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AllQuestion and Answers: Page 209

Question Number 190732    Answers: 3   Comments: 0

Question Number 190731    Answers: 2   Comments: 0

(4a^2 −19a−5)x^2 +a^2 x+a+3=0 x_1 ,x_2 are roots when , x_1 <0 ,x_2 >0 , ∣x_1 ∣−x_2 >0 interval of max(a)=? solution??

$$\left(\mathrm{4a}^{\mathrm{2}} −\mathrm{19a}−\mathrm{5}\right)\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \mathrm{x}+\mathrm{a}+\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} \mathrm{are}\:\mathrm{roots} \\ $$$$\mathrm{when}\:,\:\mathrm{x}_{\mathrm{1}} <\mathrm{0}\:\:\:,\mathrm{x}_{\mathrm{2}} >\mathrm{0}\:\:,\:\mid\mathrm{x}_{\mathrm{1}} \mid−\mathrm{x}_{\mathrm{2}} >\mathrm{0} \\ $$$$\mathrm{interval}\:\mathrm{of}\:\:\:\mathrm{max}\left(\mathrm{a}\right)=? \\ $$$$\mathrm{solution}?? \\ $$

Question Number 190730    Answers: 3   Comments: 0

∣x^2 −8x+18∣+∣y−3∣=5 all value of y=?? how money value of y is possible??

$$\mid\mathrm{x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{18}\mid+\mid\mathrm{y}−\mathrm{3}\mid=\mathrm{5} \\ $$$$\mathrm{all}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}=?? \\ $$$$\mathrm{how}\:\mathrm{money}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:\mathrm{is}\:\mathrm{possible}?? \\ $$

Question Number 190738    Answers: 0   Comments: 0

∫_0 ^( (π/2)) (((sin((x/2^n )))/(sinx))) dx , n ∈ N

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\left(\frac{{sin}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)}{{sinx}}\right)\:{dx}\:,\:{n}\:\in\:\mathbb{N} \\ $$

Question Number 190719    Answers: 0   Comments: 0

Find the real part of Re(((𝚪(a+1))/((1−a)^(a+1) )))=?

$$\boldsymbol{\mathrm{F}{ind}}\:\boldsymbol{{the}}\:\boldsymbol{{real}}\:\boldsymbol{{part}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{\mathrm{R}{e}}\left(\frac{\boldsymbol{\Gamma}\left({a}+\mathrm{1}\right)}{\left(\mathrm{1}−{a}\right)^{{a}+\mathrm{1}} }\right)=? \\ $$

Question Number 190717    Answers: 2   Comments: 0

if x^2 +(m−2)x+2m=0 and (x_1 −1)(x_2 −1)=1 then find the value of m=?

$${if}\:\:{x}^{\mathrm{2}} +\left({m}−\mathrm{2}\right){x}+\mathrm{2}{m}=\mathrm{0}\:\:{and} \\ $$$$\left({x}_{\mathrm{1}} −\mathrm{1}\right)\left({x}_{\mathrm{2}} −\mathrm{1}\right)=\mathrm{1}\:\:{then}\:{find}\:{the}\:{value} \\ $$$${of}\:\:\:{m}=? \\ $$

Question Number 190716    Answers: 0   Comments: 0

if x+2+((m+2)/(m−2))=1 and x_1 ∙x_2 =2 then find the value of m=?

$${if}\:{x}+\mathrm{2}+\frac{{m}+\mathrm{2}}{{m}−\mathrm{2}}=\mathrm{1}\:\:{and}\:\:\:{x}_{\mathrm{1}} \centerdot{x}_{\mathrm{2}} =\mathrm{2}\:\:{then} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{m}=? \\ $$

Question Number 190715    Answers: 1   Comments: 0

if (5m−1)x^2 −(5m+2)x+3m−2=0 and x_1 =x_2 then find m=?

$${if}\:\left(\mathrm{5}{m}−\mathrm{1}\right){x}^{\mathrm{2}} −\left(\mathrm{5}{m}+\mathrm{2}\right){x}+\mathrm{3}{m}−\mathrm{2}=\mathrm{0} \\ $$$${and}\:\:{x}_{\mathrm{1}} ={x}_{\mathrm{2}} \:\:{then}\:{find}\:\:{m}=? \\ $$

Question Number 190708    Answers: 1   Comments: 0

Question Number 190705    Answers: 1   Comments: 0

Question Number 190704    Answers: 1   Comments: 0

f(x+y)=f(x)+f(y)+x∙y f(4)=10 finde f(2022)=?

