Question Number 194131 by cortano12 last updated on 28/Jun/23 Commented by BaliramKumar last updated on 28/Jun/23 $$\mathrm{25} \\ $$ Answered by MM42 last updated on…
Question Number 193951 by Erico last updated on 23/Jun/23 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}!}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} {t}^{{n}} {e}^{−{t}} {dt}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by senestro last updated on…
Question Number 193235 by mathlove last updated on 08/Jun/23 Answered by a.lgnaoui last updated on 08/Jun/23 $$\boldsymbol{\mathrm{T}}\mathrm{otale}\:\mathrm{Area}=\mathrm{22}+\mathrm{A}\:\:\:\:\:\:\left(\mathrm{A}=\boldsymbol{\mathrm{xy}}\right) \\ $$$$\mathrm{22}+\boldsymbol{\mathrm{xy}}=\mathrm{6}\boldsymbol{\mathrm{x}}+\left(\mathrm{8}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{xy}}=\mathrm{8}\boldsymbol{\mathrm{y}}+\mathrm{6}\boldsymbol{\mathrm{x}}−\mathrm{22} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{xy}}=\mathrm{4}\boldsymbol{\mathrm{y}}+\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{11}\:\:\:\left(\mathrm{1}\right)…
Question Number 130795 by mr W last updated on 29/Jan/21 Commented by mr W last updated on 29/Jan/21 $${find}\:{the}\:{locus}\:{of}\:{point}\:{P}. \\ $$ Answered by mr W…
Question Number 65022 by ajfour last updated on 24/Jul/19 Commented by MJS last updated on 24/Jul/19 $$\mathrm{I}\:\mathrm{used}\:\mathrm{a}\:\mathrm{calculator}.\:\mathrm{I}'\mathrm{ve}\:\mathrm{got}\:\mathrm{an}\:\mathrm{old}\:\mathrm{TI}−\mathrm{89} \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{use}\:\mathrm{any}\:\mathrm{calculator}\:\mathrm{which}\:\mathrm{is}\:\mathrm{able}\:\mathrm{to} \\ $$$$\mathrm{approximately}\:\mathrm{solve}\:\mathrm{equations}\:\mathrm{and}\:\mathrm{integrals} \\ $$$$\mathrm{select}\:\mathrm{a}\:\mathrm{value}\:\mathrm{for}\:{r} \\ $$$$\mathrm{calculate}\:{P},\:{Q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{integrals}…
Question Number 64968 by ajfour last updated on 23/Jul/19 Commented by ajfour last updated on 25/Jul/19 $${Instead}\:{let}\:\:{y}={Ax}^{\mathrm{2}} \:,\:{find}\:{side} \\ $$$${length}\:{of}\:{such}\:{a}\:{rhombus}\:{that} \\ $$$${fits}\:{in},\:{the}\:{way}\:{shown}.\:{Also} \\ $$$${find}\:{A}.\:\:\:\:\:\:\: \\…
Question Number 130358 by ajfour last updated on 24/Jan/21 Commented by ajfour last updated on 24/Jan/21 $${Two}\:{identical}\:{ellipses}. \\ $$$${Find}\:{maximum}\:{value}\:{of}\:{b}/{a}. \\ $$ Commented by MJS_new last…
Question Number 130263 by pete last updated on 23/Jan/21 Answered by Olaf last updated on 23/Jan/21 $$\mathrm{B}\begin{pmatrix}{{x}_{\mathrm{B}} \:=\:\mathrm{12}−\mathrm{2}{y}_{\mathrm{B}} \:=\:\mathrm{12}}\\{\mathrm{0}}\end{pmatrix} \\ $$$$\mathrm{E}\begin{pmatrix}{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{2}}\:=\:\frac{{y}_{\mathrm{E}} }{{x}_{\mathrm{B}} }\:\Rightarrow\:{y}_{\mathrm{E}} \:=\:\mathrm{6}}\end{pmatrix} \\…
Question Number 64709 by ajfour last updated on 20/Jul/19 Commented by ajfour last updated on 20/Jul/19 $${If}\:{regions}\:{A}\:{and}\:{B}\:{have}\:{the}\:{same} \\ $$$${area},\:{and}\:{both}\:{parabolas}\:{have} \\ $$$${the}\:{same}\:{shape}\:{but}\:{their}\:{axis}\:\bot\:{to} \\ $$$${each}\:{other},\:{then}\:{determine} \\ $$$${the}\:{equation}\:{of}\:{the}\:{red}\:{parabola}.…
Question Number 64436 by ajfour last updated on 17/Jul/19 Commented by ajfour last updated on 17/Jul/19 $${Find}\:{radius}\:{of}\:{arc}\:{length}\:{s}\:,\:{if} \\ $$$${area}\:{between}\:{parabola}\:{and}\:{arc} \\ $$$${is}\:{a}\:{maximum}. \\ $$ Answered by…