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Question Number 149415 Answers: 1 Comments: 1

show that ∫_0 ^∞ (((sint−tcost)/t^3 ))^2 dt=(Π/(15))

$$\mathrm{show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{sint}−\mathrm{tcost}}{\mathrm{t}^{\mathrm{3}} }\right)^{\mathrm{2}} \mathrm{dt}=\frac{\Pi}{\mathrm{15}} \\ $$

Question Number 149410 Answers: 1 Comments: 0

((log_2 2^(20) + log_2 20 ∙ log_2 5 - 2 log_2 2^5 )/(log_2 20 + 2 log_2 5)) = ?

$$\frac{{log}_{\mathrm{2}} \:\mathrm{2}^{\mathrm{20}} \:+\:{log}_{\mathrm{2}} \:\mathrm{20}\:\centerdot\:{log}_{\mathrm{2}} \:\mathrm{5}\:-\:\mathrm{2}\:{log}_{\mathrm{2}} \:\mathrm{2}^{\mathrm{5}} }{{log}_{\mathrm{2}} \:\mathrm{20}\:+\:\mathrm{2}\:{log}_{\mathrm{2}} \:\mathrm{5}}\:=\:? \\ $$

Question Number 149408 Answers: 0 Comments: 2

cos((π/2) - (1/2) arccos (4/5)) = ?

$${cos}\left(\frac{\pi}{\mathrm{2}}\:-\:\frac{\mathrm{1}}{\mathrm{2}}\:{arccos}\:\frac{\mathrm{4}}{\mathrm{5}}\right)\:=\:? \\ $$

Question Number 149406 Answers: 0 Comments: 0

if x has a binomial distribution with n=10 and p=(1/3).Find E(e^(3x) )

$${if}\:{x}\:{has}\:{a}\:{binomial}\:{distribution}\:{with}\:{n}=\mathrm{10}\:{and}\:{p}=\frac{\mathrm{1}}{\mathrm{3}}.{Find}\:{E}\left({e}^{\mathrm{3}{x}} \right) \\ $$

Question Number 149405 Answers: 0 Comments: 2

if ∫f(x)dx = x^3 −3x^2 −c find f(−2) = ?

$${if}\:\:\:\int{f}\left({x}\right){dx}\:=\:{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −{c} \\ $$$${find}\:\:\:{f}\left(−\mathrm{2}\right)\:=\:? \\ $$

Question Number 149400 Answers: 3 Comments: 0

Question Number 149395 Answers: 1 Comments: 0

Question Number 149385 Answers: 4 Comments: 0

Question Number 149383 Answers: 1 Comments: 1

Question Number 149378 Answers: 3 Comments: 0

Question Number 149377 Answers: 1 Comments: 0

Question Number 149372 Answers: 1 Comments: 0

Question Number 149373 Answers: 1 Comments: 0

Question Number 149428 Answers: 2 Comments: 3

Question Number 149425 Answers: 1 Comments: 0

Question Number 149354 Answers: 1 Comments: 5

z>0 z^2 + 12(√z) = 5 z + 2(√z) = ?

$${z}>\mathrm{0} \\ $$$${z}^{\mathrm{2}} \:+\:\mathrm{12}\sqrt{{z}}\:=\:\mathrm{5} \\ $$$${z}\:+\:\mathrm{2}\sqrt{{z}}\:=\:? \\ $$

Question Number 149346 Answers: 2 Comments: 1

lim_(x→∞) (((3x+12)/(6x−20)))^(2x) =?

$${li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{\mathrm{3}{x}+\mathrm{12}}{\mathrm{6}{x}−\mathrm{20}}\right)^{\mathrm{2}{x}} =? \\ $$

Question Number 149342 Answers: 1 Comments: 1

is this true and is there a proof? ∀k∈N∣k>1 ((Σ_(n=1) ^(k^2 −1) (√(k+(√n))))/(Σ_(n=1) ^(k^2 −1) (√(k−(√n)))))=1+(√2)

$$\mathrm{is}\:\mathrm{this}\:\mathrm{true}\:\mathrm{and}\:\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{proof}? \\ $$$$\forall{k}\in\mathbb{N}\mid{k}>\mathrm{1} \\ $$$$\frac{\underset{{n}=\mathrm{1}} {\overset{{k}^{\mathrm{2}} −\mathrm{1}} {\sum}}\sqrt{{k}+\sqrt{{n}}}}{\underset{{n}=\mathrm{1}} {\overset{{k}^{\mathrm{2}} −\mathrm{1}} {\sum}}\sqrt{{k}−\sqrt{{n}}}}=\mathrm{1}+\sqrt{\mathrm{2}} \\ $$

Question Number 149341 Answers: 0 Comments: 3

Question Number 149349 Answers: 0 Comments: 0

Question Number 149339 Answers: 1 Comments: 0

...nice......mathematics... ln( 2) −Σ_(n=1 ) ^∞ ((ζ ( 2n+1 )−1)/(n + 1)) = ? ....m.n....

$$\:\:\:\:\:\:\:\:\:\:...{nice}......{mathematics}... \\ $$$$\:\:\:\:\:\:{ln}\left(\:\mathrm{2}\right)\:−\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\zeta\:\left(\:\mathrm{2}{n}+\mathrm{1}\:\right)−\mathrm{1}}{{n}\:+\:\mathrm{1}}\:=\:? \\ $$$$\:\:\:\:....{m}.{n}.... \\ $$

Question Number 149331 Answers: 1 Comments: 2

Question Number 149329 Answers: 1 Comments: 1

Question Number 149323 Answers: 2 Comments: 0

How many ordered pairs (a,b) with b < a < 100 , a,b ∈ N such that (a/b) both ((a+1)/(b+1)) are integers .

$${How}\:\:{many}\:\:{ordered}\:\:{pairs}\:\left({a},{b}\right)\:{with}\:\:{b}\:<\:{a}\:<\:\mathrm{100}\:\:,\:\:{a},{b}\:\in\:\mathbb{N}\:\:{such}\:\:{that}\:\:\frac{{a}}{{b}}\:\:{both}\:\:\:\frac{{a}+\mathrm{1}}{{b}+\mathrm{1}}\:\:{are}\:\:{integers}\:\:.\: \\ $$

Question Number 149322 Answers: 0 Comments: 5

((Σ_(n=1) ^(99) ((√(10 + (√n)))))/(Σ_(n=1) ^(99) ((√(10 - (√n)))))) = ?

$$\frac{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:+\:\sqrt{\boldsymbol{{n}}}}\right)}{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:-\:\sqrt{\boldsymbol{{n}}}}\right)}\:=\:? \\ $$

Question Number 149317 Answers: 2 Comments: 0

lim_(x→∞) (√(x^6 +5x^3 ))−x

$${lim}_{{x}\rightarrow\infty} \sqrt{{x}^{\mathrm{6}} +\mathrm{5}{x}^{\mathrm{3}} }−{x} \\ $$

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