Question Number 76724 by Rio Michael last updated on 29/Dec/19 $$\int_{\mathrm{0}} ^{\mathrm{3}} \mid\mathrm{x}^{\mathrm{2}} −\mathrm{1}\mid\:\mathrm{dx}\:\equiv\: \\ $$ Commented by abdomathmax last updated on 30/Dec/19 $$\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 76725 by Rio Michael last updated on 29/Dec/19 $$\mathrm{To}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{x}^{\mathrm{2}} >\mathrm{y}^{\mathrm{2}} ,\:\mathrm{it}\:\mathrm{is}\:\mathrm{sufficient}\:\mathrm{to}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{A}.\:\mathrm{x}\:>\:\mathrm{y} \\ $$$$\mathrm{B}.\:\mathrm{x}^{\mathrm{3}} >\mathrm{y}^{\mathrm{3}} \\ $$$$\mathrm{C}.\:\mid\mathrm{x}\mid\:>\:\mid\mathrm{y}\mid \\ $$$$\mathrm{D}.\:\mathrm{x}\:>\:\mathrm{3y} \\…
Question Number 142256 by rs4089 last updated on 28/May/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}^{\mathrm{1}−{a}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 28/May/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 76723 by Rio Michael last updated on 29/Dec/19 $$\mathrm{the}\:\mathrm{maclaurin}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{ln}\:\left(\mathrm{3}\:+\:\mathrm{4}{x}\right)\:{is}\:{valid}\:{for} \\ $$$$\left.{A}\right)\:\:−\frac{\mathrm{3}}{\mathrm{4}}\:\leqslant\:\mathrm{x}<\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\left.\mathrm{B}\right)\:−\frac{\mathrm{3}}{\mathrm{4}}<\:\mathrm{x}\:\leqslant\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\left.\mathrm{C}\right)\:−\frac{\mathrm{1}}{\mathrm{4}}<\:\mathrm{x}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{D}\right)\:−\frac{\mathrm{3}}{\mathrm{4}}<\:\mathrm{x}\:<\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$ Terms of Service Privacy…
Question Number 76721 by Rio Michael last updated on 29/Dec/19 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{4x}^{\mathrm{2}\:} }\:\:\mathrm{for}\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by MJS last updated on 30/Dec/19 $$\mathrm{mean}\:\left({f}\left({x}\right)\right)\:\mathrm{with}\:{a}\leqslant{x}\leqslant{b} \\ $$$$\frac{\mathrm{1}}{{b}−{a}}\underset{{a}} {\overset{{b}}…
Question Number 142253 by mathdave last updated on 28/May/21 Answered by mr W last updated on 28/May/21 $$\mathrm{3}\:{black} \\ $$$$\mathrm{4}\:{white} \\ $$$$\mathrm{5}\:{red} \\ $$$$\Sigma=\mathrm{12}\:{balls} \\…
Question Number 76718 by peter frank last updated on 29/Dec/19 $${For}\:{n}\:\in\:{N}\:{prove}\:{by}\:{mathematical} \\ $$$${induction}\:{that} \\ $$$$\mathrm{cos}\:\alpha+\mathrm{cos}\:\left(\alpha+\beta\right)+\mathrm{cos}\:\left[\alpha+\left({n}−\mathrm{1}\right)\beta\right]+…\mathrm{cos}\:\left[\alpha+\left({n}−\mathrm{1}\right)\beta\right]= \\ $$$$\frac{\mathrm{cos}\:\left[\alpha+\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right)\beta\right]\mathrm{sin}\:\frac{{n}\beta}{\mathrm{2}}}{\mathrm{sin}\:\frac{{n}}{\mathrm{2}}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 11183 by Nayon last updated on 15/Mar/17 Answered by mrW1 last updated on 16/Mar/17 $${let}\:{x}=\frac{{AD}}{{AB}} \\ $$$$\Rightarrow{DE}={x}×{BC} \\ $$$${a}={ABC}=\frac{\mathrm{1}}{\mathrm{2}}×{BC}×{h} \\ $$$${ADC}=\frac{\mathrm{1}}{\mathrm{2}}×{DE}×{h}=\frac{\mathrm{1}}{\mathrm{2}}×{x}×{BC}×{h}={xa} \\ $$$${ADE}=\frac{\mathrm{1}}{\mathrm{2}}×{DE}×{x}×{h}=\frac{\mathrm{1}}{\mathrm{2}}×{x}×{BC}×{x}×{h}={x}^{\mathrm{2}}…
Question Number 142252 by Algoritm last updated on 28/May/21 Answered by MJS_new last updated on 29/May/21 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{for}\:{x}\:\mathrm{then}\:\mathrm{insert}\:\mathrm{into}\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}} \\ $$$$\mathrm{let}\:{y}=\mathrm{2arctan}\:{t} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{t} \\ $$$$\mathrm{check}\:\mathrm{all}\:\mathrm{solutions} \\…
Question Number 142255 by gsk2684 last updated on 28/May/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{x}^{\mathrm{4}} −\mathrm{5x}^{\mathrm{2}} +\mathrm{4}}\:\mathrm{dx}? \\ $$$$\mathrm{solution}\:\mathrm{please}. \\ $$ Answered by mindispower last updated on 28/May/21…