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AlgebraQuestion and Answers: Page 1

Question Number 226912 Answers: 1 Comments: 0

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if x+y=2 with x, y >0, find the minimum of x+(√(x^2 +3y^2 )).

$${if}\:{x}+{y}=\mathrm{2}\:{with}\:{x},\:{y}\:>\mathrm{0},\:{find}\:{the} \\ $$$${minimum}\:{of}\:{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} }. \\ $$

Question Number 226812 Answers: 2 Comments: 1

if 28x+30y+31z=360 with x, y, z being positive integers, find x+y+z=?

$${if}\:\mathrm{28}{x}+\mathrm{30}{y}+\mathrm{31}{z}=\mathrm{360}\:{with}\:{x},\:{y},\:{z} \\ $$$${being}\:{positive}\:{integers},\:{find} \\ $$$${x}+{y}+{z}=? \\ $$

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Prove:(1/(2ne))<(1/e)−(1−(1/n))^n <(1/(ne))

$$ \\ $$$${Prove}:\frac{\mathrm{1}}{\mathrm{2}{ne}}<\frac{\mathrm{1}}{{e}}−\left(\mathrm{1}−\frac{\mathrm{1}}{{n}}\right)^{{n}} <\frac{\mathrm{1}}{{ne}} \\ $$

Question Number 226728 Answers: 2 Comments: 0

Find: ∫_0 ^( (𝛑/4)) (dx/(1 + sin^2 x)) = ?

$$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:=\:? \\ $$

Question Number 226713 Answers: 0 Comments: 0

If p=(1/x)−(1/x^2 ) what should p=(((N)_4 )/((D)_4 )) (N)_4 means numerator of p in quaternary for x to be 777?

$$\:\:{If}\: \\ $$$${p}=\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$${what}\:{should}\:{p}=\frac{\left({N}\right)_{\mathrm{4}} }{\left({D}\right)_{\mathrm{4}} } \\ $$$$\left({N}\right)_{\mathrm{4}} \:{means}\:{numerator}\:{of}\:{p}\:\:{in} \\ $$$${quaternary}\:{for}\:{x}\:{to}\:{be}\:\mathrm{777}? \\ $$

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Question Number 226603 Answers: 3 Comments: 0

Formulate the differential equation of the solution (a)y=Ae^(bx+1) (b)y=Asin x+Bcos x

$${Formulate}\:{the}\:{differential} \\ $$$${equation}\:{of}\:{the}\:{solution} \\ $$$$\left({a}\right){y}={Ae}^{{bx}+\mathrm{1}} \\ $$$$\left({b}\right){y}={A}\mathrm{sin}\:{x}+{B}\mathrm{cos}\:{x} \\ $$$$ \\ $$

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a^4 + b^4 + c^4 = 2d^2 Prove that the equation has an infinite number of natural solutions

$$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:=\:\mathrm{2d}^{\mathrm{2}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{solutions} \\ $$

Question Number 226536 Answers: 2 Comments: 0

If (x+(2a^2 +5))(x−(2a^2 +7)) ≤ 0 x∈[−(a^2 +8a−10) ; (a^2 +9a−11)] Find: a = ?

$$\mathrm{If}\:\:\:\left(\mathrm{x}+\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{5}\right)\right)\left(\mathrm{x}−\left(\mathrm{2a}^{\mathrm{2}} +\mathrm{7}\right)\right)\:\leqslant\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\mathrm{x}\in\left[−\left(\mathrm{a}^{\mathrm{2}} +\mathrm{8a}−\mathrm{10}\right)\:;\:\left(\mathrm{a}^{\mathrm{2}} +\mathrm{9a}−\mathrm{11}\right)\right] \\ $$$$\mathrm{Find}:\:\boldsymbol{\mathrm{a}}\:=\:? \\ $$

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Question Number 226509 Answers: 1 Comments: 0

Find: Σ_(n=1) ^∞ (1/(n∙(2n + 1)^2 )) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}\centerdot\left(\mathrm{2n}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 226471 Answers: 2 Comments: 2

If, x^2 +2y^2 ∞xy then prove that, 2x^2 +y^2 ∞xy

$$\:{If},\:{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} \infty{xy}\: \\ $$$$\:\:{then}\:{prove}\:{that},\:\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \infty{xy} \\ $$

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