Question Number 73550 by Rio Michael last updated on 13/Nov/19 $${solve}\: \\ $$$$\:\:\mathrm{87}{x}\:\equiv\:\mathrm{3}\:\left({mod}\:\mathrm{5}\right)\:{and} \\ $$$$\:\mathrm{55}{x}\:\equiv\:\mathrm{35}\:\left({mod}\:\mathrm{75}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8015 by tawakalitu last updated on 28/Sep/16 $$\int\frac{\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }}{\mathrm{1}\:+\:{x}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73551 by Rio Michael last updated on 13/Nov/19 $${how}\:{many}\:{divisors}\:{does}\:\mathrm{38500}\:{have}? \\ $$ Answered by mind is power last updated on 13/Nov/19 $$\mathrm{38500} \\ $$$$=\mathrm{10}^{\mathrm{2}}…
Question Number 8013 by Yozzia last updated on 28/Sep/16 $${Prove}\:{that},\:\forall{m}\in\mathbb{N}, \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{m}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}−\mathrm{1}}\end{pmatrix}\:\left(\mathrm{2}{r}−\mathrm{1}\right)^{\mathrm{2}{m}−\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{{m}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}}\end{pmatrix}\:\left(\mathrm{2}{r}\right)^{\mathrm{2}{m}−\mathrm{1}} . \\ $$ Commented by FilupSmith last updated…
Question Number 139081 by BHOOPENDRA last updated on 22/Apr/21 Commented by BHOOPENDRA last updated on 22/Apr/21 $${help}\:{me}\:{out}\:{this}\: \\ $$ Commented by BHOOPENDRA last updated on…
Question Number 73544 by Rio Michael last updated on 13/Nov/19 $${expressf}\left(\theta\right)=\:\mathrm{8}{cos}\theta\:−\mathrm{15}{sin}\theta\:{in}\:{the}\:{form} \\ $$$$\:{rcos}\left(\theta\:+\:\alpha\right),\:{where}\:{r}>\mathrm{0}\:{and}\:\alpha\:{is}\:{a}\:{positive}\:{acute}\:{angle} \\ $$$${hence} \\ $$$${find}\:{the}\:{general}\:{solution}\:{of}\:{the}\:{equation} \\ $$$$\:\:\mathrm{80}{cos}\:\theta\:−\mathrm{150}{sin}\theta\:=\:\mathrm{13} \\ $$$${the}\:{maximum}\:{and}\:{minimum}\:{value}\:{of}\:\:\frac{\mathrm{5}}{{f}\left(\theta\right)\:+\:\mathrm{3}} \\ $$ Answered by…
Question Number 73545 by Rio Michael last updated on 13/Nov/19 $${evaluate}\:\:\int{lnx}\:{dx} \\ $$ Commented by Tony Lin last updated on 13/Nov/19 $${integration}\:{by}\:{part} \\ $$$$\int{f}\:'\left({x}\right){g}\left({x}\right)={f}\left({x}\right){g}\left({x}\right)−\int{f}\left({x}\right){g}\:'\left({x}\right) \\…
Question Number 73542 by Rio Michael last updated on 13/Nov/19 $${Given}\:{that}\:{the}\:{function}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} \:{is}\:{differentiable} \\ $$$${in}\:{the}\:{interval}\:\left(−\mathrm{2},\mathrm{2}\right),\:{Use}\:{the}\:{mean}\:{value}\:{theorem} \\ $$$${to}\:{find}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{the}\:{tangent}\:{to}\:{the}\:{curve} \\ $$$${is}\:{parallel}\:{to}\:{the}\:{chord}\:{through}\:{the}\:{point}\:\left(−\mathrm{2},\mathrm{8}\right)\:{and}\:\left(\mathrm{2},\mathrm{8}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 139076 by bramlexs22 last updated on 22/Apr/21 $$\lceil\:\mathrm{3x}\:+\:\mathrm{5}\lfloor\:\mathrm{x}\:\rfloor\:\rceil\:=\:\mathrm{9} \\ $$ Answered by mathmax by abdo last updated on 22/Apr/21 $$\Rightarrow\left[\mathrm{3x}\right]+\mathrm{5}\left[\mathrm{x}\right]=\mathrm{9}\:\:\:\mathrm{let}\:\left[\mathrm{x}\right]=\mathrm{n}\:\Rightarrow\mathrm{n}\leqslant\mathrm{x}<\mathrm{n}+\mathrm{1}\:\Rightarrow\mathrm{3n}\leqslant\mathrm{3x}<\mathrm{3n}+\mathrm{3} \\ $$$$\mathrm{if}\:\mathrm{3n}\leqslant\mathrm{3x}<\mathrm{3n}+\mathrm{1}\:\Rightarrow\left[\mathrm{3x}\right]=\mathrm{3n}\:\:\mathrm{and}\:\mathrm{e}\Rightarrow\mathrm{3n}+\mathrm{5n}=\mathrm{9}\:\Rightarrow\mathrm{8n}=\mathrm{9}\:\:\mathrm{impossible} \\…
Question Number 139079 by peter frank last updated on 22/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com