$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+{x}\centerdot{y} \\ $$$${f}\left(\mathrm{4}\right)=\mathrm{10}\:\:{finde}\:{f}\left(\mathrm{2022}\right)=? \\ $$

Question Number 190702    Answers: 0   Comments: 0

Calcule: I=∫_o ^(𝛑/3) x^2 (sinx)^2 dx

$$\boldsymbol{\mathrm{Calcule}}:\:\:\boldsymbol{\mathrm{I}}=\int_{\boldsymbol{\mathrm{o}}} ^{\frac{\boldsymbol{\pi}}{\mathrm{3}}} \boldsymbol{\mathrm{x}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{sinx}}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dx}} \\ $$

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

calculate 𝛗 = ∫_0 ^( ∞) (( sin^( 3) (x ) ln( x ))/x) dx = ? @ nice − mathematics

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{sin}^{\:\mathrm{3}} \left({x}\:\right)\:\mathrm{ln}\left(\:{x}\:\right)}{{x}}\:\mathrm{d}{x}\:=\:?\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:@\:\mathrm{nice}\:−\:\mathrm{mathematics}\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 190686    Answers: 2   Comments: 0

find the value of x e^(ln(2x+5)) =lne(8x+3)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x} \\ $$$${e}^{\mathrm{ln}\left(\mathrm{2}{x}+\mathrm{5}\right)} =\mathrm{ln}{e}\left(\mathrm{8}{x}+\mathrm{3}\right) \\ $$

Question Number 190679    Answers: 2   Comments: 0

lim_(x→∞) (e^x /x^(60!) )=? pleas solve this

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{e}^{{x}} }{{x}^{\mathrm{60}!} }=? \\ $$$${pleas}\:{solve}\:{this} \\ $$

Question Number 190678    Answers: 2   Comments: 0

Question Number 190677    Answers: 0   Comments: 0

If x ∈ R a_1 ,a_2 ,a_3 , b_1 ,b_2 ,b_3 > 0 Then prove that: a_1 ^(sin^2 x) b_1 ^(cos^2 x) + a_2 ^(sin^2 x) b_2 ^(cos^2 x) + a_3 ^(sin^2 x) b_3 ^(cos^2 x) ≤ ≤ (a_1 + a_2 + a_3 )^(sin^2 x) (b_1 + b_2 + b_3 )^(cos^2 x)

$$\mathrm{If}\:\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} \:,\:\mathrm{b}_{\mathrm{1}} ,\mathrm{b}_{\mathrm{2}} ,\mathrm{b}_{\mathrm{3}} \:>\:\mathrm{0} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{a}_{\mathrm{1}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{1}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:+\:\mathrm{a}_{\mathrm{2}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{2}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:+\:\mathrm{a}_{\mathrm{3}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{3}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\leqslant \\ $$$$\leqslant\:\left(\mathrm{a}_{\mathrm{1}} +\:\mathrm{a}_{\mathrm{2}} +\:\mathrm{a}_{\mathrm{3}} \right)^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\left(\mathrm{b}_{\mathrm{1}} +\:\mathrm{b}_{\mathrm{2}} +\:\mathrm{b}_{\mathrm{3}} \right)^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \\ $$

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^(−1) (2x(√(1−x^2 ))) where x∈[−(1/( (√2))), (1/( (√2)))], then find (dy/dx).

$${if}\:{y}\:=\:{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{where}\:{x}\in\left[−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right],\:{then}\:{find}\:\frac{{dy}}{{dx}}. \\ $$

Question Number 190659    Answers: 0   Comments: 0

Prove that: ((cos (π/9)))^(1/3) − ((cos ((2π)/9)))^(1/3) − ((cos ((4π)/9)))^(1/3) = ((3 − (3/2) (9)^(1/3) ))^(1/3)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{\mathrm{3}\:−\:\frac{\mathrm{3}}{\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{9}}}\: \\ $$

Question Number 190652    Answers: 0   Comments: 0

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