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Author: Tinku Tara

Question-154142

Question Number 154142 by EDWIN88 last updated on 14/Sep/21 Answered by mr W last updated on 14/Sep/21 $${y}={a}\left({x}−\mathrm{4}\right)\left({x}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$\mathrm{8}={a}\left(−\mathrm{4}\right)\left(+\mathrm{2}\right)^{\mathrm{2}} \:\Rightarrow{a}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${y}=−\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{4}\right)\left({x}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$\frac{{dy}}{{dx}}=−\frac{\mathrm{1}}{\mathrm{2}}\left[\left({x}+\mathrm{2}\right)^{\mathrm{2}}…

A-rocket-accelerates-straight-up-by-ejecting-gas-downwards-In-a-small-time-interval-t-it-ejects-a-gas-of-mass-m-at-a-relative-speed-u-Calculate-KE-of-the-entire-system-at-t-t-and-t-and-show-th

Question Number 23066 by Tinkutara last updated on 25/Oct/17 $$\mathrm{A}\:\mathrm{rocket}\:\mathrm{accelerates}\:\mathrm{straight}\:\mathrm{up}\:\mathrm{by} \\ $$$$\mathrm{ejecting}\:\mathrm{gas}\:\mathrm{downwards}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{small} \\ $$$$\mathrm{time}\:\mathrm{interval}\:\Delta{t},\:\mathrm{it}\:\mathrm{ejects}\:\mathrm{a}\:\mathrm{gas}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\Delta{m}\:\mathrm{at}\:\mathrm{a}\:\mathrm{relative}\:\mathrm{speed}\:{u}.\:\mathrm{Calculate}\:\mathrm{KE} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{entire}\:\mathrm{system}\:\mathrm{at}\:{t}\:+\:\Delta{t}\:\mathrm{and}\:{t}\:\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{device}\:\mathrm{that}\:\mathrm{ejects}\:\mathrm{gas} \\ $$$$\mathrm{does}\:\mathrm{work}\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\Delta{mu}^{\mathrm{2}} \:\mathrm{in}\:\mathrm{this}\:\mathrm{time} \\ $$$$\mathrm{interval}\:\left(\mathrm{neglect}\:\mathrm{gravity}\right).…

Given-f-x-x-1-x-2-1-3-x-1-x-2-1-3-Find-f-1-x-

Question Number 154133 by qaz last updated on 14/Sep/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}+\sqrt[{\mathrm{3}}]{\mathrm{x}−\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }} \\ $$$$\mathrm{Find}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$ Answered by EDWIN88 last updated on 14/Sep/21 $$\Leftrightarrow{y}−\sqrt[{\mathrm{3}}]{{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…

solve-for-x-C-cos-x-a-bi-

Question Number 88594 by mr W last updated on 11/Apr/20 $${solve}\:{for}\:{x}\in\mathbb{C} \\ $$$$\mathrm{cos}\:\left({x}\right)={a}+{bi} \\ $$ Commented by abdomathmax last updated on 11/Apr/20 $$\Rightarrow{ch}\left({ix}\right)\:={a}+{bi}\:\Rightarrow\frac{{e}^{{ix}} \:+{e}^{−{ix}} }{\mathrm{2}}={a}+{bi}\:\Rightarrow…

Question-23059

Question Number 23059 by Physics lover last updated on 25/Oct/17 Commented by Physics lover last updated on 25/Oct/17 $${In}\:{the}\:{arrangement}\:{shown}\:{here}\: \\ $$$${friction}\:{between}\:{the}\:{spool}\: \\ $$$$\left({of}\:{mass}\:{m},\:{moment}\:{of}\:{inertia}\:{I}\:\right) \\ $$$${and}\:{the}\:{plank}\:\left({of}\:{mass}\:{M}\right)…