Question Number 142116 by Eric002 last updated on 26/May/21 $${use}\:{trigonometric}\:{substitution}\:{to}\:{solve} \\ $$$$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by ZiYangLee last updated on 27/May/21 $$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}}…
Question Number 76580 by Rio Michael last updated on 28/Dec/19 $$\mathrm{how}\:\mathrm{many}\:\mathrm{divisors}\:\mathrm{does}\:\mathrm{180045}\:\mathrm{has}? \\ $$ Commented by mr W last updated on 28/Dec/19 $$\frac{\mathrm{180045}}{\mathrm{5}}=\mathrm{36009} \\ $$$$\frac{\mathrm{36009}}{\mathrm{3}}=\mathrm{12003} \\…
Question Number 76579 by Rio Michael last updated on 28/Dec/19 $$\mathrm{A}\:\mathrm{uniform}\:\mathrm{ladder}\:\mathrm{of}\:\mathrm{weight}\:{W}\:\mathrm{and}\:\mathrm{length} \\ $$$$\mathrm{2}{a}\:\mathrm{rest}\:\mathrm{in}\:\mathrm{limiting}\:\mathrm{equilibrium}\:\mathrm{with}\:\mathrm{one}\: \\ $$$$\mathrm{end}\:\mathrm{on}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{horizontal}\:\mathrm{ground}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{other}\:\mathrm{end}\:\mathrm{on}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{vertical}\:\mathrm{wall}. \\ $$$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ladder} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{and}\:\mathrm{between}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{wall}\:\mathrm{are}\:\mathrm{respectively}\:\mu\:\mathrm{and}\:\lambda\:.\:\mathrm{If}\:\mathrm{the}\:\mathrm{ladder} \\ $$$$\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{where}\:\mathrm{tan}\:\theta\:=\:\frac{\mathrm{5}}{\mathrm{12}},…
Question Number 11042 by Mahmoud A.R last updated on 09/Mar/17 $$\int{cos}\left({x}\right)\sqrt{\frac{{sin}\left({x}\right)+\mathrm{1}}{{sin}\left({x}\right)−\mathrm{1}}\:}\:{dx} \\ $$ Answered by ajfour last updated on 09/Mar/17 $$\:\:\int\mathrm{cos}\:\left({x}\right)\sqrt{−\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{sin}\:{x}}}\:{dx} \\ $$$$=\sqrt{−\mathrm{1}}\:\int\mathrm{cos}\:\left({x}\right)\sqrt{\frac{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)}{\left(\mathrm{1}−\mathrm{sin}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)}}\:{dx} \\ $$$$=\:{i}\int\mathrm{cos}\:\left({x}\right)\left(\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\right){dx}…
Question Number 142115 by mathmax by abdo last updated on 26/May/21 $$\mathrm{simplify}\:\:\mathrm{A}_{\mathrm{n}} \left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}\right)^{\mathrm{n}} +\left(\mathrm{1}−\mathrm{ix}\right)^{\mathrm{n}} \:\:\:\mathrm{x}\:\mathrm{from}\:\mathrm{C} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 76576 by Rio Michael last updated on 28/Dec/19 $${Compute}\:{the}\:{Gcd}\:\left({greatest}\:{common}\:{divisor}\right) \\ $$$${of}\:\:\mathrm{45}\:{and}\:\mathrm{1287}\: \\ $$ Answered by john santu last updated on 28/Dec/19 $$\mathrm{45}\:=\:\mathrm{3}^{\mathrm{2}} ×\mathrm{5}…
Question Number 76577 by Rio Michael last updated on 28/Dec/19 $$\:{given}\:{a}\:{sequence}\:{defined}\:{by}\:\:\left\{\frac{\mathrm{3}{n}}{\mathrm{2}{n}+\:\mathrm{5}}\right\}_{{n}=\mathrm{1}} ^{\infty} ,\:{does}\:{this}\: \\ $$$${sequence}\:{converge}\:{or}\:{diverge},\:{explain} \\ $$ Answered by john santu last updated on 28/Dec/19…
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Question Number 76575 by Rio Michael last updated on 28/Dec/19 $${define}\:{the}\:{concept}\:{of}\:{a}\:\boldsymbol{{contingency}} \\ $$$${Which}\:{of}\:{the}\:{following}\:{is}\:{a}\:{contingency}\: \\ $$$${and}\:{which}\:{is}\:{a}\:{tautology} \\ $$$$\left.\mathrm{1}\right)\:\left({P}\:\Rightarrow\sim{P}\right)\:\vee\:{Q}\:\: \\ $$$$\left.\mathrm{2}\right)\:\left({P}\:\Rightarrow\:\sim{P}\right)\:\Rightarrow\:{Q} \\ $$ Answered by benjo 1/2…