Question Number 25934 by ajfour last updated on 16/Dec/17 Commented by ajfour last updated on 16/Dec/17 $${Q}.\mathrm{25828}\:\:\:\left({another}\:{solution}\:{continued}\:\right) \\ $$ Commented by ajfour last updated on…
Question Number 25899 by maheshagarwal last updated on 16/Dec/17 $$\mathrm{8}{a}^{\mathrm{6}} +\mathrm{5}{a}^{\mathrm{3}} +\mathrm{1}={factorize} \\ $$ Commented by sushmitak last updated on 16/Dec/17 $${a}^{\mathrm{3}} ={x} \\ $$$${x}=\frac{−\mathrm{5}\pm\sqrt{\mathrm{25}−\mathrm{32}}}{\mathrm{16}}=\frac{−\mathrm{5}\pm\iota\sqrt{\mathrm{7}}}{\mathrm{16}}…
Question Number 25894 by tawa tawa last updated on 16/Dec/17 Commented by math solver last updated on 16/Dec/17 $$\mathrm{1}.\mathrm{7}\:\left(\mathrm{iii}\right)\:−\mathrm{1}. \\ $$$$ \\ $$ Terms of…
Question Number 91421 by M±th+et+s last updated on 30/Apr/20 $$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{1}}{{x}\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}}{dx} \\ $$ Commented by abdomathmax last updated on 30/Apr/20 $${I}\:=\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\frac{{dx}}{{x}\sqrt{\mathrm{3}{x}^{\mathrm{2}}…
Question Number 25854 by rita1608 last updated on 15/Dec/17 $${find}\:\frac{{dy}}{{dx}}\:{for}\:{y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}………}}}} \\ $$ Answered by ibraheem160 last updated on 15/Dec/17 $${y}^{\mathrm{2}} ={x}+{y} \\ $$$$\mathrm{2}{y}\frac{{dy}}{{dx}}=\mathrm{1}+\frac{{dy}}{{dx}} \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{\mathrm{2}{y}−\mathrm{1}}…
Question Number 25846 by rita1608 last updated on 15/Dec/17 $${determine}\:{the}\:{interval}\:{on}\:{which}\:{the} \\ $$$${given}\:{function}\:{is}\:{continuous}\: \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{sin}\:\frac{\mathrm{1}}{{x}}}&{{x}\neq\mathrm{0}}\\{{x}}&{{x}=\mathrm{0}}\end{cases} \\ $$ Commented by kaivan.ahmadi last updated on 15/Dec/17 $$\mathrm{since}\:\:\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}sin}\frac{\mathrm{1}}{\mathrm{x}}\:\neq\mathrm{f}\left(\mathrm{0}\right)\:,\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{continuous}.…
Question Number 25838 by ajfour last updated on 15/Dec/17 Commented by ajfour last updated on 15/Dec/17 $$\left({i}\right)\:{Determine}\:\angle\:\theta\:{such}\:{that}\: \\ $$$${projectile}\:{hits}\:{inclined}\:{plane} \\ $$$${perpendicularly}\:{at}\:{P}. \\ $$$$\left({ii}\right)\:{Find}\:{the}\:{coefficient}\:{of} \\ $$$${restitution}\:\boldsymbol{{e}}\:{such}\:{that}\:{after}\:…
Question Number 91375 by banusalem last updated on 30/Apr/20 $${x}\mathrm{4}+\mathrm{2}{x}\mathrm{3}−\mathrm{5}{x}\mathrm{2}+\mathrm{6}{x}+\mathrm{2}/{x}\mathrm{2}−\mathrm{2}{x}+\mathrm{2}^{} \\ $$ Commented by Kunal12588 last updated on 30/Apr/20 $$\frac{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}}? \\…
Question Number 91374 by Rio Michael last updated on 30/Apr/20 $$\mathrm{A}\:\mathrm{car}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{700}\:\mathrm{kg}\:\mathrm{has}\:\mathrm{maximum}\:\mathrm{power}\:{P}\:\:,\mathrm{at}\:\mathrm{all}\:\mathrm{times}, \\ $$$$\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{non}\:\mathrm{gravitational}\:{R}\:\mathrm{to}\:\mathrm{the}\:\mathrm{motion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}. \\ $$$$\mathrm{the}\:\mathrm{car}\:\mathrm{moves}\:\mathrm{along}\:\mathrm{an}\:\mathrm{inclined}\:\mathrm{of}\:\mathrm{angle}\:\theta\:\mathrm{where}\:\mathrm{10}\:\mathrm{sin}\theta\:=\:\mathrm{1}.\:\mathrm{The} \\ $$$$\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{up}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{speed}\:\mathrm{down}\:\mathrm{the}\:\mathrm{plane}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{R}. \\ $$$$\:\mathrm{on}\:\mathrm{level}\:\mathrm{road}\:\mathrm{the}\:\mathrm{car}\:\mathrm{has}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{20}\:\mathrm{ms}^{−\mathrm{1}} . \\…
Question Number 25828 by Tinkutara last updated on 15/Dec/17 $${Two}\:{particles}\:{A}\:{and}\:{B}\:{of}\:{equal}\:{masses} \\ $$$${m}\:{are}\:{tied}\:{with}\:{an}\:{inextensible}\:{string} \\ $$$${of}\:{length}\:\mathrm{2}{l}.\:{The}\:{initial}\:{distance} \\ $$$${between}\:{A}\:{and}\:{B}\:{is}\:{l}.\:{Particle}\:{A}\:{is} \\ $$$${given}\:{speed}\:{v}.\:{Find}\:{the}\:{speed}\:{of} \\ $$$${particle}\:{A}\:{and}\:{B}\:{just}\:{after}\:{the}\:{string} \\ $$$${becomes}\:{taut}. \\ $$ Commented…