Question Number 73757 by Maclaurin Stickker last updated on 15/Nov/19 $$\mathrm{cos}\:\mathrm{70}°+\mathrm{sin}\:\mathrm{200}°=? \\ $$ Commented by mathmax by abdo last updated on 15/Nov/19 $$\mathrm{70}^{{o}} =\frac{\mathrm{70}\pi}{\mathrm{180}}\:=\frac{\mathrm{7}\pi}{\mathrm{18}}\:\:\:{and}\:\mathrm{200}^{{o}} =\frac{\mathrm{200}\pi}{\mathrm{180}}\:=\frac{\mathrm{20}\pi}{\mathrm{18}}\:\Rightarrow…
Question Number 139288 by 7770 last updated on 25/Apr/21 $$\boldsymbol{{IF}}\:\frac{\boldsymbol{{x}}^{\mathrm{3}} +\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1}}=\boldsymbol{{x}}+\sqrt{\frac{\mathrm{6}}{\boldsymbol{{x}}}} \\ $$$$\mathrm{6}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{{x}}+\mathrm{4}=?? \\ $$ Answered by MJS_new last updated on 25/Apr/21 $$\frac{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…
Question Number 73755 by ~blr237~ last updated on 15/Nov/19 $${show}\:{that}\:\:\:{for}\:{all}\:{integer}\:\:{n}\:,\:\:{n}+\mathrm{1}\:{divides}\:\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix} \\ $$ Answered by mind is power last updated on 15/Nov/19 $$\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}=\frac{\left(\mathrm{2}{n}\right)!}{{n}!{n}!}\in\mathbb{N} \\ $$$$\frac{{n}}{{n}+\mathrm{1}}\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}=\frac{\mathrm{2}{n}!}{{n}!.\left({n}\right)!}.\frac{{n}}{{n}+\mathrm{1}}=\frac{\mathrm{2}{n}!}{\left({n}−\mathrm{1}\right)!.\left({n}+\mathrm{1}\right)!}=\begin{pmatrix}{\mathrm{2}{n}}\\{{n}+\mathrm{1}}\end{pmatrix} \\…
Question Number 8217 by tawakalitu last updated on 02/Oct/16 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{x}^{\mathrm{5}} \right)^{\mathrm{6}} \\ $$ Commented by 123456 last updated on…
Question Number 139290 by mathdanisur last updated on 25/Apr/21 $$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{{sin}\left({x}^{\mathrm{2}} −{arctan}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\right)}{\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx} \\ $$ Answered by Ar Brandon last updated on 25/Apr/21…
Question Number 139285 by mohammad17 last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({x}\right){cos}^{\mathrm{6}} \left({x}\right){dx} \\ $$ Answered by qaz last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}}…
Question Number 73751 by ~blr237~ last updated on 15/Nov/19 $${Find}\:\:{out}\:{the}\:{value}\:{of}\:\:\: \\ $$$$\:\:{J}=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{2}{e}^{−\mathrm{2}{xy}} −{e}^{−{xy}} \right){dxdy}\: \\ $$ Commented by mathmax by abdo…
Question Number 139286 by qaz last updated on 25/Apr/21 $$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{{n}} }=\left(\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\right)+\left(\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\right){x}+\left(\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\right){x}^{\mathrm{2}} +\left(\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\right){x}^{\mathrm{3}} +… \\ $$ Commented by mr W last updated on 25/Apr/21 $${wrong}! \\…
Question Number 73746 by mhmd last updated on 15/Nov/19 $${total}\:{numper}\:{of}\:{words}\:{formed}\:{by}\:\mathrm{2}\:{vowels}\:{and}\:\mathrm{3}\:{consonants}\:{take}\:{from}\:{vowels}\:{and}\:\mathrm{5}\:{consonants}\:{is}\:{equal}\:{to}\:? \\ $$$${pleas}\:{sir}\:{help}\:{me}\:? \\ $$ Commented by MJS last updated on 15/Nov/19 $$\mathrm{something}'\mathrm{s}\:\mathrm{missing} \\ $$ Answered…
Question Number 139283 by qaz last updated on 25/Apr/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{ln}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{8}{a}}\left(\pi^{\mathrm{2}} +\mathrm{4}{ln}^{\mathrm{2}} {a}\right)\:\:\:\:\:\:\:\:\:,{a}>\mathrm{0} \\ $$ Answered by Ar Brandon last updated…