Question Number 61039 by mathsolverby Abdo last updated on 28/May/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left(\frac{\mathrm{2}}{\mathrm{1}+{x}}\right){dx} \\ $$ Commented by maxmathsup by imad last updated on 29/May/19 $${let}\:{A}\:=\int_{\mathrm{0}}…
Question Number 126575 by amns last updated on 22/Dec/20 $$\boldsymbol{{Solve}}:\:{sin}\theta\:+\:{cos}\theta\:=\:\mathrm{1},\:\boldsymbol{{when}}\:\mathrm{0}°\:\leqslant\:\theta\:\leqslant\:\mathrm{90}° \\ $$ Commented by amns last updated on 22/Dec/20 $${I}\:{need}\:{a}\:{help}\:{to}\:{solve}\:{it},\:\boldsymbol{{Help}}\:\boldsymbol{{me}}. \\ $$ Commented by benjo_mathlover…
Question Number 126572 by sdfg last updated on 22/Dec/20 Answered by liberty last updated on 22/Dec/20 $$\:\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid^{\mathrm{2}} =\:\mid\overset{\rightarrow} {{a}}\mid^{\mathrm{2}} +\mid\overset{\rightarrow} {{b}}\mid^{\mathrm{2}} +\mathrm{2}\mid\overset{\rightarrow} {{a}}\mid\mid\overset{\rightarrow}…
Question Number 192105 by Spillover last updated on 08/May/23 Answered by mehdee42 last updated on 09/May/23 $$\left.\:{a}\right)\:\:\:{lema}\::\:{if}\:\:\mathrm{0}<{x}<\mathrm{1}\:\Rightarrow\:\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}{ix}^{{i}} =\frac{{x}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }\:\:\:\&\:\:\:\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}{i}^{\mathrm{2}} {x}^{{i}} =\frac{{x}\left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}−{x}\right)^{\mathrm{3}}…
Question Number 192104 by Spillover last updated on 08/May/23 Answered by otchereabdullai@gmail.com last updated on 08/May/23 $${a}.\:\frac{\mathrm{12}!}{\mathrm{2}!\mathrm{2}!\mathrm{2}!}\:=\mathrm{59875200}\:{ways} \\ $$$${b}.\:\:\frac{\mathrm{11}!}{\mathrm{2}!\mathrm{2}!}\:=\:\mathrm{9979200}\:{ways} \\ $$ Commented by Spillover last…
Question Number 126571 by benjo_mathlover last updated on 22/Dec/20 $$\:\:\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}\:^{\mathrm{2}} {x}−\mathrm{1}}}\:{dx}\:?\: \\ $$ Answered by MJS_new last updated on 22/Dec/20 $$\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}^{\mathrm{2}} \:{x}\:−\mathrm{1}}}{dx}=\int\sqrt{\frac{\mathrm{tan}\:{x}}{\mathrm{tan}^{\mathrm{2}} \:{x}\:−\mathrm{1}}}{dx}= \\ $$$$=−\frac{\mathrm{i}}{\:\sqrt{\mathrm{2}}}\int\sqrt{\mathrm{tan}\:\mathrm{2}{x}}{dx}…
Question Number 126567 by sdfg last updated on 21/Dec/20 Answered by physicstutes last updated on 22/Dec/20 $$\:\boldsymbol{\mathrm{A}}\:=\:\left({k},{k}\right)\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:=\:\left(−\mathrm{3},\mathrm{4}\right) \\ $$$$\boldsymbol{\mathrm{A}}.\boldsymbol{\mathrm{B}}\:=\:\mid\boldsymbol{\mathrm{A}}\mid\mid\boldsymbol{\mathrm{B}}\mid\:\mathrm{cos}\:\theta \\ $$$$\Rightarrow\:−\mathrm{3}{k}+\mathrm{4}{k}\:=\:{k} \\ $$$$\Rightarrow\:{k}\:=\:\sqrt{{k}^{\mathrm{2}} +{k}^{\mathrm{2}} }\:.\sqrt{\left(−\mathrm{3}\right)^{\mathrm{2}}…
Question Number 61030 by aanur last updated on 28/May/19 Commented by prakash jain last updated on 28/May/19 $${x}^{\mathrm{2}} =\mathrm{3}\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{4}} =\mathrm{9}×\mathrm{3}=\mathrm{27}=\mathrm{3}^{\mathrm{3}} \Rightarrow{x}=\mathrm{3}^{\mathrm{3}/\mathrm{4}} \\ $$$${y}^{\mathrm{2}}…
Question Number 192103 by Spillover last updated on 08/May/23 Answered by otchereabdullai@gmail.com last updated on 08/May/23 $${the}\:{most}\:{important}\:{thing}\:{to}\:{know}\:{is} \\ $$$${we}\:{cant}\:{start}\:{the}\:{number}\:{with}\:{zero} \\ $$$${since}\:{is}\:{a}\:{four}\:{digit}\:{mumber}\:{without} \\ $$$${repetition} \\ $$$${the}\:{first}\:{can}\:{be}\:{chosen}\:{in}\:\mathrm{5}\:{ways},…
Question Number 126562 by mey3nipaba last updated on 21/Dec/20 $${Prove}\:{that}\:\mathrm{2sin}\:\frac{\theta+\phi}{\mathrm{2}}\mathrm{cos}\:\frac{\theta−\phi}{\mathrm{2}}=\mathrm{sin}\:\theta+\mathrm{sin}\:\emptyset \\ $$$${I}\:{need}\:{help}\:{immediately}\:{please} \\ $$ Commented by mr W last updated on 21/Dec/20 $$\theta=\frac{\theta+\varphi}{\mathrm{2}}+\frac{\theta−\varphi}{\mathrm{2}} \\ $$$$\varphi=\frac{\theta+\varphi}{\mathrm{2}}−\frac{\theta−\varphi}{\mathrm{2}}…