Question Number 175285 by MathsFan last updated on 26/Aug/22 $$\mathrm{simplfy} \\ $$$$\:\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{log}}\mathrm{2}\right) \\ $$ Answered by MJS_new last updated on 26/Aug/22 $$\mathrm{sinh}\:{x}\:=\frac{\mathrm{e}^{{x}} −\mathrm{e}^{−{x}} }{\mathrm{2}} \\…
Question Number 44214 by 12344 last updated on 23/Sep/18 $$\mathrm{find}\:\mathrm{x}\:\mathrm{inthe}\:\mathrm{eqn}. \\ $$$$\mathrm{3}^{\mathrm{x}} −\mathrm{1}=\mathrm{x}^{\mathrm{3}} \\ $$ Answered by MJS last updated on 23/Sep/18 $$\mathrm{two}\:\mathrm{solutions}\:\mathrm{are}\:\mathrm{obvious} \\ $$$${x}=\mathrm{0}…
Question Number 109749 by mathdave last updated on 25/Aug/20 Answered by 1549442205PVT last updated on 26/Aug/20 $$\mathrm{By}\:\mathrm{obtained}\:\mathrm{result}\:\mathrm{above}\:\mathrm{we}\:\mathrm{have} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{324}}{\mathrm{x}^{\mathrm{6}} +\mathrm{27}}\mathrm{dx}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\frac{\mathrm{12}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)}+\frac{\mathrm{6}\left(\mathrm{x}+\mathrm{2}\right)}{\mathrm{x}^{\mathrm{2}}…
Question Number 175280 by naka3546 last updated on 26/Aug/22 $$\mathrm{A}\:\mathrm{biology}\:\:\mathrm{class}\:\mathrm{at}\:\mathrm{central}\:\:\mathrm{high}\:\:\mathrm{school} \\ $$$$\mathrm{predicted}\:\:\mathrm{that}\:\:\mathrm{a}\:\:\mathrm{local}\:\:\mathrm{population}\:\:\mathrm{of}\:\:\:\mathrm{animals} \\ $$$$\mathrm{will}\:\:\mathrm{double}\:\:\mathrm{in}\:\:\mathrm{size}\:\:\mathrm{every}\:\:\mathrm{12}\:\:\mathrm{years}. \\ $$$$\mathrm{The}\:\:\mathrm{population}\:\:\mathrm{at}\:\:\mathrm{the}\:\:\mathrm{beginning}\:\:\mathrm{of}\:\:\mathrm{2014} \\ $$$$\mathrm{was}\:\:\mathrm{estimated}\:\:\mathrm{to}\:\mathrm{be}\:\:\mathrm{50}\:\:\mathrm{animals}. \\ $$$$\mathrm{If}\:\:{P}\:\:\mathrm{represents}\:\:\mathrm{the}\:\:\mathrm{population}\:\:{n}\:\:\mathrm{years}\:\:\mathrm{after}\:\:\mathrm{2014}. \\ $$$$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{equations}\:\:\mathrm{represents}\:\:\mathrm{the}\:\:\mathrm{class}\:\:\mathrm{model} \\ $$$$\mathrm{of}\:\:\mathrm{the}\:\:\mathrm{population}\:\:\mathrm{over}\:\:\mathrm{time}? \\…
Question Number 175279 by naka3546 last updated on 26/Aug/22 $$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{angle}\:\:\mathrm{between}\:\:\mathrm{the}\:\:\mathrm{lines} \\ $$$${r}\:=\:\begin{pmatrix}{\mathrm{1}}\\{\mathrm{0}}\\{\mathrm{4}}\end{pmatrix}\:\:+\:\lambda\begin{pmatrix}{\mathrm{2}}\\{−\mathrm{1}}\\{−\mathrm{1}}\end{pmatrix} \\ $$$${r}\:=\:\begin{pmatrix}{\mathrm{1}}\\{\mathrm{0}}\\{\mathrm{4}}\end{pmatrix}\:\:+\:\lambda\begin{pmatrix}{\mathrm{3}}\\{\mathrm{0}}\\{\mathrm{1}}\end{pmatrix} \\ $$$$ \\ $$ Answered by mahdipoor last updated on 26/Aug/22…
Question Number 109738 by Khalmohmmad last updated on 25/Aug/20 $$\frac{\frac{\mathrm{x}}{\mathrm{y}}−\frac{\mathrm{y}}{\mathrm{x}}}{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }}=\frac{\mathrm{9}}{\mathrm{4}} \\ $$$$\frac{\mathrm{x}}{\mathrm{y}}=? \\ $$ Commented by nimnim last updated on 25/Aug/20…
Question Number 109734 by mathdave last updated on 25/Aug/20 $${solve}\:{the}\:{following}\:{integral} \\ $$$$\left.\mathrm{1}\right)\int_{\mathrm{3}} ^{\mathrm{7}} \mathrm{4}\sqrt{\left({x}−\mathrm{3}\right)\left(\mathrm{7}−{x}\right)}{dx} \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{0}} ^{\infty} \frac{{x}\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }{dx} \\ $$$$\left.\mathrm{3}\right)\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left[\mathrm{ln}\left(\mathrm{1}−\mathrm{tan}{x}\right)\right]^{\mathrm{2}} {dx}=\frac{\pi}{\mathrm{2}}\mathrm{ln2}−\mathrm{2}{G}…
Question Number 44194 by peter frank last updated on 23/Sep/18 Commented by maxmathsup by imad last updated on 23/Sep/18 $$\left.{ii}\right)\:{fog}\left({x}\right)={f}\left({g}\left({x}\right)\right)=\mid{x}−\mathrm{2}\mid^{\mathrm{2}} −\mathrm{1}=\left({x}−\mathrm{2}\right)^{\mathrm{2}} −\mathrm{1}={x}^{\mathrm{2}} \:−\mathrm{4}{x}+\mathrm{4}−\mathrm{1}={x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3} \\…
Question Number 175264 by Beginner last updated on 25/Aug/22 Answered by Rasheed.Sindhi last updated on 25/Aug/22 $${S}_{{n}} =\mathrm{5}{n}^{\mathrm{2}} −\mathrm{2}{n}={n}\left(\mathrm{5}{n}−\mathrm{2}\right) \\ $$$${U}_{{r}} ={S}_{{r}} −{S}_{{r}−\mathrm{1}} =\left(\mathrm{5}{r}^{\mathrm{2}} −\mathrm{2}{r}\right)−\left(\:\mathrm{5}\left({r}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 175251 by MathsFan last updated on 24/Aug/22 $$\boldsymbol{\mathrm{Given}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\mathrm{4}\left(\boldsymbol{\mathrm{x}}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{9}\left(\boldsymbol{\mathrm{y}}+\mathrm{2}\right)^{\mathrm{2}} =\mathrm{27} \\ $$$$\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{ellipse}} \\ $$ Answered by MJS_new last updated on 26/Aug/22…