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AlgebraQuestion and Answers: Page 62

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

Question Number 189461    Answers: 0   Comments: 0

Question Number 189446    Answers: 1   Comments: 0

x^2 =(2)^(1/5) +y y^2 =(2)^(1/5) +x x∙y=? x≠y

$${x}^{\mathrm{2}} =\sqrt[{\mathrm{5}}]{\mathrm{2}}+{y} \\ $$$${y}^{\mathrm{2}} =\sqrt[{\mathrm{5}}]{\mathrm{2}}+{x} \\ $$$${x}\centerdot{y}=?\:\:\:\:\:\:\:\:\:\:\:{x}\neq{y} \\ $$

Question Number 189417    Answers: 1   Comments: 0

Question Number 189407    Answers: 0   Comments: 1

determiner l heure de depart par un auto qui part pour rejiindre la gare B juste a l′ arrivee du train partant a 7h,de la ville A vers la ville B a vitesse de 180km/h.?

$${determiner}\:{l}\:{heure}\:{de}\: \\ $$$${depart}\:{par}\:\:{un}\:{auto}\:{qui}\: \\ $$$${part}\:{pour}\:{rejiindre}\:{la} \\ $$$${gare}\:\:{B}\:{juste}\:{a}\:{l}'\:{arrivee} \\ $$$${du}\:{train}\:\:{partant}\:{a}\:\mathrm{7}{h},{de}\:{la}\:{ville}\:{A} \\ $$$${vers}\:{la}\:{ville}\:{B}\:{a}\:{vitesse}\:{de}\: \\ $$$$\mathrm{180}{km}/{h}.? \\ $$$$ \\ $$

Question Number 189302    Answers: 1   Comments: 2

Q: find the number of the solutions for : ( x_( 1) + x_( 2) )^( 3) + x_( 3) + x_( 4) + x_( 5) =11 Hint: ( x_( i) ∈ Z^( +) ∪ { 0 } )

$$ \\ $$$$\:\:\:\:{Q}:\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{the}\:\:\mathrm{solutions}\:\:\mathrm{for}\:: \\ $$$$ \\ $$$$\:\:\left(\:{x}_{\:\mathrm{1}} \:+\:{x}_{\:\mathrm{2}} \:\right)^{\:\mathrm{3}} \:+\:{x}_{\:\mathrm{3}} \:+\:{x}_{\:\mathrm{4}} \:+\:{x}_{\:\mathrm{5}} \:=\mathrm{11} \\ $$$$\:\:\: \\ $$$$\:\:\:\:{Hint}:\:\:\:\left(\:{x}_{\:{i}} \:\:\in\:\:\mathbb{Z}^{\:\:+} \:\:\cup\:\left\{\:\mathrm{0}\:\right\}\:\:\right) \\ $$$$\: \\ $$

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