Question Number 141786 by Rankut last updated on 23/May/21 $$\boldsymbol{\mathrm{If}}\:\:\boldsymbol{\mathrm{y}}=\mathrm{1}−\boldsymbol{\mathrm{cos}}\mathrm{2}\boldsymbol{\mathrm{t}}\:\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{x}}=\sqrt{\mathrm{1}+\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\:.\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\frac{\mathrm{2}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{t}}}{\boldsymbol{\mathrm{t}}} \\ $$$$\boldsymbol{\mathrm{Help}}\:\boldsymbol{\mathrm{please}}. \\ $$ Answered by iloveisrael last updated on 23/May/21…
Question Number 141783 by mohammad17 last updated on 23/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76245 by vishalbhardwaj last updated on 25/Dec/19 $$\mathrm{The}\:\mathrm{lines}\:{ax}+\mathrm{2}{y}+\mathrm{1}=\mathrm{0},\:{bx}+\mathrm{3}{y}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{and}\:{cx}+\mathrm{4}{y}+\mathrm{1}=\mathrm{0}\:\mathrm{are}\:\mathrm{concurrent} \\ $$$$\mathrm{if}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{G}.\mathrm{P}.\:?? \\ $$ Answered by MJS last updated on 25/Dec/19 $$\mathrm{no},\:\mathrm{they}\:\mathrm{are}\:\mathrm{parallel}\:\mathrm{if}\:{a}=\mathrm{2}{k}\wedge{b}=\mathrm{3}{k}\wedge{c}=\mathrm{4}{k} \\…
Question Number 141776 by 7770 last updated on 23/May/21 $$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{volume}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sphere}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{increasing}} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{constant}}\:\boldsymbol{\mathrm{rate}}\:\boldsymbol{\mathrm{of}}\:\mathrm{10}\boldsymbol{\mathrm{cm}}^{\mathrm{3}} /\boldsymbol{\mathrm{sec}}. \\ $$$$\boldsymbol{\mathrm{Calculate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{rate}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{increase}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{instant}}\:\boldsymbol{\mathrm{when}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{is}}\:\mathrm{5}\boldsymbol{\mathrm{cm}}.\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sphere}}\:\boldsymbol{\mathrm{when}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{increasing}} \\ $$$$\boldsymbol{\mathrm{at}}\:\mathrm{2}\boldsymbol{\mathrm{cm}}^{\mathrm{2}} /\boldsymbol{\mathrm{sec}}. \\…
Question Number 141769 by 7770 last updated on 23/May/21 $$\boldsymbol{\mathrm{If}}\:\:\boldsymbol{\mathrm{y}}=\mathrm{2}\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{tanx}},\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }=\mathrm{2}\boldsymbol{\mathrm{sinx}}\left(\boldsymbol{\mathrm{sec}}^{\mathrm{3}} \boldsymbol{\mathrm{x}}−\mathrm{1}\right) \\ $$$$\boldsymbol{\mathrm{Any}}\:\boldsymbol{\mathrm{detailed}}\:\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{please}}. \\ $$ Answered by physicstutes last updated on…
Question Number 76228 by arkanmath7@gmail.com last updated on 25/Dec/19 $${prove}\:{that}\:\mathrm{6}^{{n}} \:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{10}\right),\:{for}\:{any}\:{n}\:\in\:{Z}^{\:+} \\ $$ Commented by turbo msup by abdo last updated on 25/Dec/19 $$\Leftrightarrow\mathrm{6}^{{n}} −\mathrm{6}\:\equiv\mathrm{0}\left[\mathrm{10}\right]\:\Leftrightarrow\:\mathrm{10}\:{divide}\:\mathrm{6}^{{n}}…
Question Number 141752 by 0731619 last updated on 23/May/21 Answered by qaz last updated on 23/May/21 $$\Omega=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{tan}^{−\mathrm{1}} {x}}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{u}}{\mathrm{tan}\:{u}+\mathrm{1}}{du}…
Question Number 76200 by Joel578 last updated on 25/Dec/19 Commented by benjo last updated on 25/Dec/19 $$\mathrm{thanks}\:\mathrm{sir}.\:\mathrm{merry}\:\mathrm{chrismastto}\:\mathrm{all} \\ $$ Commented by Rio Michael last updated…
Question Number 141715 by SOMEDAVONG last updated on 22/May/21 $$\mathrm{Find}\:\mathrm{x}\:\mathrm{if}\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\mathrm{24}} {\sum}}\frac{\mathrm{250}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} }\:=\:\mathrm{5000}. \\ $$ Answered by mathmax by abdo last updated on 22/May/21 $$\sum_{\mathrm{n}=\mathrm{2}}…
Question Number 10612 by FilupS last updated on 20/Feb/17 Commented by FilupS last updated on 20/Feb/17 $$\mathrm{Solve}\:\mathrm{for}\:\boldsymbol{{A}}'\:\mathrm{and}\:\boldsymbol{{B}}'\:\mathrm{via}: \\ $$$$\mathrm{1}.\:\:\mathrm{Vectors} \\ $$$$\mathrm{2}.\:\:\mathrm{Triganometry} \\ $$ Answered by…