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Question Number 95966    Answers: 1   Comments: 0

find all pairs of integer for xy+3x−4y = 29

$$\mathrm{find}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{for}\: \\ $$$$\mathrm{xy}+\mathrm{3x}−\mathrm{4y}\:=\:\mathrm{29}\: \\ $$

Question Number 95967    Answers: 1   Comments: 1

Question Number 95933    Answers: 2   Comments: 2

y′′′+2y′−3y= e^x (x+3)

$$\mathrm{y}'''+\mathrm{2y}'−\mathrm{3y}=\:\mathrm{e}^{\mathrm{x}} \:\left(\mathrm{x}+\mathrm{3}\right)\: \\ $$

Question Number 95924    Answers: 1   Comments: 1

form a Lagrangian to maximize x^2 −y^2 subject to the constraint 2x+y = 3?

$$\mathrm{form}\:\mathrm{a}\:\mathrm{Lagrangian}\:\mathrm{to}\:\mathrm{maximize} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \:\mathrm{subject}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{constraint}\:\mathrm{2x}+\mathrm{y}\:=\:\mathrm{3}? \\ $$

Question Number 95920    Answers: 3   Comments: 0

((54+(√x)))^(1/(3 )) + ((54−(√x)))^(1/(3 )) = ((18))^(1/(3 )) x = ?

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}+\sqrt{\mathrm{x}}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}−\sqrt{\mathrm{x}}}\:=\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{18}}\: \\ $$$$\mathrm{x}\:=\:?\: \\ $$

Question Number 95919    Answers: 1   Comments: 0

∫3^(−4x^2 ) dx=? (0,∞)

$$ \\ $$$$\int\mathrm{3}^{−\mathrm{4x}^{\mathrm{2}} } \mathrm{dx}=?\:\:\:\:\left(\mathrm{0},\infty\right) \\ $$

Question Number 95941    Answers: 0   Comments: 0

prove that (1/(sinx)) =Σ_(n=−∞) ^(+∞) (((−1)^n )/(x+nπ))

$$\mathrm{prove}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{sinx}}\:=\sum_{\mathrm{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{x}+\mathrm{n}\pi} \\ $$

Question Number 95912    Answers: 0   Comments: 2

(((2n)),(n) ) = 20 find n?

$$\begin{pmatrix}{\mathrm{2n}}\\{\mathrm{n}}\end{pmatrix}\:=\:\mathrm{20}\: \\ $$$$\mathrm{find}\:\mathrm{n}? \\ $$

Question Number 95903    Answers: 2   Comments: 3

Question Number 95901    Answers: 1   Comments: 0

(1/(998!)) + (1/(999!)) = (x^3 /(100!))

$$\frac{\mathrm{1}}{\mathrm{998}!}\:+\:\frac{\mathrm{1}}{\mathrm{999}!}\:=\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{100}!}\: \\ $$

Question Number 95898    Answers: 0   Comments: 0

x^2 +xy+(y^3 /3)=25 (y^2 /3)+z^2 =9 z^2 +zx+x^2 =16 so xy+2yz+3zx=?

$${x}^{\mathrm{2}} +{xy}+\frac{{y}^{\mathrm{3}} }{\mathrm{3}}=\mathrm{25} \\ $$$$\frac{{y}^{\mathrm{2}} }{\mathrm{3}}+{z}^{\mathrm{2}} =\mathrm{9} \\ $$$${z}^{\mathrm{2}} +{zx}+{x}^{\mathrm{2}} =\mathrm{16} \\ $$$${so}\:{xy}+\mathrm{2}{yz}+\mathrm{3}{zx}=? \\ $$

Question Number 95897    Answers: 2   Comments: 0

If x∈C . find solution of 3+i(√2) = e^(ix)

$$\mathrm{If}\:{x}\in\mathbb{C}\:.\:\mathrm{find}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\mathrm{3}+{i}\sqrt{\mathrm{2}}\:=\:{e}^{{ix}} \: \\ $$

Question Number 95888    Answers: 1   Comments: 0

(1−2x)^5 (2+x)^6 = a+bx+cx^2 +dx^3 +... find : a,b,c and d

$$\left(\mathrm{1}−\mathrm{2x}\right)^{\mathrm{5}} \left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{6}} =\:\mathrm{a}+\mathrm{bx}+\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}^{\mathrm{3}} +... \\ $$$$\mathrm{find}\::\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\: \\ $$

Question Number 96026    Answers: 0   Comments: 1

sin (p/x)=1

$$\mathrm{sin}\:\frac{\mathrm{p}}{\mathrm{x}}=\mathrm{1} \\ $$

Question Number 95860    Answers: 1   Comments: 0

A^− ∙(B+B^− )∙(C+C^− )∙(D+D^− )

$$\overset{−} {{A}}\centerdot\left({B}+\overset{−} {{B}}\right)\centerdot\left({C}+\overset{−} {{C}}\right)\centerdot\left({D}+\overset{−} {{D}}\right) \\ $$

Question Number 95849    Answers: 2   Comments: 0

lim_(n→∞) (1/(n+1)) + (1/(n+2)) + (1/(n+3)) + ... + (1/(n+n))??

