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…
Question Number 13068 by tawa tawa last updated on 13/May/17 $$\mathrm{If}\:\:\:\mathrm{y}\:=\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}\:\:\:\:\:\mathrm{Find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\mathrm{from}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle} \\ $$ Answered by ajfour last updated on 13/May/17 $$\frac{{dy}}{{dx}}=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}+{h}\right)^{\mathrm{1}/\mathrm{3}} −{x}^{\mathrm{1}/\mathrm{3}} }{{h}} \\…
Question Number 78581 by john santu last updated on 18/Jan/20 $$\int\:\frac{\mathrm{2}{x}\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{2}{x}−\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$ Commented by john santu last updated on 19/Jan/20 $${consider}\: \\ $$$$\frac{\mathrm{2}{x}\:\mathrm{sin}\:\mathrm{2}{x}}{\left(\mathrm{2}{x}−\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}}…
Question Number 424 by 123456 last updated on 25/Jan/15 $${f}\left({x},{y}\right)=\frac{\left({x}+{y}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$$$\begin{cases}{\frac{\partial{f}}{\partial{u}}=?}\\{\frac{\partial{f}}{\partial{v}}=?}\end{cases} \\ $$$$\begin{cases}{{x}={uv}}\\{{y}={u}+{v}}\end{cases} \\ $$ Answered by prakash jain last updated…
Question Number 131481 by bemath last updated on 05/Feb/21 $$\mathrm{In}\:\mathrm{1790}\:\mathrm{the}\:\mathrm{population}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{United}\:\mathrm{States}\:\mathrm{was}\:\mathrm{3}.\mathrm{93}\:\mathrm{million} \\ $$$$\mathrm{and}\:\mathrm{in}\:\mathrm{1890}\:\mathrm{it}\:\mathrm{was}\:\mathrm{62}.\mathrm{98}\:\mathrm{million} \\ $$$$\mathrm{Using}\:\mathrm{the}\:\mathrm{Malthusian}\:\mathrm{model}\:, \\ $$$$\mathrm{estimate}\:\mathrm{the}\:\mathrm{U}.\mathrm{S}\:\mathrm{population}\:\mathrm{as} \\ $$$$\mathrm{a}\:\mathrm{function}\:\mathrm{of}\:\mathrm{time} \\ $$ Answered by EDWIN88…
Question Number 131470 by bemath last updated on 05/Feb/21 $${Consider}\:{a}\:{large}\:{tank}\:{holding} \\ $$$$\mathrm{1000}\:{L}\:{of}\:{pure}\:{water}\:{into} \\ $$$${which}\:{a}\:{brine}\:{solution}\:{of} \\ $$$${salt}\:{begins}\:{to}\:{flow}\:{at}\:{constant} \\ $$$${rate}\:{of}\:\mathrm{6}{L}/{min}.\:{The}\:{solution} \\ $$$${inside}\:{the}\:{tank}\:{is}\:{kept}\:{well} \\ $$$${stirred}\:{and}\:{is}\:{flowing}\:{out}\:{of} \\ $$$${the}\:{tank}\:{at}\:{rate}\:{of}\:\mathrm{6}{L}/{min}. \\…
Question Number 352 by Vishal Bhardwaj last updated on 25/Jan/15 $${Q}.\:\:{Define}\:\bullet\bullet\:\:{LHD}\left({left}\:{hand}\right. \\ $$$$\left.{derivative}\right)\:=\:{f}\left({a}−\mathrm{0}\right) \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {{lim}}\:\frac{{f}\left({a}−{h}\right)−{f}\left({a}\right)}{−{h}} \\ $$$$ \\ $$$$ \\ $$ Commented by prakash…
Question Number 356 by 123456 last updated on 25/Jan/15 $${f}_{\mathrm{0}} \left({x}\right)=\mathrm{1} \\ $$$${f}_{\mathrm{1}} \left({x}\right)={x} \\ $$$${f}_{{n}+\mathrm{1}} \left({x}\right)={x}^{{f}_{{n}} \left({x}\right)} \\ $$$$\frac{\partial{f}_{{n}} }{\partial{x}}=?,{n}\in\mathbb{N}^{\ast} \\ $$ Answered by…