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AlgebraQuestion and Answers: Page 85

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

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

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

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

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

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

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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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In △ABC holds: (√2) a cos (B/2) cos (C/2) = s ⇒ sec (2B) + tan (2B) = ((c + b)/(c − b))

$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\sqrt{\mathrm{2}}\:\mathrm{a}\:\mathrm{cos}\:\frac{\mathrm{B}}{\mathrm{2}}\:\mathrm{cos}\:\frac{\mathrm{C}}{\mathrm{2}}\:=\:\mathrm{s} \\ $$$$\Rightarrow\:\mathrm{sec}\:\left(\mathrm{2B}\right)\:+\:\mathrm{tan}\:\left(\mathrm{2B}\right)\:=\:\frac{\mathrm{c}\:+\:\mathrm{b}}{\mathrm{c}\:−\:\mathrm{b}} \\ $$

Question Number 189135 Answers: 2 Comments: 0

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It is known that x is rational x (√(28 + 3(√(28 + 3(√(28 + 3(√?))))))) Find the dufference of possible vaules of x

$$\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\:\mathrm{x}\:\:\mathrm{is}\:\mathrm{rational} \\ $$$$\mathrm{x}\:\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{\mathrm{28}\:+\:\mathrm{3}\sqrt{?}}}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{dufference}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{vaules} \\ $$$$\mathrm{of}\:\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 189133 Answers: 1 Comments: 0

Convert hexadecimal number 4 A F_(16) to decimal

$$\mathrm{Convert}\:\mathrm{hexadecimal}\:\mathrm{number} \\ $$$$\mathrm{4}\:\mathrm{A}\:\mathrm{F}_{\mathrm{16}} \:\:\mathrm{to}\:\mathrm{decimal} \\ $$

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Find the value of a+b+c+d+e in the system of equations: { ((13a+2b+c+6d+2e=96)),((5a+9b+2c+7d+3e=75)),((7a+8b+17c+11d+7e=99)),((3a+3b+3c+d+8e=55)),((a+7b+6c+4d+9e=79)) :}

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\begin{cases}{\mathrm{13a}+\mathrm{2b}+\mathrm{c}+\mathrm{6d}+\mathrm{2e}=\mathrm{96}}\\{\mathrm{5a}+\mathrm{9b}+\mathrm{2c}+\mathrm{7d}+\mathrm{3e}=\mathrm{75}}\\{\mathrm{7a}+\mathrm{8b}+\mathrm{17c}+\mathrm{11d}+\mathrm{7e}=\mathrm{99}}\\{\mathrm{3a}+\mathrm{3b}+\mathrm{3c}+\mathrm{d}+\mathrm{8e}=\mathrm{55}}\\{\mathrm{a}+\mathrm{7b}+\mathrm{6c}+\mathrm{4d}+\mathrm{9e}=\mathrm{79}}\end{cases} \\ $$

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