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AllQuestion and Answers: Page 34

Question Number 210688 Answers: 0 Comments: 1

In a convex quadrilateral ABCD, diagonals AC and BD intersect at E, while perpendicular bisectors of AB and CD intersect at F, and those of BC and DA intersect at G. Prove: (1) E, F, and G are collinear, (2) AE:EC = BF:FD, and (3) CG:GD = AF:FB.

$$ \\ $$In a convex quadrilateral ABCD, diagonals AC and BD intersect at E, while perpendicular bisectors of AB and CD intersect at F, and those of BC and DA intersect at G. Prove: (1) E, F, and G are collinear, (2) AE:EC = BF:FD, and (3) CG:GD = AF:FB.

Question Number 210687 Answers: 0 Comments: 2

Question Number 210685 Answers: 3 Comments: 0

find ∫(1/x)dx

$${find} \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx} \\ $$

Question Number 210677 Answers: 1 Comments: 0

Question Number 210674 Answers: 1 Comments: 0

Question Number 210666 Answers: 1 Comments: 0

prove that p(n) is integer ∀ n∈Z p(n) = ((3n^7 +7n^3 +11n)/(21))

$$\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{p}\left(\mathrm{n}\right)\:\mathrm{is}\:\mathrm{integer}\:\forall\:\mathrm{n}\in\mathbb{Z} \\ $$$$\:\:\:\mathrm{p}\left(\mathrm{n}\right)\:=\:\frac{\mathrm{3n}^{\mathrm{7}} +\mathrm{7n}^{\mathrm{3}} +\mathrm{11n}}{\mathrm{21}} \\ $$

Question Number 210664 Answers: 0 Comments: 1

Question Number 210667 Answers: 3 Comments: 0

Question Number 210661 Answers: 0 Comments: 0

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Question Number 210652 Answers: 0 Comments: 0

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Question Number 210639 Answers: 3 Comments: 0

given that the roots of the equation 3x^2 −(4+2k)x+2k=0 are α and β find the value of k for which β=3α

$${given}\:{that}\:{the}\:{roots} \\ $$$$\:{of}\:{the}\:{equation} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} −\left(\mathrm{4}+\mathrm{2}{k}\right){x}+\mathrm{2}{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta \\ $$$${find}\:{the}\:{value}\:{of}\:{k} \\ $$$${for}\:{which}\:\beta=\mathrm{3}\alpha \\ $$

Question Number 210630 Answers: 1 Comments: 0

Question Number 210629 Answers: 2 Comments: 0

Question Number 210679 Answers: 2 Comments: 0

Question Number 210608 Answers: 2 Comments: 1

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Question Number 210601 Answers: 1 Comments: 0

Find the value of : Ω = ∫_0 ^( 1) ∫_0 ^( (√(1−x^2 ))) ∫_(√( x^( 2) +y^( 2) )) ^( (√(2−x^2 −y^2 ))) xy dz dy dx =?

$$ \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:\:{the}\:\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\sqrt{\:{x}^{\:\mathrm{2}} \:+{y}^{\:\mathrm{2}} }} ^{\:\sqrt{\mathrm{2}−{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} }} \:{xy}\:{dz}\:{dy}\:{dx}\:=?\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 210593 Answers: 1 Comments: 0

∫ ((sin x cos x)/( ((cos 2x))^(1/3) + (√(cos 2x)))) dx =? ∫ (dx/(sec x ((sin x))^(1/2) + cos x ((cosec^5 x))^(1/3) )) =?

$$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{2x}}\:+\:\sqrt{\mathrm{cos}\:\mathrm{2x}}}\:\mathrm{dx}\:=? \\ $$$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}\:\sqrt[{\mathrm{2}}]{\mathrm{sin}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}\:\sqrt[{\mathrm{3}}]{\mathrm{cosec}\:^{\mathrm{5}} \mathrm{x}}}\:=? \\ $$

Question Number 210591 Answers: 3 Comments: 0

If a + b = 1 a^2 + b^2 = 2 then, a^(11) + b^(11) = ??

$$\mathrm{If} \\ $$$$\:\:\:\:\mathrm{a}\:\:+\:\:\mathrm{b}\:\:=\:\:\mathrm{1} \\ $$$$\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{b}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{then},\:\:\:\:\:\mathrm{a}^{\mathrm{11}} \:\:+\:\:\mathrm{b}^{\mathrm{11}} \:\:=\:\:?? \\ $$

Question Number 210590 Answers: 0 Comments: 0

Question Number 210587 Answers: 0 Comments: 3

f(x)= (√( 13 −12(√x) )) + (√(25 −24(√(1−x)) )) find : Min ( f )=?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mathrm{13}\:−\mathrm{12}\sqrt{{x}}\:\:}\:+\:\sqrt{\mathrm{25}\:−\mathrm{24}\sqrt{\mathrm{1}−{x}}\:} \\ $$$$ \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\:\mathrm{M}{in}\:\left(\:{f}\:\right)=? \\ $$$$ \\ $$$$ \\ $$

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