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Question Number 209544 Answers: 1 Comments: 0

∫_0 ^4 (dx/(∣x−1∣+∣x−2∣+∣x−4∣))

$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{4}} \frac{{dx}}{\mid{x}−\mathrm{1}\mid+\mid{x}−\mathrm{2}\mid+\mid{x}−\mathrm{4}\mid} \\ $$$$ \\ $$

Question Number 209543 Answers: 1 Comments: 2

∫(dx/(x^4 +4))

$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{4}} +\mathrm{4}} \\ $$$$ \\ $$

Question Number 209542 Answers: 2 Comments: 0

∫(dx/(x^(15) −x^(11) ))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{15}} −{x}^{\mathrm{11}} } \\ $$$$ \\ $$$$ \\ $$

Question Number 209540 Answers: 3 Comments: 0

Question Number 209539 Answers: 0 Comments: 0

Question Number 209531 Answers: 0 Comments: 1

(y^(′′) /y) = 4x^2 + 2

$$\frac{\mathrm{y}^{''} }{\mathrm{y}}\:\:=\:\:\mathrm{4x}^{\mathrm{2}} \:\:+\:\:\mathrm{2} \\ $$

Question Number 209529 Answers: 1 Comments: 1

Question Number 209521 Answers: 1 Comments: 0

find the integral ∫ (dx/(x^4 +a^4 )) by complex number ?

$${find}\:{the}\:{integral}\:\int\:\frac{{dx}}{{x}^{\mathrm{4}} +{a}^{\mathrm{4}} }\:{by}\:{complex}\:{number}\:?\: \\ $$

Question Number 209520 Answers: 1 Comments: 1

At what value of a does the system of equations have 4 solutions ? { x^2 −y^2 =0 {(x−a)^2 +y^2 =1

$$ \\ $$$$\:\:\:{At}\:{what}\:{value}\:{of}\:\:{a}\:{does}\:{the}\:{system} \\ $$$$\:\:\:{of}\:{equations}\:{have}\:\mathrm{4}\:{solutions}\:? \\ $$$$\:\:\:\left\{\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{0}\right. \\ $$$$\:\:\:\left\{\left({x}−{a}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right. \\ $$$$ \\ $$

Question Number 209519 Answers: 0 Comments: 3

Is there any n∈N such that sin(n)∈Q ?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:{n}\in\mathbb{N}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{sin}\left({n}\right)\in\mathbb{Q}\:? \\ $$

Question Number 209832 Answers: 0 Comments: 0

Question Number 209514 Answers: 1 Comments: 0

If Σ a_n is absolutely convergent, prove that Σ (a_n /n) is also absolutely convergent.

$$\mathrm{If}\:\Sigma\:{a}_{{n}} \:\mathrm{is}\:\mathrm{absolutely}\:\mathrm{convergent},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\Sigma\:\frac{{a}_{{n}} }{{n}}\:\mathrm{is}\:\mathrm{also}\:\mathrm{absolutely}\:\mathrm{convergent}. \\ $$

Question Number 209510 Answers: 0 Comments: 0

three points are randomly selected on a circle to form a triangle. 1) find the probability that the center of the circle lies inside the triangle. 2) find the probability that the triangle is an acute triangle.

$${three}\:{points}\:{are}\:{randomly}\:{selected} \\ $$$${on}\:{a}\:{circle}\:{to}\:{form}\:{a}\:{triangle}.\: \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{probability}\:{that}\:{the}\:{center} \\ $$$${of}\:{the}\:{circle}\:{lies}\:{inside}\:{the}\:{triangle}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{probability}\:{that}\:{the}\: \\ $$$${triangle}\:{is}\:{an}\:{acute}\:{triangle}. \\ $$

Question Number 209506 Answers: 0 Comments: 2

Question Number 209495 Answers: 1 Comments: 1

Question Number 209484 Answers: 0 Comments: 0

∫_e^x ^e^2 ((1/(2+ln t)) )dt =?

$$\:\:\:\:\:\:\:\underset{\mathrm{e}^{\mathrm{x}} } {\overset{\mathrm{e}^{\mathrm{2}} } {\int}}\:\left(\frac{\mathrm{1}}{\mathrm{2}+\mathrm{ln}\:\mathrm{t}}\:\right)\mathrm{dt}\:=? \\ $$

Question Number 209474 Answers: 2 Comments: 1

Question Number 209465 Answers: 1 Comments: 0

Question Number 209460 Answers: 0 Comments: 0

Question Number 209458 Answers: 0 Comments: 3

Question Number 209456 Answers: 2 Comments: 0

Question Number 209455 Answers: 1 Comments: 0

Question Number 209453 Answers: 2 Comments: 1

Question Number 209452 Answers: 2 Comments: 0

Question Number 209450 Answers: 1 Comments: 0

Question Number 209436 Answers: 1 Comments: 2

{ ((x + y + z = 1)),((42x + 44y + 30z = 42)) :} (x,y,z)=(1,0,0) yes, but solution...

$$\begin{cases}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1}}\\{\mathrm{42x}\:+\:\mathrm{44y}\:+\:\mathrm{30z}\:=\:\mathrm{42}}\end{cases} \\ $$$$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(\mathrm{1},\mathrm{0},\mathrm{0}\right)\:\mathrm{yes},\:\mathrm{but}\:\mathrm{solution}... \\ $$

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