Question Number 18456 by Tinkutara last updated on 21/Jul/17 $$\mathrm{The}\:\mathrm{complete}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:\mathrm{2}{x}\:−\:\mathrm{12}\left(\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\right)\:+\:\mathrm{12}\:=\:\mathrm{0}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by} \\ $$$$\left(\mathrm{1}\right)\:{x}\:=\:\mathrm{2}{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right)\frac{\pi}{\mathrm{4}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{2}\right)\:{x}\:=\:{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\pi,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{3}\right)\:{x}\:=\:\mathrm{2}{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\pi,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{4}\right)\:{x}\:=\:{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right)\pi,\:{n}\:\in\:{Z} \\ $$ Answered…
Question Number 18455 by Tinkutara last updated on 21/Jul/17 $$\mathrm{The}\:\mathrm{equation}\:\mathrm{cosec}\:\frac{{x}}{\mathrm{2}}\:+\:\mathrm{cosec}\:\frac{{y}}{\mathrm{2}}\:+ \\ $$$$\mathrm{cosec}\:\frac{{z}}{\mathrm{2}}\:=\:\mathrm{6},\:\mathrm{where}\:\mathrm{0}\:<\:{x},\:{y},\:{z}\:<\:\frac{\pi}{\mathrm{2}}\:\mathrm{and} \\ $$$${x}\:+\:{y}\:+\:{z}\:=\:\pi,\:\mathrm{have} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Three}\:\mathrm{ordered}\:\mathrm{triplet}\:\left({x},\:{y},\:{z}\right) \\ $$$$\mathrm{solutions} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Two}\:\mathrm{ordered}\:\mathrm{triplet}\:\left({x},\:{y},\:{z}\right) \\ $$$$\mathrm{solutions} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Just}\:\mathrm{one}\:\mathrm{ordered}\:\mathrm{triplet}\:\left({x},\:{y},\:{z}\right) \\…
Question Number 83991 by Rio Michael last updated on 08/Mar/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{points}\:\mathrm{represented}\:\mathrm{by} \\ $$$$\mathrm{the}\:\mathrm{complex}\:\mathrm{number}\:,{z},\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{2}\mid{z}−\mathrm{3}\mid\:=\:\mid{z}−\mathrm{6i}\mid \\ $$ Commented by mathmax by abdo last updated on…
Question Number 149527 by fotosy2k last updated on 06/Aug/21 Commented by fotosy2k last updated on 06/Aug/21 $${help}\:{me}\:{out} \\ $$$$ \\ $$ Answered by puissant last…
Question Number 83989 by Rio Michael last updated on 08/Mar/20 $$\mathrm{find}\:\: \\ $$$$\mathrm{a}.\:\:\:\int\mathrm{cos}\:\mathrm{3}{x}\:\mathrm{cos}\:\mathrm{5}{x}\:{dx} \\ $$$$\mathrm{b}.\:\:\int{x}\mathrm{ln}\:\mathrm{2}{x}\:{dx} \\ $$ Commented by jagoll last updated on 08/Mar/20 $$\mathrm{a}.\:\int\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos}\:\mathrm{8x}+\mathrm{cos}\:\mathrm{2x}\right)\:\mathrm{dx}\:=…
Question Number 18450 by aalieff last updated on 21/Jul/17 $${A}\:\$\mathrm{4000}\:{note}\:{is}\:{signed},\:{for}\:\mathrm{30}\:{days} \\ $$$${at}\:{a}\:{discount}\:{rate}\:{of}\:\mathrm{12\%}.\:{Find}\:{the} \\ $$$${proceeds}. \\ $$$$ \\ $$$${I}'{m}\:{not}\:{sure}\:{whether}\:{the}\:\$\mathrm{4000}\:{is} \\ $$$${bank}\:{discount},\:{principal}\:{or}\:{maturity}\:{value}. \\ $$$$ \\ $$$${Please}\:{help}\:{me} \\…
Question Number 83984 by M±th+et£s last updated on 08/Mar/20 $$\int{cos}^{\mathrm{7}} \left({x}\right)\:{dx} \\ $$ Answered by TANMAY PANACEA last updated on 08/Mar/20 $$\int{cos}^{\mathrm{6}} {x}×{cosxdx} \\ $$$$\int\left(\mathrm{1}−{sin}^{\mathrm{2}}…
Question Number 149516 by mathdanisur last updated on 05/Aug/21 $$\Omega\:=\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{3}} {\int}}\:\left(\sqrt{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} \:-\:\mathrm{8}{x}}\right)\:{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on 05/Aug/21 $$\:\:=\int_{\mathrm{0}} ^{\mathrm{3}}…
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Question Number 83977 by john santu last updated on 08/Mar/20 $$\mathrm{find}\:\mathrm{range}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{x}\sqrt{\mathrm{7x}−\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\mathrm{without} \\ $$$$\mathrm{calculus} \\ $$ Answered by john santu last updated on…