Question Number 133611 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{Given}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\: \\ $$$$\begin{cases}{\mathrm{2x}−\mathrm{3y}\:=\:\mathrm{13}}\\{\mathrm{3x}+\mathrm{2y}\:=\:\mathrm{b}}\end{cases}\:,\:\mathrm{where}\:\mathrm{l}\:\leqslant\:\mathrm{b}\leqslant\:\mathrm{100}\:\mathrm{and} \\ $$$$\mathrm{b}\:\mathrm{is}\:\mathrm{integer}.\:\mathrm{Suppose}\:\mathrm{n}^{\mathrm{2}} \:=\:\mathrm{x}+\mathrm{y}\:\mathrm{where} \\ $$$$\mathrm{x},\mathrm{y}\:\mathrm{is}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{given}\:\mathrm{system}\: \\ $$$$\mathrm{of}\:\mathrm{equation}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n} \\ $$$$\mathrm{for}\:\mathrm{n}\:\mathrm{is}\:\mathrm{integer}\: \\ $$ Answered by…
Question Number 133610 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mid\mathrm{tan}\:\mathrm{x}\mid\:,\:\mathrm{find}\: \\ $$$$\:\frac{\mathrm{df}\left(\mathrm{x}\right)}{\mathrm{dx}}\mid_{\mathrm{x}=\mathrm{k}} \:\mathrm{where}\:\frac{\pi}{\mathrm{2}}<\mathrm{k}<\pi \\ $$ Answered by guyyy last updated on 23/Feb/21 Answered by liberty…
Question Number 68073 by necxxx last updated on 04/Sep/19 $$\:{A}\:{straight}\:{rod}\:{AB}\:{which}\:{is}\:\mathrm{60}{cm}\:{long},{is} \\ $$$${in}\:{equilibrum}\:{when}\:{horizontal}\:{and} \\ $$$${supported}\:{at}\:{a}\:{point}\:{C},\mathrm{10}{cm}\:{from}\:{A}, \\ $$$${with}\:{masses}\:\mathrm{6}{kg}\:{and}\:\mathrm{1}{kg}\:{attached}\:{to}\:{the} \\ $$$${rod}\:{at}\:{A}\:{and}\:{B}\:{respectively}.{It}\:{is}\:{also}\:{in} \\ $$$${equilibrum}\:{and}\:{horizontal}\:{when}\: \\ $$$${supported}\:{at}\:{another}\:{pivott}\:{at}\:{its}\:{mid}- \\ $$$${point},{with}\:{masses}\:{of}\:\mathrm{2}{kg}\:{and}\:\mathrm{5}{kg}\: \\…
Question Number 68068 by mhmd last updated on 04/Sep/19 $${find}\:{e}^{\mathrm{1}/{ln}\mathrm{2}} \:\:=? \\ $$ Commented by peter frank last updated on 04/Sep/19 $${e}^{{x}} =\mathrm{1}+{x}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}+\frac{{x}^{\mathrm{4}}…
Question Number 133601 by help last updated on 23/Feb/21 Answered by benjo_mathlover last updated on 23/Feb/21 $$\:\frac{\mathrm{sin}^{\mathrm{2}} \:\theta}{\mathrm{sin}\:\theta−\mathrm{cos}\:\theta}\:+\:\frac{\mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\:= \\ $$$$\:\frac{\mathrm{cos}\:^{\mathrm{2}} \theta−\mathrm{sin}\:^{\mathrm{2}} \theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\:=\:\mathrm{cos}\:\theta+\mathrm{sin}\:\theta \\ $$…
Question Number 68062 by aseer imad last updated on 04/Sep/19 Commented by mind is power last updated on 04/Sep/19 $$\mathrm{2}=\frac{\mathrm{5}}{\mathrm{3}}+\frac{\mathrm{5}}{{R}}\Rightarrow{R}=\mathrm{15}\Omega \\ $$$${E}=\mathrm{10}.\mathrm{2}+\mathrm{2}.\mathrm{2}+\left(\frac{\mathrm{3}.\mathrm{15}}{\mathrm{3}+\mathrm{15}}\right).\mathrm{2}=\mathrm{24}+\mathrm{5}=\mathrm{29}{v} \\ $$ Terms…
Question Number 68063 by TawaTawa last updated on 04/Sep/19 Answered by MJS last updated on 04/Sep/19 $$\mathrm{tricky}\:\mathrm{but}\:\mathrm{easy} \\ $$$$\left(\mathrm{1}\right)\:\:{x}^{\mathrm{3}} −\mathrm{3}{y}^{\mathrm{2}} {x}={a}+\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\:{y}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}={a}…
Question Number 2526 by Filup last updated on 22/Nov/15 $$\mathrm{Evaluate}:\:\underset{−\infty} {\overset{\infty} {\int}}{e}^{−{x}^{\mathrm{2}} } {dx} \\ $$$$\mathrm{Please}\:\mathrm{show}\:\mathrm{and}\:\mathrm{explain}\:\mathrm{working} \\ $$ Commented by Filup last updated on 22/Nov/15…
Question Number 2524 by 123456 last updated on 21/Nov/15 $${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$${f}\left({x},{y}\right)={x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:{y}\geqslant\mathrm{0} \\ $$$${f}\left({x},{y}\right)={x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:{y}\leqslant\mathrm{0} \\ $$$$\mathrm{find} \\ $$$$\left({x},{y}\right)\:\mathrm{for}\:\mathrm{min}\:{f}\left({x},{y}\right) \\ $$$$\left({x},{y}\right)\:\mathrm{for}\:{f}\left({x},{y}\right)=\mathrm{1}…
Question Number 133589 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{For}\:\mathrm{all}\:\mathrm{real}\:\mathrm{number}\:\mathrm{f}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\: \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{m}\:\mathrm{sin}\:\mathrm{x}\:,\:\mathrm{if}\:\mathrm{x}\:<\:\mathrm{0}}\\{\mathrm{n}\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\:\mathrm{x}−\mathrm{2}\:,\:\mathrm{if}\:\mathrm{x}\geqslant\mathrm{0}}\end{cases} \\ $$$$\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{m}\:\mathrm{and}\:\mathrm{n}\:\mathrm{is}\:\mathrm{f}\: \\ $$$$\mathrm{differentiable}\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{0}\:? \\ $$ Answered by benjo_mathlover last updated…