Menu Close

Category: None

Let-a-is-a-real-number-How-many-solutions-can-the-equation-in-sin-cos-sin-cos-1-a-have-for-0-lt-lt-pi-2-

Question Number 59113 by naka3546 last updated on 04/May/19 $${Let}\:\:{a}\:\:{is}\:\:{a}\:\:{real}\:\:{number}\:.\:\:{How}\:\:{many}\:\:{solutions} \\ $$$${can}\:\:{the}\:\:{equation}\:\:{in}\:\:\theta\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{sin}\:\theta\:+\:\mathrm{cos}\:\theta\right)\left(\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta\:−\:\mathrm{1}\right)\:\:=\:\:{a} \\ $$$${have}\:\:{for}\:\:\mathrm{0}\:<\:\theta\:<\:\frac{\pi}{\mathrm{2}}\:\:? \\ $$ Answered by MJS last updated on 05/May/19…

Question-190169

Question Number 190169 by sonukgindia last updated on 29/Mar/23 Commented by Frix last updated on 29/Mar/23 $$\mathrm{Folks}\:\mathrm{2}\:\mathrm{questions}: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{does}\:\mathrm{a}\:\mathrm{polynome} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{of}\:\mathrm{degree}\:{n}\:\mathrm{have}? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Do}\:\mathrm{you}\:\mathrm{ever}\:\mathrm{test}\:\mathrm{your}\:\mathrm{solutions}? \\ $$…

I-saw-this-in-a-book-without-explanation-Please-show-how-It-is-given-that-tan-2-B-A-C-A-B-C-R-Find-cos-2-

Question Number 190151 by Matica last updated on 28/Mar/23 $${I}\:{saw}\:{this}\:{in}\:{a}\:{book}\:\left({without}\:{explanation}\right).\:{Please}\:{show}\:{how}. \\ $$$${It}\:{is}\:{given}\:{that}\:\mathrm{tan}\:\mathrm{2}\theta=\frac{{B}}{{A}−{C}}\:\:\left({A},{B},{C}\:\in\mathbb{R}\right)\:.\:{Find}\:\mathrm{cos}\:\mathrm{2}\theta. \\ $$ Commented by mr W last updated on 28/Mar/23 $${i}\:{saw}\:{this}\:{in}\:{an}\:{other}\:{book}\:\left({without}\:\right. \\ $$$$\left.{explanation},\:{because}\:{nobody}\:{needs}\right).\:…

Question-190140

Question Number 190140 by otchereabdullai last updated on 28/Mar/23 Commented by Frix last updated on 28/Mar/23 $$\mathrm{The}\:\mathrm{text}\:\mathrm{is}\:\mathrm{strange}\:\mathrm{anyway}.\:“…\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{is}\:\mathrm{increased}\:\mathrm{by}\:\mathrm{8}\:\mathrm{and}\:\mathrm{then}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}''\:\mathrm{would}\:\mathrm{mean}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:{after}\:\mathrm{adding}\:\mathrm{8}.\:\mathrm{But}\:\mathrm{then}\:\mathrm{we} \\ $$$$\mathrm{get}\:\mathrm{no}\:\mathrm{reasonable}\:\mathrm{result}.…

Question-190138

Question Number 190138 by 073 last updated on 28/Mar/23 Answered by Pengu last updated on 29/Mar/23 $$\mathrm{Notice}\:\mathrm{that}\:\mathrm{for}\:{a}=\mathrm{4}: \\ $$$$\underset{{x}\rightarrow\mathrm{4}^{−} } {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\underset{{x}\rightarrow\mathrm{4}^{−} } {\mathrm{lim}}\:\frac{\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{4}} \\…