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given-the-polar-equation-r-a-2-sin2-show-the-tangents-at-the-poles-of-this-polar-equation-is-pi-4-3pi-4-5pi-4-7pi-4-

Question Number 90099 by Rio Michael last updated on 21/Apr/20 $$\:\mathrm{given}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{equation} \\ $$$$\:{r}\:=\:{a}^{\mathrm{2}} \:\mathrm{sin2}\theta\:\:\mathrm{show}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{at}\: \\ $$$$\mathrm{the}\:\mathrm{poles}\:\mathrm{of}\:\mathrm{this}\:\mathrm{polar}\:\mathrm{equation}\:\mathrm{is}. \\ $$$$\:\theta\:=\:\left\{\frac{\pi}{\mathrm{4}},\frac{\mathrm{3}\pi}{\mathrm{4}},\frac{\mathrm{5}\pi}{\mathrm{4}},\frac{\mathrm{7}\pi}{\mathrm{4}}\right\} \\ $$ Commented by jagoll last updated…

Question-24539

Question Number 24539 by ajfour last updated on 20/Nov/17 Commented by ajfour last updated on 20/Nov/17 $${If}\:{the}\:{system}\:{is}\:{released}\:{with} \\ $$$${the}\:{rod}\:{vertical}\:\left(\theta=\mathrm{0}\right)\:,\:{and}\:{the} \\ $$$${rod}\:{being}\:{attached}\:{to}\:{the}\:{center} \\ $$$${of}\:{disc}\:{with}\:{a}\:{frictionless}\:{axle}, \\ $$$${then}\:{as}\:{the}\:{rod}\:{inclines}\:{down},…

Question-24526

Question Number 24526 by ajfour last updated on 20/Nov/17 Commented by ajfour last updated on 20/Nov/17 $${A}\:{thin}\:{rod}\:{rotates}\:{in}\:{horizontal} \\ $$$${plane}\:{with}\:{a}\:{constant}\:{angular}\: \\ $$$${velocity}\:\boldsymbol{\omega}.{From}\:{its}\:{farther}\:{end} \\ $$$${a}\:{needle}\:{emerges}\:{at}\:{a}\:{constant} \\ $$$${relative}\:{velocity}\:\boldsymbol{{u}}\:{along}\:{the}\:{rod}.…

A-particle-moves-in-a-straight-line-along-x-axis-At-t-0-it-passes-origin-with-some-velocity-towards-positive-x-axis-and-with-an-acceleration-a-which-is-given-as-a-Kx-where-x-is-in-metre-and-K

Question Number 24520 by Tinkutara last updated on 19/Nov/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{along} \\ $$$${x}-\mathrm{axis}.\:\mathrm{At}\:{t}\:=\:\mathrm{0}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{origin}\:\mathrm{with} \\ $$$$\mathrm{some}\:\mathrm{velocity}\:\mathrm{towards}\:\mathrm{positive}\:{x}-\mathrm{axis} \\ $$$$\mathrm{and}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration}\:{a}\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{as},\:{a}\:=\:−\:{Kx},\:\mathrm{where}\:{x}\:\mathrm{is}\:\mathrm{in}\:\mathrm{metre} \\ $$$$\mathrm{and}\:{K}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{constant}.\:\mathrm{The}\:\mathrm{time} \\ $$$$\mathrm{at}\:\mathrm{which}\:\mathrm{its}\:\mathrm{velocity}\:\mathrm{becomes}\:\mathrm{half}\:\mathrm{of}\:\mathrm{its} \\ $$$$\mathrm{value}\:\mathrm{at}\:{t}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{time},\:\mathrm{is} \\…

A-spot-light-S-rotates-in-a-horizontal-plane-with-a-constant-angular-velocity-of-0-1-rad-s-The-spot-of-light-P-moves-along-the-wall-at-a-distance-3-m-What-is-the-velocity-of-the-spot-P-when-45-

Question Number 24506 by Tinkutara last updated on 19/Nov/17 $$\mathrm{A}\:\mathrm{spot}\:\mathrm{light}\:{S}\:\mathrm{rotates}\:\mathrm{in}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{plane}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{angular}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{0}.\mathrm{1}\:\mathrm{rad}/\mathrm{s}.\:\mathrm{The}\:\mathrm{spot}\:\mathrm{of}\:\mathrm{light}\:{P}\:\mathrm{moves} \\ $$$$\mathrm{along}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{3}\:\mathrm{m}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{spot}\:{P}\:\mathrm{when}\:\theta\:=\:\mathrm{45}°? \\ $$ Commented by Tinkutara last updated…

e-x-dx-

Question Number 90023 by Rio Michael last updated on 20/Apr/20 $$\:\int\:{e}^{\mid{x}\mid} \:{dx}\:=\:??? \\ $$ Answered by MJS last updated on 21/Apr/20 $$\mathrm{e}^{\mid{x}\mid} =\begin{cases}{\mathrm{e}^{−{x}} ;\:{x}<\mathrm{0}}\\{\mathrm{e}^{{x}} ;\:{x}\geqslant\mathrm{0}}\end{cases}\:\Rightarrow\:\int\mathrm{e}^{\mid{x}\mid}…