Question Number 144525 by imjagoll last updated on 26/Jun/21 $$\:\mathrm{If}\:\mathrm{y}=\mathrm{cosh}\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{1}\right) \\ $$$$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=? \\ $$ Answered by EDWIN88 last updated on 26/Jun/21 $$\:\mathrm{let}\:\mathrm{q}\:=\:\mathrm{x}^{\mathrm{2}}…
Question Number 78974 by ~blr237~ last updated on 22/Jan/20 $$\left\{_{\mathrm{3e}^{\mathrm{2x}} −\mathrm{y}^{\mathrm{2}} =\mathrm{2}\:\:\:} ^{\mathrm{e}^{\mathrm{x}} −\mathrm{y}^{\mathrm{2}} =\mathrm{2lny}−\mathrm{x}} \right. \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{on}\:\mathbb{R}\ast\mathbb{R} \\ $$ Commented by jagoll last updated…
Question Number 13429 by sergiosba last updated on 20/May/17 Commented by prakash jain last updated on 20/May/17 $${x}=−\mathrm{2cos}\:\theta \\ $$$${y}=\mathrm{3sin}\:\theta \\ $$$$\mathrm{cos}\:\theta=−\frac{{x}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\theta=\frac{{y}}{\mathrm{3}} \\…
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Question Number 144389 by liberty last updated on 25/Jun/21 $$\:\int\:\left(\mathrm{x}−\mathrm{1}\right)\mathrm{h}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\mathrm{x}^{\mathrm{3}} −\mathrm{sin}\:\mathrm{2x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:+\:\mathrm{c}\: \\ $$$$\Rightarrow\mathrm{h}\:'\left(\mathrm{1}\right)=\:? \\ $$ Answered by mathmax by abdo last updated on 25/Jun/21…
Question Number 144351 by mnjuly1970 last updated on 24/Jun/21 $$ \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:{Evaluate}\:\:\::: \\ $$$$\:\: \\ $$$$\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\left.\:{sin}\:\sqrt[{\:\mathrm{3}\:}]{{x}}\:\right){log}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{{x}}{dx}=? \\ $$$$\:\:\: \\ $$$$ \\…
Question Number 144311 by mnjuly1970 last updated on 24/Jun/21 $$ \\ $$$$\:\:\:\:\:\:……\mathrm{Nice}\:\:\:\:….\:\:\:\:\mathrm{Calculus}…… \\ $$$$\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\Theta\::=\underset{{n}\:=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{4}^{\:{n}} \:{cos}^{\:\mathrm{2}} \:\left(\frac{\:\pi}{\:\mathrm{2}^{\:{n}\:+\:\mathrm{2}} }\:\right)\:\:}\:=? \\ $$$$\:\:\:\:……….…
Question Number 144301 by liberty last updated on 24/Jun/21 Answered by imjagoll last updated on 24/Jun/21 $$\mathrm{we}\:\mathrm{convert}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{2t}+\mathrm{3}\:\mathrm{liters} \\ $$$$\mathrm{per}\:\mathrm{minute}\:\mathrm{to}\:\mathrm{60}\left(\mathrm{2t}+\mathrm{3}\right)=\mathrm{120t}+\mathrm{180} \\ $$$$\mathrm{liters}\:\mathrm{per}\:\mathrm{hours}.\:\mathrm{The}\:\mathrm{total}\:\mathrm{amount} \\ $$$$\mathrm{of}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{time}\:\mathrm{T} \\ $$$$\mathrm{hours}\:\mathrm{past}\:\mathrm{noon}\:\mathrm{is}\:\mathrm{the}\:\mathrm{integral}…
Question Number 13226 by chux last updated on 16/May/17 $$\mathrm{if}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} =\mathrm{3axy},\mathrm{find}\:\mathrm{dy}/\mathrm{dx}\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{dy}/\mathrm{dx}\: \\ $$$$\mathrm{cannot}\:\mathrm{be}\:\mathrm{equal}\:\mathrm{to}\:-\mathrm{1}\:\mathrm{for}\:\mathrm{finite} \\ $$$$\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{except}\:\mathrm{x}=\mathrm{y}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\: \\…
Question Number 144200 by bramlexs22 last updated on 23/Jun/21 $$\mathrm{Find},\:\mathrm{among}\:\mathrm{all}\:\mathrm{right}\:\mathrm{circular} \\ $$$$\mathrm{cylinders}\:\mathrm{of}\:\mathrm{fixed}\:\mathrm{volume}\:\mathrm{V}\: \\ $$$$\mathrm{that}\:\mathrm{one}\:\mathrm{with}\:\mathrm{smallest}\:\mathrm{surface}\:\mathrm{area} \\ $$$$\left(\mathrm{counting}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{faces}\:\right. \\ $$$$\left.\mathrm{at}\:\mathrm{top}\:\mathrm{and}\:\mathrm{bottom}\:\right) \\ $$ Answered by MJS_new last updated…