right)\boldsymbol{\mathrm{k}}\:\mathrm{are}\:\mathrm{coplanar} \\ $$$$\mathrm{for} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 09/Dec/18…
Question Number 49463 by Pk1167156@gmail.com last updated on 07/Dec/18 $$\mathrm{If}\:\:\:\mathrm{7}^{\mathrm{log}\:_{\mathrm{7}} \left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}\right)} =\:{x}−\mathrm{1},\:\:{x}\:\mathrm{may}\:\mathrm{have} \\ $$$$\mathrm{values} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 07/Dec/18 $${a}^{{x}}…