Question Number 64860 by Tawa1 last updated on 22/Jul/19 Commented by Tawa1 last updated on 22/Jul/19 $$\mathrm{Number}\:\mathrm{11}\:\mathrm{and}\:\mathrm{13} \\ $$ Commented by mathmax by abdo last…
Question Number 130307 by mnjuly1970 last updated on 24/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:….\:\:\:\:\:{cslculus}… \\ $$$$\:\:\:{evaluate}\::::\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\:\left({x}\:\right)}{\:\sqrt{{x}}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:{dx}=? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last updated…
Find-the-angle-between-y-2-8x-and-x-2-y-2-16-at-their-point-of-intersection-for-which-y-is-positive-
Question Number 130294 by bramlexs22 last updated on 24/Jan/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{y}^{\mathrm{2}} =\mathrm{8x}\: \\ $$$$\mathrm{and}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{16}\:\mathrm{at}\:\mathrm{their}\:\mathrm{point}\:\mathrm{of} \\ $$$$\mathrm{intersection}\:\mathrm{for}\:\mathrm{which}\:\mathrm{y}\:\mathrm{is}\:\mathrm{positive} \\ $$ Answered by benjo_mathlover last updated on…
Question Number 130213 by benjo_mathlover last updated on 23/Jan/21 $$\:\mathrm{The}\:\mathrm{closest}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\mathrm{on}\: \\ $$$$\mathrm{the}\:\mathrm{ellipse}\:\mathrm{2x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\mathrm{8}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}=\mathrm{5x} \\ $$$$\mathrm{is}\:\_\_ \\ $$ Answered by liberty last updated on 23/Jan/21…
Question Number 130198 by mnjuly1970 last updated on 23/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{calculate}:: \\ $$$$\:\:\:\:\:\:\mathscr{L}\:\left[{e}^{−{t}} .\:\sqrt{{t}\:}\:\right]\:\underset{{transform}} {\overset{{Laplace}} {=}}\:?\:… \\ $$$$\:\:\: \\ $$ Answered by Dwaipayan Shikari…
Question Number 130200 by mnjuly1970 last updated on 23/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{cslculus}… \\ $$$$\:\:\:\:\:\:\:\:{find}\:::\:\:\:\:\:\:\mathscr{L}\:\left(\:{te}^{−{t}} {ln}\left({t}\right)\right)\:\underset{{transform}} {\overset{{laplace}} {=}}? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$ Answered by Dwaipayan Shikari…
Question Number 64574 by ajfour last updated on 19/Jul/19 Commented by ajfour last updated on 19/Jul/19 $${Find}\:{polynomial}\:{function}\:{p}\left({x}\right) \\ $$$${if}\:{coloured}\:{area}\:{is}\:{a}\:{maximum}. \\ $$ Commented by mr W…
Question Number 130087 by bobhans last updated on 22/Jan/21 $$\frac{{dx}}{{dy}}\:=\:{a}\:+\:\frac{\left({b}−{a}\right){y}}{{c}}\:+\:\frac{\left({b}−{a}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi{y}}{{c}}\right)}{\mathrm{2}\pi} \\ $$$${for}\:{a}>\mathrm{0}\:,\:{b}>\mathrm{0},\:{c}>\mathrm{0}\:{on}\:{x}\geqslant\mathrm{0}\: \\ $$ Answered by benjo_mathlover last updated on 22/Jan/21 $$\mathrm{dx}\:=\:\mathrm{a}\:\mathrm{dy}\:+\:\frac{\left(\mathrm{b}−\mathrm{a}\right)}{\mathrm{c}}\:\mathrm{y}\:\mathrm{dy}\:+\:\frac{\mathrm{b}−\mathrm{a}}{\mathrm{2}\pi}\:\mathrm{sin}\:\left(\frac{\mathrm{2}\pi\mathrm{y}}{\mathrm{c}}\right)\:\mathrm{dy} \\ $$$$\mathrm{x}=\:\mathrm{ay}\:+\frac{\left(\mathrm{b}−\mathrm{a}\right)\mathrm{y}^{\mathrm{2}} }{\mathrm{2c}}\:−\frac{\left(\mathrm{b}−\mathrm{a}\right)\mathrm{c}}{\mathrm{4}\pi^{\mathrm{2}}…
Question Number 130077 by benjo_mathlover last updated on 22/Jan/21 $$\:\mathrm{If}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4}\:,\:\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{x}}{\mathrm{y}+\mathrm{3}}. \\ $$ Answered by liberty last updated on 22/Jan/21 Answered by…
Question Number 64514 by Mikael last updated on 18/Jul/19 $${y}={arc}\:{tan}\left[\sqrt{\frac{\mathrm{1}−{cosx}}{\mathrm{1}+{cosx}}}\right] \\ $$$${y}^{} =? \\ $$ Commented by mathmax by abdo last updated on 18/Jul/19 $${we}\:{have}\:\frac{\mathrm{1}−{cosx}}{\mathrm{1}+{cosx}}\:=\frac{\mathrm{2}{sin}^{\mathrm{2}}…