Question Number 214449 by ajfour last updated on 08/Dec/24 Commented by ajfour last updated on 09/Dec/24 https://youtu.be/mVW8FiNpKjk?si=q68kdETxCuqwyZ3- Answered by mr W last updated on 14/Dec/24…
Question Number 214419 by 2universe456 last updated on 08/Dec/24 Answered by golsendro last updated on 08/Dec/24 $$\:\:\:\:\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{2xy}=\mathrm{25}}\\{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{47}=\mathrm{10xy}}\end{cases}\Rightarrow\mathrm{2xy}+\mathrm{47}=\mathrm{10xy}+\mathrm{25} \\ $$$$\:\:\:\mathrm{8xy}=\:\mathrm{22}\Rightarrow\mathrm{4xy}=\mathrm{11} \\ $$$$\:\:\:\mathrm{4x}\left(\mathrm{5}−\mathrm{x}\right)=\mathrm{11}\:\Rightarrow\mathrm{4x}^{\mathrm{2}}…
Question Number 214414 by ChantalYah last updated on 07/Dec/24 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}=\mathrm{0}\:\mathrm{are}\:\alpha\:\mathrm{and}\:\beta, \\ $$$$\:\mathrm{show}\:\mathrm{that}; \\ $$$$\lambda\mu\mathrm{b}^{\mathrm{2}} =\mathrm{ac}\left(\lambda+\mu\right)^{\mathrm{2}} \:\mathrm{where}\:\frac{\alpha}{\beta}=\frac{\lambda}{\mu} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Mr}\:{Hans} \\ $$ Answered by…
Question Number 214398 by mr W last updated on 07/Dec/24 Commented by mr W last updated on 07/Dec/24 $${find}\:{acceleration}\:{of}\:{wedge}\:{A}=? \\ $$$${cylinder}\:{with}\:{mass}\:{m}\:{and}\:{radius}\:{r}\: \\ $$$${rolls}\:{along}\:{the}\:{wedge}\:{with}\:{mass}\:{M}. \\ $$…
Question Number 214408 by Abdullahrussell last updated on 07/Dec/24 Answered by A5T last updated on 07/Dec/24 $${Let}\:{f}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{3}} +\mathrm{37}{x}^{\mathrm{2}} −\mathrm{60}{x}+\mathrm{32} \\ $$$${f}\left(\mathrm{1}\right)={f}\left(\mathrm{4}\right)=\mathrm{0}\Rightarrow{f}\left({x}\right)=\left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}\right)\left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{8}\right) \\…
Question Number 214409 by ajfour last updated on 07/Dec/24 Answered by A5T last updated on 07/Dec/24 Commented by A5T last updated on 07/Dec/24 $${AB}=\sqrt{\left({r}+{R}\right)^{\mathrm{2}} −\left({R}−{r}\right)^{\mathrm{2}}…
Question Number 214395 by mr W last updated on 07/Dec/24 Commented by mr W last updated on 07/Dec/24 $${find}\:{acceleration}\:{of}\:{wedge}\:{A}=? \\ $$ Answered by mr W…
Question Number 214402 by golsendro last updated on 07/Dec/24 $$\:\:\:\mathrm{If}\:\frac{\mathrm{a}+\mathrm{b}}{\mathrm{c}}\:=\:\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}}\:=\:\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}\:\mathrm{then}\:\mathrm{find}\: \\ $$$$\:\:\:\:\frac{\mathrm{a}+\mathrm{b}}{\mathrm{c}}\:. \\ $$ Answered by efronzo1 last updated on 07/Dec/24 $$\:\:\:\:\mathrm{Let}\:\frac{\mathrm{a}+\mathrm{b}}{\mathrm{c}}\:=\:\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}}\:=\:\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}\:=\:\mathrm{m}\: \\ $$$$\:\:\:\:\:\mathrm{then}\:\mathrm{a}+\mathrm{b}\:=\:\mathrm{mc}\:;\:\mathrm{b}+\mathrm{c}\:=\:\mathrm{ma}\:;\:\mathrm{a}+\mathrm{c}\:=\:\mathrm{mb} \\…
Question Number 214366 by issac last updated on 06/Dec/24 $${f}\left(\alpha\right)=\int_{−\infty} ^{\:\infty} \:{e}^{−\alpha{x}^{\mathrm{2}} } \mathrm{d}{x} \\ $$$$\int\:\:{e}^{−\alpha{t}^{\mathrm{2}} } \mathrm{d}{t}=\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\pi}{\alpha}}\centerdot\mathrm{erf}\left(\sqrt{\alpha}{t}\right)+\mathrm{Const} \\ $$$$\therefore\int_{−\infty} ^{\:\infty} \:{e}^{−\alpha{t}^{\mathrm{2}} } \mathrm{d}{t}=\sqrt{\frac{\pi}{\alpha}}\:,\:\alpha\in\left(\mathrm{0},\infty\right) \\…
Question Number 214360 by shunmisaki007 last updated on 06/Dec/24 $$\mathrm{Find}\:\underset{−\infty} {\overset{\infty} {\int}}{e}^{−{ax}^{\mathrm{2}} } {dx}\:\mathrm{when}\:{a}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{without}\:\mathrm{changing}\:\mathrm{the}\:\mathrm{coordinate}. \\ $$ Answered by mathmax last updated on 06/Dec/24 $$=\mathrm{2}\int_{\mathrm{0}} ^{\infty}…