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{n}}?? \\ $$

Question Number 95848    Answers: 4   Comments: 0

∫_0 ^(π/2) (dx/(√(1+sin x))) ?

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{dx}}{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\:?\: \\ $$

Question Number 95845    Answers: 1   Comments: 0

calculate ∫_0 ^1 (−1)^([(2/x)]) dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(−\mathrm{1}\right)^{\left[\frac{\mathrm{2}}{\mathrm{x}}\right]} \:\mathrm{dx} \\ $$

Question Number 95844    Answers: 2   Comments: 0

cacuate ∫_(−(π/4)) ^(π/4) ln(1+a cos^2 t)dt with ∣a∣<1

$$\mathrm{cacuate}\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{1}+\mathrm{a}\:\mathrm{cos}^{\mathrm{2}} \mathrm{t}\right)\mathrm{dt}\:\mathrm{with}\:\mid\mathrm{a}\mid<\mathrm{1} \\ $$

Question Number 95843    Answers: 1   Comments: 0

((((√(3x−7)))^2 −2)/(x−3)) ≤ ((3−((√x))^2 )/(x−3)) find the solution

$$\frac{\left(\sqrt{\mathrm{3x}−\mathrm{7}}\right)^{\mathrm{2}} −\mathrm{2}}{\mathrm{x}−\mathrm{3}}\:\leqslant\:\frac{\mathrm{3}−\left(\sqrt{\mathrm{x}}\right)^{\mathrm{2}} }{\mathrm{x}−\mathrm{3}}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$

Question Number 95839    Answers: 1   Comments: 1

solve y^((3)) −2y^((2)) +3y −2y =sinx

$$\mathrm{solve}\:\mathrm{y}^{\left(\mathrm{3}\right)} −\mathrm{2y}^{\left(\mathrm{2}\right)} \:+\mathrm{3y}\:\:−\mathrm{2y}\:=\mathrm{sinx} \\ $$

Question Number 95838    Answers: 1   Comments: 0

determine L(f^((3)) (x) with L is laplace transform

$$\mathrm{determine}\:\mathrm{L}\left(\mathrm{f}^{\left(\mathrm{3}\right)} \left(\mathrm{x}\right)\:\:\mathrm{with}\:\mathrm{L}\:\mathrm{is}\:\mathrm{laplace}\:\mathrm{transform}\right. \\ $$

Question Number 95837    Answers: 2   Comments: 0

let p(x)=(1+ix+x^2 )^n −(1−ix +x^2 )^n 1) determine roots of p(x) 2) find p(x) at form Σ a_i x^i 3)ddtermne p(x) at form arctan 4) factorize p(x) inside C[x] 5) calculate ∫_0 ^1 p(x)dxand ∫_1 ^∞ (dx/(p(x)))

$$\mathrm{let}\:\mathrm{p}\left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} −\left(\mathrm{1}−\mathrm{ix}\:+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{determine}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{p}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{at}\:\mathrm{form}\:\Sigma\:\mathrm{a}_{\mathrm{i}} \:\mathrm{x}^{\mathrm{i}} \\ $$$$\left.\mathrm{3}\right)\mathrm{ddtermne}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{at}\:\mathrm{form}\:\mathrm{arctan} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$$$\left.\mathrm{5}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{p}\left(\mathrm{x}\right)\mathrm{dxand}\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\mathrm{p}\left(\mathrm{x}\right)} \\ $$

Question Number 95832    Answers: 2   Comments: 0

find without using l′hopital lim_(x→2) ((e^(2−x) −1)/(x^2 −4))

$${find}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{{e}^{\mathrm{2}−{x}} −\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$

Question Number 95830    Answers: 2   Comments: 0

Question Number 95868    Answers: 1   Comments: 1

5^(10) (mod 11)=?

$$\mathrm{5}^{\mathrm{10}} \left({mod}\:\mathrm{11}\right)=? \\ $$

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