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1. ### F = (cos x) i  + e^y j  + (4x − 3y − 3z)k,?

...sin t) − 3(√6/2 sin t + 3√2/2 cos t) − 3(√6/2 sin t − 3√2/2 cos t)) kc F · dr = ∫ [0 to 2π] F(r(t)) · r'(t) dt = ∫ [0 to 2π...

2 Answers · Science & Mathematics · 28/07/2017

2. ### Prove that (A+B)^n = sum[k=0->+infinity] C(n,k) A^k.B^(n-k), with A and B square matrices?

...^k) + B^(n+1) = A^(n+1) + [Σ(k = 1 to n) (C(n, k) + C(n, k-1)) A^(n-k+1) B^k] + B^(n+1) = A^(n+1) + [...

2 Answers · Science & Mathematics · 27/05/2017

3. ### Use Stokes' Theorem to evaluate?

By Stokes ∫[C] • = ∬[S] curl()• where S is the enclosed area with upwards normal curl() = (1−x,−1,z−6) Applying polars x=rcosθ, y=rsinθ gives S as = (rcosθ, rsinθ,rsinθ+8), r∈[0,1], θ∈[0,2π...

2 Answers · Science & Mathematics · 23/05/2017

4. ### Probability and combinatorics help before an exam!?

... use that as the probability in the binomial probability formula: P(X = k) = C(n, k) * p^k * q^(n-k) n : number of trials (10) k : number...

2 Answers · Science & Mathematics · 30/05/2017

5. ### Use Stokes' Theorem to evaluate ∫F · dr?

∫c F · dr = ∫∫s curl F · dS, where we take S as the surface on z = 5 bounded by x^2 + y^2 = 16 = ∫∫ <xe^(xy) - 9x, y - ye^(xy), 8z> · <-z_x, -z_y, 1> dA = ∫∫ <xe^(xy) - 9x, y - ye^(xy), 8 * 5> · <0, 0...

1 Answers · Science & Mathematics · 03/05/2017

6. ### Prove that the Cauchy product of two absolutely convergent series converges absolutely?

...(n) = Σ(k=0 to n) |a(k)|, B(n) = Σ(k=0 to n) |b(k)|, C(n) = Σ(k=0 to n) |c(k)|. Then, C(n) = |a(0) b(0...

2 Answers · Science & Mathematics · 02/05/2017

7. ### Let R be the region in the first quadrant under the graph of y=8/cubed root of x for the interval from 1 to 8?

a. The equation can be rewritten 8x^(-1/3). The question is essentially asking for the definite integral of the equation from 1 to 8. The integral of the equation is (12)x^(2/3). By subtracting 1 plugged into the integral, (12)(1)^(2/3), from 8...

1 Answers · Science & Mathematics · 02/05/2017

8. ### Can someone help me with this equation? y^2-k^2-k^2(y')^2=0?

...−k²) dy = ∫ ±1/k dx ln(√(y²−k²) + y) = ±x/k + c Solve for y: √(y²−k²) + y = Ce^(±x/k) √(y²...

1 Answers · Science & Mathematics · 14/04/2017

9. ### I have problem with two differential equations. k is a const. Can someone give me some tips? y'=(y-kx)/(ky+x) and y'=(2k-y-x)/(y-x)?

...+1) du = ∫ 1/(x−k) dx tan⁻¹(u) − 1/2 ln(u²+1) = ln|x−k| + C tan⁻¹((y−k)/(x−k)) − 1/2 ln((y−k)²/(x−k)²+1...

2 Answers · Science & Mathematics · 14/04/2017

10. ### Calculus Question (Coffee Problem?? HELP!)?

...'(t) = -2 cos(0.5t) Integrate C(t) = -2 sin(0.5t) /0.5 + K C(t) = -4 sin(0.5t) + K C(12) = 40 40 = -4 sin(0.5*12) + K K...

1 Answers · Science & Mathematics · 10/04/2017