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Question Number 215778 Answers: 0 Comments: 0

Question Number 215777 Answers: 0 Comments: 0

Question Number 215776 Answers: 0 Comments: 0

Question Number 215775 Answers: 0 Comments: 0

∫_0 ^( s) (√(1−s^2 ))(1+(√(1−((x/s))^2 ))−(√(1−x^2 )))dx

$$\:\:\underset{\mathrm{0}} {\overset{\:\:{s}} {\int}}\sqrt{\mathrm{1}−{s}^{\mathrm{2}} }\left(\mathrm{1}+\sqrt{\mathrm{1}−\left(\frac{{x}}{{s}}\right)^{\mathrm{2}} }−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right){dx} \\ $$

Question Number 215774 Answers: 0 Comments: 0

let's say there are two circles with their centers A1 and A2 and their radii are equal to r1 and r2 ,let n be the distance between the centers of the two circles and n

$$ \\ $$let's say there are two circles with their centers A1 and A2 and their radii are equal to r1 and r2 ,let n be the distance between the centers of the two circles and n<r1+r2. Is there a way to find how much is the area that is formed when the two circles are overlapping ?

Question Number 215769 Answers: 1 Comments: 1

In △ABC, it is given that AC⊥CB, CD⊥AB, and CD = 12, AC = BC + 5. Please solve for the value of BC using a purely geometric method.

Question Number 215760 Answers: 1 Comments: 0

Let g(x) = 3f((x/3)) + f(3 − x) and f ′′(x) > 0 for all x ∈ (0, 3). If g is decreasing in (0, α) and increasing in (α, 3) then find 8α.

$$\mathrm{Let}\:{g}\left({x}\right)\:=\:\mathrm{3}{f}\left(\frac{{x}}{\mathrm{3}}\right)\:+\:{f}\left(\mathrm{3}\:−\:{x}\right)\:\mathrm{and}\: \\ $$$${f}\:''\left({x}\right)\:>\:\mathrm{0}\:\mathrm{for}\:\mathrm{all}\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{3}\right).\:\mathrm{If}\:{g}\:\mathrm{is}\: \\ $$$$\mathrm{decreasing}\:\mathrm{in}\:\left(\mathrm{0},\:\alpha\right)\:\mathrm{and}\:\mathrm{increasing}\:\mathrm{in} \\ $$$$\left(\alpha,\:\mathrm{3}\right)\:\mathrm{then}\:\mathrm{find}\:\mathrm{8}\alpha. \\ $$

Question Number 215748 Answers: 0 Comments: 0

lim_(n→∞) [Π_(k=1) ^(n+1) Γ((1/k))]^(1/(n+1)) −[Π_(k=1) ^n Γ((1/k))]^(1/n)

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[\underset{{k}=\mathrm{1}} {\overset{{n}+\mathrm{1}} {\prod}}\Gamma\left(\frac{\mathrm{1}}{{k}}\right)\right]^{\frac{\mathrm{1}}{{n}+\mathrm{1}}} −\left[\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\Gamma\left(\frac{\mathrm{1}}{{k}}\right)\right]^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 215754 Answers: 1 Comments: 0

Question Number 215755 Answers: 1 Comments: 0

Tow men complet a work in 3hr, three women complet it in 5hr, and five children complet it in 10hr. if we consider among these one man, one woman and one child in how much time they will complet it together?

$${Tow}\:{men}\:{complet}\:{a}\:{work}\:{in}\:\mathrm{3}{hr},\:{three} \\ $$$${women}\:{complet}\:{it}\:{in}\:\mathrm{5}{hr},\:{and}\:{five}\: \\ $$$${children}\:{complet}\:{it}\:{in}\:\mathrm{10}{hr}.\:{if}\:{we}\:{consider} \\ $$$${among}\:{these}\:{one}\:{man},\:{one}\:{woman}\:{and}\:{one} \\ $$$${child}\:{in}\:{how}\:{much}\:{time}\:{they}\:{will} \\ $$$${complet}\:{it}\:{together}? \\ $$

Question Number 215739 Answers: 0 Comments: 0

Question Number 215737 Answers: 2 Comments: 1

Question Number 215730 Answers: 1 Comments: 0

Determine a, b, c [Lazy problem] J181-2. x^3 −6x^2 +15x−7=(x+a)^3 +bx+c J182-(1) x^3 +ax+2=(x+1)(x^2 +bx+c)

$$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:\left[\mathrm{Lazy}\:\mathrm{problem}\right] \\ $$$$\mathrm{J181}-\mathrm{2}.\:{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} +\mathrm{15}{x}−\mathrm{7}=\left({x}+{a}\right)^{\mathrm{3}} +{bx}+{c} \\ $$$$\mathrm{J182}-\left(\mathrm{1}\right)\:{x}^{\mathrm{3}} +{ax}+\mathrm{2}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +{bx}+{c}\right) \\ $$

Question Number 215723 Answers: 2 Comments: 0

Question Number 215718 Answers: 1 Comments: 0

lim_(x→∞) (ln(9/2))^((1/2)x) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({ln}\frac{\mathrm{9}}{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}{x}} =? \\ $$$$ \\ $$

Question Number 215715 Answers: 1 Comments: 1

Question Number 215708 Answers: 1 Comments: 0

Question Number 215704 Answers: 1 Comments: 1

Question Number 215710 Answers: 0 Comments: 0

3 different integer numbers are chosen from 0 to 10. what is the probability that they form 1 Cluster 3 Clusters 2 Clusters A cluster is a set of numbers that has maximum range of 2. for example 0,1,2 forms only one cluster. 0,1,4 forms 2 {0,1} and {4}. 0,1,3 also forms 2 {0,1} and {1,2}

$$ \\ $$3 different integer numbers are chosen from 0 to 10. what is the probability that they form 1 Cluster 3 Clusters 2 Clusters A cluster is a set of numbers that has maximum range of 2. for example 0,1,2 forms only one cluster. 0,1,4 forms 2 {0,1} and {4}. 0,1,3 also forms 2 {0,1} and {1,2}

Question Number 215696 Answers: 2 Comments: 0

Question Number 215687 Answers: 2 Comments: 0

Question Number 215679 Answers: 2 Comments: 0

Question Number 215764 Answers: 0 Comments: 0

∫_0 ^1 x^(99) cos^4 (x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{99}} \mathrm{cos}^{\mathrm{4}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 215667 Answers: 2 Comments: 0

lim_(x→1) sec((π/2)x)(arctanx−(π/4))=?

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{sec}\left(\frac{\pi}{\mathrm{2}}{x}\right)\left({arctanx}−\frac{\pi}{\mathrm{4}}\right)=? \\ $$

Question Number 215757 Answers: 0 Comments: 0

Question Number 215659 Answers: 2 Comments: 0

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