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Question Number 38012 by Rio Mike last updated on 20/Jun/18 $${The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{3}\:=\:\mathrm{0}\:{are}\:\alpha\:{and}\:\beta \\ $$$${if}\:{the}\:{roots}\:{of}\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{px}\:+\:{q}=\mathrm{0}\: \\ $$$${are}\:\alpha\:+\:\frac{\mathrm{1}}{\alpha}\:{and}\:\beta\:+\:\frac{\mathrm{1}}{\beta\:}\:{find}\:{the}\:{value} \\ $$$${of}\:{p}\:{and}\:{q}. \\ $$$$\: \\ $$…
Question Number 38011 by Rio Mike last updated on 20/Jun/18 $${Show}\:{that}\: \\ $$$$\:\:\frac{{sin}\mathrm{2}{A}}{\mathrm{1}+\:{cos}\mathrm{2}{A}}\:=\:{TanA} \\ $$ Answered by MJS last updated on 20/Jun/18 $$\mathrm{sin}\:\mathrm{2}\alpha=\mathrm{2sin}\:\alpha\:\mathrm{cos}\:\alpha \\ $$$$\mathrm{cos}\:\mathrm{2}\alpha=\mathrm{2cos}^{\mathrm{2}}…
Question Number 103510 by 175mohamed last updated on 15/Jul/20 Commented by Worm_Tail last updated on 15/Jul/20 $${y}={cot}^{−\mathrm{1}} \left({x}\right)\Rightarrow{cot}\left({y}\right)={x} \\ $$$${tan}\left({y}\right)=\frac{\mathrm{1}}{{x}}\Rightarrow{y}={tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}} \\ $$$${cot}^{−\mathrm{1}} {x}={tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}}…
Question Number 37972 by Rio Mike last updated on 20/Jun/18 $$\:{The}\:{distance}\:{S}\:{metres}\:{is}\: \\ $$$${given}\:{as}\:{a}\:{funtion}\: \\ $$$${f}\left({t}\right)\:{where}\:{is}\:{time}\:{taken}… \\ $$$${if}\:{S}\:=\:{t}^{\mathrm{3}} \:+\:{t}^{\mathrm{2}} \:+\:\mathrm{4} \\ $$$${find}\:{the}\:{velocity}\:{and}\:{acceleration} \\ $$ Answered by…
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Question Number 103503 by 175mohamed last updated on 15/Jul/20 $$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{Solve}\:: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}^{{x}} \:=\:\mathrm{4}{x} \\ $$ Answered by Dwaipayan Shikari last updated on 15/Jul/20…
Question Number 37948 by Fawomath last updated on 19/Jun/18 $${If}\:{x}\:\in\mathbb{R} \\ $$$${show}\:{that}\:\left(\mathrm{2}+{i}\right){e}^{\left(\mathrm{1}+\mathrm{3}{i}\right)} +\left(\mathrm{2}−{i}\right){e}^{\left(\mathrm{1}−\mathrm{3}{i}\right)} \:{is}\:{also}\:{real}. \\ $$ Commented by prof Abdo imad last updated on 19/Jun/18…
Question Number 37940 by Rio Mike last updated on 19/Jun/18 $${Which}\:{of}\:{the}\:{following}\: \\ $$$${expressions}\:{are}\:{positive}\:{for} \\ $$$${all}\:{real}\:{values}\:{of}\:\:{x}? \\ $$$$\left.{a}\left.\right)\:{x}^{\mathrm{2}} −\:\mathrm{2}{x}\:+\:\mathrm{5}\:\:\:{b}\right)\:{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}\: \\ $$$$\left.{c}\left.\right)\:{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\:\:\:\:\:\:{d}\right)\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{6}{x}\:+\:\mathrm{5} \\ $$…
Question Number 37915 by gunawan last updated on 19/Jun/18 $$\mathrm{If}\:{y}=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}\:,\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{85}}{\mathrm{169}}+\underset{{i}=\mathrm{1}} {\overset{\mathrm{84}} {\Sigma}}\:\frac{\mathrm{1}}{{y}\left({i}\right)}\: \\ $$ Answered by ajfour last updated on 19/Jun/18 $${S}−\frac{\mathrm{85}}{\mathrm{169}}=\underset{{r}=\mathrm{1}}…