Question Number 193671 by cherokeesay last updated on 17/Jun/23 Answered by mr W last updated on 17/Jun/23 $${R}={radius} \\ $$$${a}={width}\:{of}\:{rectangle} \\ $$$$\mathrm{4}^{\mathrm{2}} −{a}^{\mathrm{2}} ={a}\left(\mathrm{2}{R}−{a}\right) \\…
Question Number 193670 by mokys last updated on 17/Jun/23 $${show}\:{that}\:\int_{{c}} \:{e}^{\frac{\mathrm{1}}{{z}^{\mathrm{2}} }} \:{dz}\:=\:\mathrm{0}\:{when}\:\mid{z}\mid\:<\mathrm{1} \\ $$ Commented by mokys last updated on 17/Jun/23 $$????? \\ $$…
Question Number 193664 by 073 last updated on 17/Jun/23 Commented by 073 last updated on 17/Jun/23 $$\mathrm{prove}\:\mathrm{that} \\ $$ Commented by 073 last updated on…
Question Number 193565 by Mingma last updated on 16/Jun/23 Answered by mr W last updated on 17/Jun/23 $${say}\:{at}\:{time}\:{x}\:{hours}\:{after}\:\mathrm{0}\:{o}'{clock}. \\ $$$${assume}\:{the}\:{hands}\:{move}\:{continuously}. \\ $$$${position}\:{of}\:{hour}\:{hand}:\:\mathrm{30}{x}\:° \\ $$$${position}\:{of}\:{minute}\:{hand}:\:\left({x}−\left[{x}\right]\right)×\mathrm{60}×\mathrm{6}\:° \\…
Question Number 193533 by horsebrand11 last updated on 16/Jun/23 $$\:\:\:\mathrm{If}\:\mathrm{cot}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}=\mathrm{4}\:\mathrm{then} \\ $$$$\:\:\:\:\mathrm{cot}\:^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{2x}}\:−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\:=? \\ $$ Answered by MM42 last updated on 16/Jun/23 $$\mathrm{1}−{tan}^{\mathrm{2}} {x}=\mathrm{4}{tanx}\Rightarrow{tan}^{\mathrm{2}}…
Question Number 193532 by horsebrand11 last updated on 16/Jun/23 $$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\pi\mathrm{x}}{\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}} }\:=? \\ $$ Answered by aba last updated on 16/Jun/23 $$\mathrm{let}\:\mathrm{t}=\mathrm{2}−\mathrm{x} \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\pi\mathrm{x}}{\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}}…
Question Number 193563 by SaRahAli last updated on 16/Jun/23 Answered by Gamil last updated on 16/Jun/23 Answered by Subhi last updated on 16/Jun/23 $$ \\…
Question Number 193525 by mustafazaheen last updated on 16/Jun/23 $$\:\:\:\:\:\frac{\mathrm{27t73}}{\mathrm{11}} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{R}=\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{t}=? \\ $$$$\:\:\:\:\:\:\mathrm{how}\:\mathrm{is}\:\mathrm{explontry}\:\mathrm{solution} \\ $$ Answered by MM42 last updated on 16/Jun/23 $$\mathrm{3}−\mathrm{7}+{t}−\mathrm{7}+\mathrm{2}=\mathrm{11}{k}\Rightarrow−\mathrm{9}+{t}=\mathrm{11}{k}\Rightarrow{t}=\mathrm{9} \\…
Question Number 193526 by SaRahAli last updated on 16/Jun/23 Answered by MM42 last updated on 16/Jun/23 $${I}=\int\:\frac{{sinx}×{cosx}}{{sinx}+{cos}^{\mathrm{2}} {x}}\:{dx}=−\int\:\frac{{sinx}×{cosx}}{{sinx}−{sinx}−\mathrm{1}}\:{dx} \\ $$$${let}\:\:\:{sinx}={u}\Rightarrow{cosxdx}={du} \\ $$$$\Rightarrow{I}=−\int\:\frac{{udu}}{{u}^{\mathrm{2}} −{u}−\mathrm{1}}\:{du}\:=\int\:\frac{{A}}{{u}−{u}_{\mathrm{1}} }\:{du}\:+\int\:\frac{{B}}{{u}−{u}_{\mathrm{2}} }\:{du}\:…
Question Number 193585 by York12 last updated on 16/Jun/23 $$ \\ $$$${There}\:{exists}\:{a}\:{unique}\:{positive}\:{integer}\:{a}\:{for} \\ $$$${which}\:{The}\:{sum}\:{u}\:\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\lfloor\frac{{n}^{\mathrm{2}} −{na}}{\mathrm{5}}\rfloor\:{is}\:{an}\:{integer} \\ $$$${trictly}\:{between}\:−\mathrm{1000}\:\&\:\mathrm{1000}\:{find}\:{a}+{u}. \\ $$ Answered by York12 last…