Question Number 81889 by rajesh4661kumar@gmail.com last updated on 16/Feb/20 Answered by john santu last updated on 16/Feb/20 $${let}\:\sqrt{{x}}\:=\:\mathrm{sin}\:{t}\:\Rightarrow{x}\:=\:\mathrm{sin}\:^{\mathrm{2}} {t} \\ $$$${dx}\:=\:\mathrm{2sin}\:{t}\:\mathrm{cos}\:{t}\:{dt}\: \\ $$$$\Rightarrow{I}\:=\:\int\:\sqrt{\frac{\mathrm{1}−\mathrm{sin}\:{t}}{\mathrm{1}+\mathrm{sin}\:{t}}\:}\:\left(\mathrm{2sin}\:{t}\:\mathrm{cos}\:{t}\:\right)\:{dt} \\ $$$$=\:\int\:\frac{\left(\mathrm{1}−\mathrm{sin}\:{t}\right)\mathrm{2sin}\:{t}\mathrm{cos}\:{t}}{\mathrm{cos}\:{t}}\:{dt}…
Question Number 81887 by lalitchand last updated on 16/Feb/20 Commented by mr W last updated on 16/Feb/20 $${let}\:\frac{{FA}}{{BA}}={k},\:\frac{\mathrm{1}}{\mathrm{2}}<{k}<\mathrm{1} \\ $$$${DF}=\frac{{BA}}{\mathrm{2}} \\ $$$$\frac{{OD}}{{OF}}=\frac{{DF}}{{FA}}=\frac{{BA}}{\mathrm{2}×{k}×{BA}}=\frac{\mathrm{1}}{\mathrm{2}{k}} \\ $$$${i}.{e}.\:\frac{{OD}}{{OD}+{DF}}=\frac{\mathrm{1}}{\mathrm{2}{k}} \\…
Question Number 81884 by rajesh4661kumar@gmail.com last updated on 16/Feb/20 Commented by mind is power last updated on 16/Feb/20 $${applie} \\ $$$${we}\:{can}\:{find}\:{triangle}\: \\ $$$${withe}\:\:\:{sin}^{−} \:{x},{sin}^{−} {y},{sin}^{−}…
Question Number 147417 by tabata last updated on 20/Jul/21 $${how}\:{can}\:{find}\:{taylor}\:{series}\:{of}\:{f}\left({z}\right)={cot}\left({z}\right)\:{when}\:{z}=\mathrm{5}\pi \\ $$ Answered by mathmax by abdo last updated on 21/Jul/21 $$\mathrm{f}\left(\mathrm{z}\right)=\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{5}\pi\right)}{\mathrm{n}!}\left(\mathrm{z}−\mathrm{5}\pi\right)^{\mathrm{n}}…
Question Number 147419 by Kunal12588 last updated on 20/Jul/21 $${How}\:{can}\:{we}\:{apply}\:{Cardano}'{s}\:{method}\:{in} \\ $$$$\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +{x}+\mathrm{2} \\ $$$$ \\ $$$${i}\:{get}\:{u}\:{and}\:{v}\:{are}\:{solution}\:{of}\:{t}^{\mathrm{2}} −\mathrm{56}{t}+\mathrm{6859}=\mathrm{0} \\ $$$${but}\:{i}\:{think}\:{it}'{s}\:{wrong}\:{pls}\:{help} \\ $$ Answered by…
Question Number 147418 by jlewis last updated on 20/Jul/21 $$\mathrm{In}\:\mathrm{an}\:\mathrm{R}{LC}\:\mathrm{series}\:\mathrm{circuit}, \\ $$$$\mathrm{R}=\mathrm{1kilo}\:\mathrm{ohms},\mathrm{L}=\mathrm{0}.\mathrm{2H},\mathrm{C}=\mathrm{1} \mathrm{F}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{voltage}\:\mathrm{source}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}: \\ $$$$\left(\mathrm{V}=\mathrm{150}\:\mathrm{sin}\:\mathrm{377t}\:\right)\mathrm{V}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{peak}\:\mathrm{current}\:\mathrm{delivered}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{source}? \\ $$ Answered by…
Question Number 147413 by pete last updated on 20/Jul/21 $$ \\ $$$$\mathrm{An}\:\mathrm{experiment}\:\mathrm{consist}\:\mathrm{of}\:\mathrm{flipping}\:\mathrm{a} \\ $$$$\mathrm{coin}\:\mathrm{and}\:\mathrm{then}\:\mathrm{flipping}\:\mathrm{it}\:\mathrm{a}\:\mathrm{second}\:\mathrm{time}\: \\ $$$$\mathrm{if}\:\mathrm{a}\:\mathrm{head}\:\mathrm{occurs}.\mathrm{If}\:\mathrm{a}\:\mathrm{tail}\:\mathrm{appears}\:\mathrm{on}\:\mathrm{thei} \\ $$$$\mathrm{first}\:\mathrm{flip}\:\mathrm{then}\:\mathrm{a}\:\mathrm{die}\:\mathrm{is}\:\mathrm{tossed}\:\mathrm{once}.\: \\ $$$$\mathrm{a}.\:\mathrm{Listthe}\:\mathrm{element}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sample}\:\mathrm{space}\:\mathrm{S}.\mathrm{b} \\ $$$$\mathrm{b}.\:\mathrm{List}\:\mathrm{the}\:\mathrm{element}\:\mathrm{of}\:\mathrm{S}\:\mathrm{corresponding} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{event}\:\mathrm{A}\:\mathrm{that}\:\mathrm{a}\:\mathrm{number}\:\mathrm{less}\:\mathrm{than}\: \\…
Question Number 147412 by vvvv last updated on 20/Jul/21 Answered by puissant last updated on 21/Jul/21 $$={lim}_{{k}\rightarrow\infty} \frac{\mathrm{1}}{{k}}\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\frac{{n}^{\mathrm{2}} +\mathrm{3}{nk}+\mathrm{9}{k}^{\mathrm{2}} {sin}\left(\frac{{n}}{{k}}\right)}{{k}^{\mathrm{2}} } \\ $$$$={lim}_{{k}\rightarrow\infty}…
Question Number 16338 by ajfour last updated on 20/Jun/17 Commented by mrW1 last updated on 20/Jun/17 $$\mathrm{x}=\frac{\mathrm{ab}\:\mathrm{sin}\:\left(\theta+\emptyset\right)}{\mathrm{a}\:\mathrm{sin}\:\theta\:+\:\mathrm{b}\:\mathrm{sin}\:\emptyset} \\ $$$$\mathrm{y}=\frac{\mathrm{a}\:\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{2ab}\:\mathrm{cos}\:\left(\theta+\emptyset\right)}\:\mathrm{sin}\:\theta}{\mathrm{a}\:\mathrm{sin}\:\theta+\:\mathrm{b}\:\mathrm{sin}\:\emptyset} \\ $$$$\mathrm{z}=\frac{\mathrm{b}\:\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{2ab}\:\mathrm{cos}\:\left(\theta+\emptyset\right)}\:\mathrm{sin}\:\emptyset}{\mathrm{a}\:\mathrm{sin}\:\theta+\:\mathrm{b}\:\mathrm{sin}\:\emptyset}…
Question Number 147411 by mnjuly1970 last updated on 20/Jul/21 Answered by mnjuly1970 last updated on 20/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\overset{\sqrt{{x}}\::=\:{y}} {=}\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{2}{y}\:{dy}}{\mathrm{1}+{e}^{\:{y}} }\:=\mathrm{2}\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ydy}}{\mathrm{1}+{e}^{\:{y}} } \\…