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AlgebraQuestion and Answers: Page 79

Question Number 189937    Answers: 0   Comments: 0

Question Number 189919    Answers: 1   Comments: 0

If x,y are real numbers satisfy ((x+40)/y)+((569)/(xy))=((26−y)/x) , then xy=?

$$\:{If}\:{x},{y}\:{are}\:{real}\:{numbers}\:{satisfy} \\ $$$$\:\frac{{x}+\mathrm{40}}{{y}}+\frac{\mathrm{569}}{{xy}}=\frac{\mathrm{26}−{y}}{{x}}\:,\:{then}\:{xy}=? \\ $$

Question Number 189916    Answers: 2   Comments: 0

when sinx×cosx=−(1/4) find sinx+cosx=?

$$\mathrm{when}\:\:\:\:\mathrm{sinx}×\mathrm{cosx}=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\:\:\:\:\:\:\mathrm{sinx}+\mathrm{cosx}=? \\ $$

Question Number 189886    Answers: 0   Comments: 0

e^( x) > 1+ x (∀ x >0 ) set: x=(√(π/e)) −1 e^( ((√π)/( (√e))) −1) > ((√π)/( (√e))) ⇒ e^( ((√π)/( (√e)))) > (√π) ( e^( ((√π)/( (√e)))) )^( (√e)) > (√π)^( (√e)) ⇒ e^( (√π)) > (√(π ))^( (√e))

$$ \\ $$$$\:\:{e}^{\:{x}} \:>\:\mathrm{1}+\:{x}\:\:\:\:\left(\forall\:{x}\:>\mathrm{0}\:\right) \\ $$$$\:\:\:{set}:\:{x}=\sqrt{\frac{\pi}{{e}}}\:−\mathrm{1} \\ $$$$\:\:\:\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:−\mathrm{1}} >\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:\Rightarrow\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \:>\:\sqrt{\pi}\: \\ $$$$\:\:\:\:\:\:\left(\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \right)^{\:\sqrt{{e}}} >\:\sqrt{\pi}\:^{\:\sqrt{{e}}} \:\Rightarrow\:{e}^{\:\sqrt{\pi}} \:>\:\sqrt{\pi\:}\:^{\:\sqrt{{e}}} \\ $$$$ \\ $$

Question Number 189859    Answers: 0   Comments: 0

Question Number 189858    Answers: 1   Comments: 0

Question Number 189838    Answers: 0   Comments: 0

Question Number 189826    Answers: 0   Comments: 0

Question Number 189823    Answers: 0   Comments: 0

If: x_0 = 1 x_(n+1) = (√(x_n ^2 + x_n )) Find: Ω =lim_(n→∞) (x_n - (n/2) + (1/8) Σ_(k=1) ^(n−1) (1/x_k ))

$$\mathrm{If}:\:\:\:\mathrm{x}_{\mathrm{0}} \:=\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}_{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:=\:\sqrt{\mathrm{x}_{\boldsymbol{\mathrm{n}}} ^{\mathrm{2}} \:+\:\mathrm{x}_{\boldsymbol{\mathrm{n}}} } \\ $$$$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{x}_{\boldsymbol{\mathrm{n}}} -\:\frac{\mathrm{n}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}−\mathrm{1}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{x}_{\boldsymbol{\mathrm{k}}} }\right) \\ $$

Question Number 189803    Answers: 3   Comments: 0

what′s the minimum value of a+(1/(b(a−b))) where a>b>0 a,b∈R

$$ \\ $$$${what}'{s}\:{the}\:{minimum}\:{value}\:{of} \\ $$$${a}+\frac{\mathrm{1}}{{b}\left({a}−{b}\right)}\:{where}\:{a}>{b}>\mathrm{0}\:{a},{b}\in\mathbb{R} \\ $$$$ \\ $$

Question Number 189763    Answers: 0   Comments: 0

Question Number 189757    Answers: 2   Comments: 0

Find: lim_(x→(𝛑/2)) (((√2) ∣ sin 4x ∣)/( (√(1 − cos 4x)))) = ? Find: lim_(x→𝛑) (((√2) ∣ sin 6x ∣)/( (√(1 − cos 6x)))) = ?

$$\mathrm{Find}:\:\:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}\:\mid\:\mathrm{sin}\:\mathrm{4x}\:\mid}{\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{4x}}}\:\:\:=\:\:\:? \\ $$$$\mathrm{Find}:\:\:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\boldsymbol{\pi}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}\:\mid\:\mathrm{sin}\:\mathrm{6x}\:\mid}{\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{6x}}}\:\:\:=\:\:\:? \\ $$

Question Number 189748    Answers: 2   Comments: 2

x−(√x)+1=0 x=??

$$ \\ $$$$\:\:\:\:\:\boldsymbol{{x}}−\sqrt{\boldsymbol{{x}}}+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\boldsymbol{{x}}=?? \\ $$

Question Number 189610    Answers: 1   Comments: 0

solve for x if log x=(x^2 /(25))

$${solve}\:{for}\:{x}\:{if}\:\:\: \\ $$$$\mathrm{log}\:{x}=\frac{{x}^{\mathrm{2}} }{\mathrm{25}} \\ $$

Question Number 189593    Answers: 0   Comments: 0

Question Number 189592    Answers: 0   Comments: 0

Question Number 189598    Answers: 0   Comments: 0

Question Number 189576    Answers: 1   Comments: 0

2^x + 2^x −4 + x = −(1/2) x = ???

$$ \\ $$$$\:\:\:\:\:\mathrm{2}^{\boldsymbol{{x}}} \:+\:\mathrm{2}^{\boldsymbol{{x}}} −\mathrm{4}\:+\:\boldsymbol{{x}}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\boldsymbol{{x}}\:=\:??? \\ $$$$ \\ $$

Question Number 189564    Answers: 1   Comments: 0

Question Number 189555    Answers: 0   Comments: 0

Question Number 189554    Answers: 0   Comments: 0

Question Number 189533    Answers: 1   Comments: 0

when a+b=60^° find ((cos^2 a−sin^2 b)/(cos(a−b)))=?

$${when}\:\:{a}+{b}=\mathrm{60}^{°} \:\:\:\:\:{find}\:\:\frac{{cos}^{\mathrm{2}} {a}−{sin}^{\mathrm{2}} {b}}{{cos}\left({a}−{b}\right)}=? \\ $$

Question Number 189531    Answers: 1   Comments: 0

The number of pairs of natural numbers (x,y) satisfy x^2 y+gcd(x,y^2 )=2023

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{natural} \\ $$$$\mathrm{numbers}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{satisfy} \\ $$$$\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{gcd}\left(\mathrm{x},\mathrm{y}^{\mathrm{2}} \right)=\mathrm{2023} \\ $$

Question Number 189514    Answers: 0   Comments: 0

Question Number 189507    Answers: 0   Comments: 0

Question Number 189473    Answers: 1   Comments: 0

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