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Question Number 210728 Answers: 1 Comments: 0

Question Number 210723 Answers: 1 Comments: 0

the volume of the region between the planes x+y+2z=2 and 2x+y+z = 4 in the first octant is

$$\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{between}\:\mathrm{the}\: \\ $$$$\mathrm{planes}\:\mathrm{x}+\mathrm{y}+\mathrm{2z}=\mathrm{2}\:\mathrm{and}\:\mathrm{2x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{4}\:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{octant}\:\mathrm{is} \\ $$

Question Number 210718 Answers: 0 Comments: 1

If sin1° = a (1/(cos1°∙cos2°)) + (1/(cos2°∙cos3°)) +...+ (1/(cos44°∙cos45°)) = ?

$$\mathrm{If}\:\:\:\mathrm{sin1}°\:=\:\mathrm{a} \\ $$$$\frac{\mathrm{1}}{\mathrm{cos1}°\centerdot\mathrm{cos2}°}\:+\:\frac{\mathrm{1}}{\mathrm{cos2}°\centerdot\mathrm{cos3}°}\:+...+\:\frac{\mathrm{1}}{\mathrm{cos44}°\centerdot\mathrm{cos45}°}\:=\:? \\ $$

Question Number 210719 Answers: 2 Comments: 0

find 63!^(36!) mod97 thanks

$${find}\:\mathrm{63}!^{\mathrm{36}!} {mod}\mathrm{97}\:\:\:{thanks} \\ $$

Question Number 210706 Answers: 0 Comments: 0

Question Number 210702 Answers: 2 Comments: 0

How many real solutions does the equation x=sin3x have?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{does}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{x}=\mathrm{sin3}{x}\:\mathrm{have}? \\ $$

Question Number 210701 Answers: 1 Comments: 0

Question Number 210695 Answers: 1 Comments: 1

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Question Number 210689 Answers: 1 Comments: 0

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))

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

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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

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