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Question Number 160314 by MathsFan last updated on 27/Nov/21 $${suppose}\:{the}\:{probability}\:{of}\:{a}\:{child} \\ $$$${being}\:{a}\:{boy}\:{is}\:\mathrm{0}.\mathrm{5}.\:{Find}\:{the}\: \\ $$$${probability}\:{that}\:{a}\:{family}\:{of}\: \\ $$$$\:\mathrm{3}\:{children}\:{will}\:{have}\: \\ $$$$\left({i}\right)\:{at}\:{least}\:{two}\:{boys} \\ $$$$\left({ii}\right)\:{exactly}\:{two}\:{boys} \\ $$$$\left({iii}\right)\:{all}\:{girls} \\ $$ Commented…
Question Number 29241 by mondodotto@gmail.com last updated on 05/Feb/18 Answered by ajfour last updated on 05/Feb/18 $${k}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)+{y}^{\mathrm{2}} +\mathrm{4}{y}−\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}=\mathrm{0} \\ $$$${coeff}.\:{of}\:{x}^{\mathrm{2}} ={coeff}.\:{of}\:{y}^{\mathrm{2}} \\…
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Question Number 94774 by Hamida last updated on 20/May/20 Commented by peter frank last updated on 20/May/20 $$\mathrm{u}=\left(\mathrm{5x}^{\mathrm{2}} −\mathrm{2x}\right)^{\mathrm{3}} \\ $$$$\frac{\mathrm{du}}{\mathrm{dx}}=\mathrm{3}\left(\mathrm{5x}^{\mathrm{2}} −\mathrm{2x}\right)^{\mathrm{2}} \left(\mathrm{10x}−\mathrm{2}\right) \\ $$$$\mathrm{t}=\mathrm{sin}\:^{\mathrm{2}}…
Question Number 94773 by Hamida last updated on 20/May/20 Answered by prakash jain last updated on 20/May/20 $${slope}=\frac{{dy}}{{dx}}=\frac{{dy}/{dt}}{{dx}/{dt}}=\frac{\mathrm{8}{t}+\mathrm{1}}{\mathrm{3}{t}^{\mathrm{2}} +\mathrm{9}} \\ $$$${at}\:{t}=\mathrm{1}\:\mathrm{slopd}=\frac{\mathrm{9}}{\mathrm{12}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{curve}\:\mathrm{at}\:{t}=\mathrm{1} \\ $$$${y}=\mathrm{5},\:{x}=\mathrm{10}…
Question Number 94768 by Hamida last updated on 20/May/20 Answered by mathmax by abdo last updated on 21/May/20 $$\mathrm{y}\left(\mathrm{x}\right)\:=\frac{\mathrm{x}^{\mathrm{4}} \:+\mathrm{6x}^{\mathrm{2}} \:+\mathrm{4}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{5}}\:\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\frac{\left(\mathrm{4x}^{\mathrm{3}} \:+\mathrm{12x}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{5}\right)−\mathrm{2x}\left(\mathrm{x}^{\mathrm{4}} \:+\mathrm{6x}^{\mathrm{2}}…
Question Number 94767 by Hamida last updated on 20/May/20 Answered by mathmax by abdo last updated on 21/May/20 $$\mathrm{y}\left(\mathrm{x}\right)\:=\mathrm{5}^{−\mathrm{x}} \:+\mathrm{5}\:\mathrm{arcsin}\left(\frac{\mathrm{x}}{\mathrm{6}}\right)\:+\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)+\mathrm{e}^{\frac{−\mathrm{7}}{\mathrm{2}}\mathrm{x}} \:+\mathrm{3}^{−\mathrm{x}} \mathrm{ln5} \\ $$$$\Rightarrow\mathrm{y}\left(\mathrm{x}\right)\:=\mathrm{u}\left(\mathrm{x}\right)+\mathrm{v}\left(\mathrm{x}\right)\:\mathrm{with}\:\mathrm{u}\left(\mathrm{x}\right)\:=\mathrm{5}^{−\mathrm{x}}…
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Question Number 94753 by Kunal12588 last updated on 20/May/20 Answered by mr W last updated on 20/May/20 $$\left({a}\right)\:{on}\:{clock}\:{B}: \\ $$$$\mathrm{25}\rightarrow\mathrm{125}:\:\frac{\mathrm{125}−\mathrm{25}}{\mathrm{290}−\mathrm{125}}×\mathrm{600}=\mathrm{363}\frac{\mathrm{7}}{\mathrm{11}}\:{s} \\ $$$$\mathrm{125}\rightarrow\mathrm{200}:\:\frac{\mathrm{200}−\mathrm{125}}{\mathrm{290}−\mathrm{125}}×\mathrm{600}=\mathrm{272}\frac{\mathrm{8}}{\mathrm{11}}\:{s} \\ $$$$\mathrm{200}\rightarrow\mathrm{290}:\:\frac{\mathrm{290}−\mathrm{209}}{\mathrm{290}−\mathrm{125}}×\mathrm{600}=\mathrm{327}\frac{\mathrm{3}}{\mathrm{11}}\:{s} \\…