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Question Number 140768 Answers: 3 Comments: 0

∫_(−∞) ^∞ ((x^2 +4)/(x^4 +16)) dx =?

$\int_{- \infty}^{\infty} \frac{x^{2} + 4}{x^{4} + 16} dx = ?$

Question Number 140767 Answers: 1 Comments: 0

Solve for x : 2cot^2 x + csc^2 x−2 = 0

$Solve for x : 2 \cot^{2} x + \csc^{2} x - 2 = 0$

Question Number 140751 Answers: 1 Comments: 0

Question Number 140750 Answers: 1 Comments: 0

Σ_(k=0) ^n cos^3 k=?

$\underset{k = 0}{\sum^{n}} \cos^{3} k = ?$

Question Number 140749 Answers: 1 Comments: 0

Σ_(k=1) ^n 5^(1/k) (1−5^(−(1/(k(k+1)))) )=?

$\underset{k = 1}{\sum^{n}} 5^{\frac{1}{k}} (1 - 5^{- \frac{1}{k (k + 1)}}) = ?$

Question Number 140748 Answers: 3 Comments: 0

Question Number 140747 Answers: 0 Comments: 0

Question Number 140746 Answers: 2 Comments: 0

Question Number 140735 Answers: 2 Comments: 0

Using vector method, prove that three median of a triangle are concurrent.

$Using vector method, prove that three$ $median of a triangle are concurrent .$

Question Number 140734 Answers: 1 Comments: 1

Let m,n be given positive integers. If x & y are positive numbers such that x+y= S , S is a constant, find the value of x and y that maximize Q=x^m y^n .

$Let m, n be given positive integers .$ $If x & y are positive numbers such that$ $x + y = S, S is a constant, find$ $the value of x and y that maximize$ $Q = x^{m} y^{n} .$

Question Number 140715 Answers: 1 Comments: 0

......advanced calculus...... prove that: 𝛗:=∫_0 ^( ∞) (x^2 /(cosh^2 (x^2 )))dx=^? (((√2) −2)/4) (√π) ζ ( (1/2) ) ..............

$. . . . . . a d v a n c e d c a l c u l u s . . . . . .$ $p r o v e t h a t :$ $ϕ := \int_{0}^{\infty} \frac{x^{2}}{{c o s h}^{2} (x^{2})} d x \overset{?}{=} \frac{\sqrt{2} - 2}{4} \sqrt{π} ζ (\frac{1}{2})$ $. . . . . . . . . . . . . .$

Question Number 140708 Answers: 0 Comments: 0

Given an Elipsis in (O;i^→ ;j^→ ) (E): (x^2 /(1/4))+(y^2 /1)=1. We admit that it image by the transformation f : { ((x′=(√2)(x+y))),((y′=(√2)(−x+y) )) :} is an elipsis (E′): 5x^2 +5y^2 +6xy−8=0 Can you help me to write the reduced equation of (E′) in (O;i^→ ;j^→ ). I mean in the similar form of (E)′s equation.

$Given an Elipsis in (O; \vec{i}; \vec{j})$ $(E) : \frac{x^{2}}{1 / 4} + \frac{y^{2}}{1} = 1 .$ $W e admit that it image by the transformation$ $f : {\begin{cases} x^{'} = \sqrt{2} (x + y) \\ y^{'} = \sqrt{2} (- x + y) \end{cases}$ $i s a n e l i p s i s (E^{'}) : 5 x^{2} + 5 y^{2} + 6 x y - 8 = 0$ $Can you help me to write the reduced$ $equation of (E^{'}) in (O; \vec{i}; \vec{j}) . I mean$ $in the similar form of {(E)}^{'} s equation .$