Question Number 69894 by Rio Michael last updated on 28/Sep/19 $$\int\:\frac{\mathrm{2}{x}^{\mathrm{5}} −{x}}{{x}^{\mathrm{3}} −\mathrm{2}}{dx} \\ $$ Commented by abdo mathsup 649 cc last updated on 29/Sep/19…
Question Number 4358 by Rasheed Soomro last updated on 12/Jan/16 $$\mathrm{Determine}\:\mathrm{integer}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{bx}^{\mathrm{a}} +\mathrm{ay}^{\mathrm{b}} =\mathrm{cz}^{\mathrm{c}} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{fixed}\:\mathrm{integers}. \\ $$ Commented by Filup last updated on…
Question Number 135431 by 777316 last updated on 13/Mar/21 Answered by SEKRET last updated on 13/Mar/21 $$\boldsymbol{\mathrm{F}}\left(\boldsymbol{\mathrm{a}}\right)=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\mathrm{1}\right)}{\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)}\:\boldsymbol{\mathrm{dx}}\:\:\:\:\:\:\boldsymbol{\mathrm{a}}=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{F}}\:'\left(\boldsymbol{\mathrm{a}}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{ax}}^{\mathrm{2}}…
Question Number 4356 by Rasheed Soomro last updated on 12/Jan/16 Commented by Rasheed Soomro last updated on 12/Jan/16 $$\mathcal{D}{etermine}\:{area}\:{of}\:{above}\:{closed} \\ $$$${figure}\:\:{in}\:{the}\:{easiest}\:{way}. \\ $$ Answered by…
Question Number 135424 by benjo_mathlover last updated on 13/Mar/21 $${Find}\:{solution}\:{set}\:{the}\:{inequality} \\ $$$$\sqrt{\mathrm{2}{x}−\mathrm{5}}\:+\:\sqrt{\mathrm{25}−\mathrm{3}{x}}\:>\:{x} \\ $$ Answered by EDWIN88 last updated on 13/Mar/21 $$\left(\mathrm{1}\right)\:\mathrm{2x}−\mathrm{5}\geqslant\mathrm{0}\rightarrow\mathrm{x}\geqslant\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{3x}−\mathrm{25}\leqslant\mathrm{0}\rightarrow\mathrm{x}\leqslant\frac{\mathrm{25}}{\mathrm{3}} \\…
Question Number 135421 by benjo_mathlover last updated on 13/Mar/21 Commented by mr W last updated on 13/Mar/21 $${radius}\:{of}\:{semicircle} \\ $$$${R}={a}+{b}−\sqrt{\mathrm{2}{ab}} \\ $$ Commented by EDWIN88…
Question Number 135420 by liberty last updated on 13/Mar/21 $${Algebra} \\ $$Pipe A can fill a tank in two hours and pipe B can fill…
Question Number 135423 by benjo_mathlover last updated on 13/Mar/21 $${If}\:\overset{\rightarrow} {{a}}=\left(\mathrm{4},\mathrm{2},−\mathrm{1}\right),\:\overset{\rightarrow} {{b}}=\left({m},\mathrm{1},\mathrm{1}\right) \\ $$$$\overset{\rightarrow} {{c}}=\left(\bar {\mathrm{3}}−\mathrm{1},\mathrm{0}\right)\:{are}\:{three}\:{vectors} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:{m}\:{such} \\ $$$${that}\:\overset{\rightarrow} {{a}},\overset{\rightarrow} {{b}}\:{and}\:\overset{\rightarrow} {{c}}\:{are}\:{coplanar}\:{and} \\ $$$${find}\:\overset{\rightarrow}…
Question Number 135419 by liberty last updated on 13/Mar/21 $$\sqrt{\mathrm{3}}\:\mathrm{tan}\:{x}.\mathrm{cot}\:{x}\:+\sqrt{\mathrm{3}}\:\mathrm{tan}\:{x}−\mathrm{cot}\:{x}−\mathrm{1}\:=\:\mathrm{0} \\ $$ Answered by benjo_mathlover last updated on 13/Mar/21 $$\Rightarrow\sqrt{\mathrm{3}}\:\mathrm{tan}\:{x}\left(\mathrm{cot}\:{x}+\mathrm{1}\right)−\left(\mathrm{cot}\:{x}+\mathrm{1}\right)=\mathrm{0} \\ $$$$\left(\sqrt{\mathrm{3}}\:\mathrm{tan}\:{x}−\mathrm{1}\right)\left(\mathrm{cot}\:{x}+\mathrm{1}\right)\:=\:\mathrm{0} \\ $$$$\begin{cases}{\mathrm{tan}\:{x}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}}\\{\mathrm{cot}\:{x}=−\mathrm{1}\Rightarrow\mathrm{tan}\:{x}=−\mathrm{1}}\end{cases} \\…
Question Number 135418 by liberty last updated on 13/Mar/21 $${Given}\:{x}+\frac{\mathrm{1}}{{x}}\:=\:\mathrm{5}\:{then}\:\frac{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }}{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}}\:? \\ $$ Answered by SEKRET last updated on 13/Mar/21 $$\:\left(\boldsymbol{\mathrm{x}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)^{\mathrm{2}} =\mathrm{5}^{\mathrm{2}} \:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}}…