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Question Number 190732 Answers: 3 Comments: 0
Question Number 190731 Answers: 2 Comments: 0
$$\left(\mathrm{4a}^{\mathrm{2}} −\mathrm{19a}−\mathrm{5}\right)\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \mathrm{x}+\mathrm{a}+\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} \mathrm{are}\:\mathrm{roots} \\ $$$$\mathrm{when}\:,\:\mathrm{x}_{\mathrm{1}} <\mathrm{0}\:\:\:,\mathrm{x}_{\mathrm{2}} >\mathrm{0}\:\:,\:\mid\mathrm{x}_{\mathrm{1}} \mid−\mathrm{x}_{\mathrm{2}} >\mathrm{0} \\ $$$$\mathrm{interval}\:\mathrm{of}\:\:\:\mathrm{max}\left(\mathrm{a}\right)=? \\ $$$$\mathrm{solution}?? \\ $$
Question Number 190730 Answers: 3 Comments: 0
$$\mid\mathrm{x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{18}\mid+\mid\mathrm{y}−\mathrm{3}\mid=\mathrm{5} \\ $$$$\mathrm{all}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}=?? \\ $$$$\mathrm{how}\:\mathrm{money}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:\mathrm{is}\:\mathrm{possible}?? \\ $$
Question Number 190738 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\left(\frac{{sin}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)}{{sinx}}\right)\:{dx}\:,\:{n}\:\in\:\mathbb{N} \\ $$
Question Number 190719 Answers: 0 Comments: 0
$$\boldsymbol{\mathrm{F}{ind}}\:\boldsymbol{{the}}\:\boldsymbol{{real}}\:\boldsymbol{{part}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{\mathrm{R}{e}}\left(\frac{\boldsymbol{\Gamma}\left({a}+\mathrm{1}\right)}{\left(\mathrm{1}−{a}\right)^{{a}+\mathrm{1}} }\right)=? \\ $$
Question Number 190717 Answers: 2 Comments: 0
$${if}\:\:{x}^{\mathrm{2}} +\left({m}−\mathrm{2}\right){x}+\mathrm{2}{m}=\mathrm{0}\:\:{and} \\ $$$$\left({x}_{\mathrm{1}} −\mathrm{1}\right)\left({x}_{\mathrm{2}} −\mathrm{1}\right)=\mathrm{1}\:\:{then}\:{find}\:{the}\:{value} \\ $$$${of}\:\:\:{m}=? \\ $$
Question Number 190716 Answers: 0 Comments: 0
$${if}\:{x}+\mathrm{2}+\frac{{m}+\mathrm{2}}{{m}−\mathrm{2}}=\mathrm{1}\:\:{and}\:\:\:{x}_{\mathrm{1}} \centerdot{x}_{\mathrm{2}} =\mathrm{2}\:\:{then} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{m}=? \\ $$
Question Number 190715 Answers: 1 Comments: 0
$${if}\:\left(\mathrm{5}{m}−\mathrm{1}\right){x}^{\mathrm{2}} −\left(\mathrm{5}{m}+\mathrm{2}\right){x}+\mathrm{3}{m}−\mathrm{2}=\mathrm{0} \\ $$$${and}\:\:{x}_{\mathrm{1}} ={x}_{\mathrm{2}} \:\:{then}\:{find}\:\:{m}=? \\ $$
Question Number 190708 Answers: 1 Comments: 0
Question Number 190705 Answers: 1 Comments: 0
Question Number 190704 Answers: 1 Comments: 0
$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+{x}\centerdot{y} \\ $$$${f}\left(\mathrm{4}\right)=\mathrm{10}\:\:{finde}\:{f}\left(\mathrm{2022}\right)=? \\ $$
Question Number 190702 Answers: 0 Comments: 0
$$\boldsymbol{\mathrm{Calcule}}:\:\:\boldsymbol{\mathrm{I}}=\int_{\boldsymbol{\mathrm{o}}} ^{\frac{\boldsymbol{\pi}}{\mathrm{3}}} \boldsymbol{\mathrm{x}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{sinx}}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dx}} \\ $$
Question Number 190700 Answers: 1 Comments: 0
Question Number 190699 Answers: 0 Comments: 0
Question Number 190694 Answers: 1 Comments: 1
Question Number 190692 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{sin}^{\:\mathrm{3}} \left({x}\:\right)\:\mathrm{ln}\left(\:{x}\:\right)}{{x}}\:\mathrm{d}{x}\:=\:?\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:@\:\mathrm{nice}\:−\:\mathrm{mathematics}\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$
Question Number 190686 Answers: 2 Comments: 0
$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x} \\ $$$${e}^{\mathrm{ln}\left(\mathrm{2}{x}+\mathrm{5}\right)} =\mathrm{ln}{e}\left(\mathrm{8}{x}+\mathrm{3}\right) \\ $$
Question Number 190679 Answers: 2 Comments: 0
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{e}^{{x}} }{{x}^{\mathrm{60}!} }=? \\ $$$${pleas}\:{solve}\:{this} \\ $$
Question Number 190678 Answers: 2 Comments: 0
Question Number 190677 Answers: 0 Comments: 0
$$\mathrm{If}\:\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} \:,\:\mathrm{b}_{\mathrm{1}} ,\mathrm{b}_{\mathrm{2}} ,\mathrm{b}_{\mathrm{3}} \:>\:\mathrm{0} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{a}_{\mathrm{1}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{1}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:+\:\mathrm{a}_{\mathrm{2}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{2}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:+\:\mathrm{a}_{\mathrm{3}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{3}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\leqslant \\ $$$$\leqslant\:\left(\mathrm{a}_{\mathrm{1}} +\:\mathrm{a}_{\mathrm{2}} +\:\mathrm{a}_{\mathrm{3}} \right)^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\left(\mathrm{b}_{\mathrm{1}} +\:\mathrm{b}_{\mathrm{2}} +\:\mathrm{b}_{\mathrm{3}} \right)^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \\ $$
Question Number 190672 Answers: 2 Comments: 0
Question Number 190667 Answers: 2 Comments: 0
Question Number 190665 Answers: 0 Comments: 0
Question Number 190660 Answers: 2 Comments: 0
$${if}\:{y}\:=\:{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{where}\:{x}\in\left[−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right],\:{then}\:{find}\:\frac{{dy}}{{dx}}. \\ $$
Question Number 190659 Answers: 0 Comments: 0
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{\mathrm{3}\:−\:\frac{\mathrm{3}}{\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{9}}}\: \\ $$
Question Number 190652 Answers: 0 Comments: 0
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