Question Number 126702 by Eric002 last updated on 30/Dec/20 $${if}\:\:\:\:{tanh}\frac{{x}}{\mathrm{2}}={t}\:\:{prove}\:{that}\:\:{cosh}\left({x}\right)=\frac{\mathrm{1}+{t}^{\mathrm{2}} }{\mathrm{1}−{t}^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by MJS_new last updated on 23/Dec/20 $$\mathrm{tanh}\:\alpha\:=\frac{\mathrm{e}^{\mathrm{2}\alpha} −\mathrm{1}}{\mathrm{e}^{\mathrm{2}\alpha}…
Question Number 126700 by Eric002 last updated on 23/Dec/20 $$\theta={sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{5}}\right)\:{find}\:{cos}\left(\theta\right)\:{and}\:{tan}\left(\theta\right) \\ $$$$ \\ $$ Answered by akornes last updated on 23/Dec/20 $${cos}\theta=\pm\frac{\sqrt{\mathrm{21}}}{\mathrm{5}}\:{and}\:{tan}\theta=\pm\frac{\mathrm{2}\sqrt{\mathrm{21}}}{\mathrm{21}} \\ $$…
Question Number 126701 by Eric002 last updated on 23/Dec/20 $${use}\:{right}\:{triangles}\:{to}\:{explain} \\ $$$${why}\:{cos}^{−\mathrm{1}} \left({x}\right)+{sin}^{−\mathrm{1}} \left({x}\right)=\pi/\mathrm{2} \\ $$ Answered by ebi last updated on 23/Dec/20 $$ \\…
Question Number 61162 by Tawa1 last updated on 29/May/19 $$\mathrm{if}\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:\:=\:\:\frac{\mathrm{x}\:−\:\mathrm{20}}{\mathrm{20}}\:\:,\:\:\:\mathrm{find}\:\:\mathrm{x} \\ $$ Commented by kaivan.ahmadi last updated on 29/May/19 $${we}\:{can}\:{find}\:{number}\:{of}\:{solution}\:{by}\:{plote} \\ $$$${y}={sinx}\:{and}\:{y}=\frac{{x}−\mathrm{20}}{\mathrm{20}} \\ $$$${this}\:{equation}\:{has}\:\mathrm{13}\:{answer} \\…
Question Number 61140 by MJS last updated on 29/May/19 $$\mathrm{can}\:\mathrm{we}\:\mathrm{find}\:\mathrm{an}\:\mathrm{exact}\:\mathrm{solution}? \\ $$$${t}^{\mathrm{6}} +\mathrm{4}{t}^{\mathrm{4}} −\mathrm{12}{t}^{\mathrm{3}} +\mathrm{24}{t}^{\mathrm{2}} −\mathrm{24}{t}+\mathrm{8}=\mathrm{0} \\ $$ Commented by ajfour last updated on 04/Jun/19…
Question Number 61137 by Tawa1 last updated on 29/May/19 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{3n}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:,\:\mathrm{if}\:\mathrm{the}\:\mathrm{sunm}\:\mathrm{of}\:\mathrm{first}\:\mathrm{n}\:\mathrm{term}\:\mathrm{is} \\ $$$$\mathrm{2n}\:\:\mathrm{and}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{2n}\:\mathrm{term}\:\mathrm{is}\:\:\mathrm{5n} \\ $$ Answered by Kunal12588 last updated on 29/May/19 $${S}_{{n}} =\mathrm{2}{n} \\ $$$$\Rightarrow\frac{{n}}{\mathrm{2}}\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right)=\mathrm{2}{n}…
Question Number 61117 by Tawa1 last updated on 29/May/19 $$\mathrm{The}\:\mathrm{2nd},\:\mathrm{4th}\:\mathrm{and}\:\mathrm{8th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{consecutive}\:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{GP}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{3rd}\:\mathrm{and}\:\mathrm{4th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}\:\mathrm{is}\:\mathrm{20}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}. \\ $$ Answered by Kunal12588 last updated on 29/May/19 $${given}\:\:{a}_{\mathrm{2}} ,{a}_{\mathrm{4}}…
Question Number 192186 by Tawa11 last updated on 11/May/23 $$\mathrm{If}\:\:\alpha,\:\beta\:\:\mathrm{and}\:\gamma\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\:\:\mathrm{x}^{\mathrm{3}} \:\:+\:\:\mathrm{px}\:\:+\:\:\mathrm{q}\:\:=\:\:\mathrm{0},\:\:\:\:\mathrm{find}\:\:\:\Sigma\alpha^{\mathrm{4}} . \\ $$ Answered by BaliramKumar last updated on 10/May/23 $$\mathrm{2p}^{\mathrm{2}} \\ $$ Commented…
Question Number 61111 by Tawa1 last updated on 29/May/19 $$\mathrm{Please}\:\mathrm{what}\:\mathrm{does}\:\mathrm{the}\:\mathrm{2}\:\mathrm{on}\:\mathrm{the}\:\mathrm{C}\:\mathrm{mean}. \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{C}_{\mathrm{1}} ^{\mathrm{2}} \:+\:\mathrm{2}\:\mathrm{C}_{\mathrm{2}} ^{\mathrm{2}} \:+\:\mathrm{3}\:\mathrm{C}_{\mathrm{3}} ^{\mathrm{2}} \:+\:…\:+\:\mathrm{n}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{2}} \:\:\:\:=\:\:\:\frac{\left(\mathrm{2n}\:−\:\mathrm{1}\right)!}{\left[\left(\mathrm{n}\:−\:\mathrm{1}\right)!\right]^{\mathrm{2}} } \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{2}\:\mathrm{on}\:\mathrm{C}\:\mathrm{mean}\:\mathrm{square}\:??…
Question Number 192173 by universe last updated on 10/May/23 $${prove}\:{that} \\ $$$$\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{4}} \:=\:\left({x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{2}} {a}^{\mathrm{2}} +{a}^{\mathrm{4}} \right)^{\mathrm{2}} +\left(\mathrm{4}{x}^{\mathrm{3}} {a}−\mathrm{4}{xa}^{\mathrm{3}} \right)^{\mathrm{2}} \\ $$ Answered…