Question Number 195518 by jubair56 last updated on 04/Aug/23 $${y}=\frac{{x}^{\mathrm{3}} −\mathrm{27}}{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{9}} \\ $$$${y}=\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}+{cosx}} \\ $$$${y}=\frac{{sinx}+{cosx}}{\:\sqrt{\mathrm{1}+{cos}\mathrm{2}{x}}} \\ $$ Answered by Calculusboy last updated on…
Question Number 195301 by SajaRashki last updated on 29/Jul/23 $$\begin{cases}{{x}^{\mathrm{2}} +{y}=\mathrm{11}}\\{{x}+{y}^{\mathrm{2}} =\mathrm{7}}\end{cases}\Rightarrow\:{x},{y}=? \\ $$ Answered by AST last updated on 30/Jul/23 $${y}=\mathrm{11}−{x}^{\mathrm{2}} \Rightarrow\left(\mathrm{11}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{7}−{x}…\left({i}\right)…
Question Number 195003 by mathlove last updated on 22/Jul/23 $${y}={lnx}^{{x}^{{x}} } \:\:\:\:\:\:\:\:\:{y}^{'} =? \\ $$ Answered by shunmisaki007 last updated on 22/Jul/23 $${y}=\mathrm{ln}\left({x}^{{x}^{{x}} } \right)={x}^{{x}}…
Question Number 194831 by necx122 last updated on 16/Jul/23 Commented by necx122 last updated on 16/Jul/23 $${I}'{ve}\:{tried}\:{attempting}\:{this}\:{question}\:{but} \\ $$$${got}\:{stuck}.{Please},\:{I}\:{need}\:{assistance}. \\ $$ Answered by dimentri last…
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Question Number 194599 by pete last updated on 10/Jul/23 $$\mathrm{A}\:\mathrm{tank}\:\mathrm{contains}\:\mathrm{300}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{fluid}\:\mathrm{in}\: \\ $$$$\mathrm{which}\:\mathrm{20}\:\mathrm{grams}\:\mathrm{of}\:\mathrm{salt}\:\mathrm{is}\:\mathrm{dissolved}.\: \\ $$$$\mathrm{Brine}\:\mathrm{containing}\:\:\mathrm{1}\:\mathrm{gm}\:\mathrm{of}\:\mathrm{salt}\:\mathrm{per}\:\mathrm{litre} \\ $$$$\:\mathrm{is}\:\mathrm{then}\:\mathrm{pumped}\:\mathrm{into}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{a}\:\mathrm{rate} \\ $$$$\:\mathrm{of}\:\mathrm{4L}/\mathrm{min};\:\mathrm{the}\:\mathrm{well}\:\mathrm{mixed}\:\mathrm{solution}\: \\ $$$$\mathrm{is}\:\mathrm{pumped}\:\mathrm{out}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{rate}. \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{N}\left(\mathrm{t}\right)\:\mathrm{of}\:\mathrm{grams}\:\mathrm{of} \\ $$$$\:\mathrm{salt}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{time}\:\mathrm{t}.\: \\…
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Question Number 193733 by Tawa11 last updated on 18/Jun/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{ordinary}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{satisfy}\:\mathrm{by}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}^{\mathrm{n}} \left(\mathrm{A}\:\:+\:\:\mathrm{Blogx}\right) \\ $$ Answered by Rajpurohith last updated on 19/Jun/23 $${y}\:'={x}^{{n}}…
Question Number 130875 by EDWIN88 last updated on 30/Jan/21 Answered by benjo_mathlover last updated on 30/Jan/21 $$\mathrm{y}''−\left(\frac{\mathrm{2x}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)\mathrm{y}'+\left(\frac{\mathrm{2}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)\mathrm{y}=\mathrm{0} \\ $$$$\:\mathrm{y}_{\mathrm{2}} '\mathrm{y}_{\mathrm{1}} −\mathrm{y}_{\mathrm{2}} \mathrm{y}_{\mathrm{1}} '=\mathrm{Ce}^{−\int\:\mathrm{a}_{\mathrm{1}}…