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1. ### F = (cos x)āiā + e^yājā + (4x ā 3y ā 3z)k,?

...sin t) ā 3(ā6/2 sin t + 3ā2/2 cos t) ā 3(ā6/2 sin t ā 3ā2/2 cos t)) k ā«c F Ā· dr = ā« [0 to 2Ļ] F(r(t)) Ā· r'(t) dt = ā« [0 to 2Ļ...

2 Answers Ā· Science & Mathematics Ā· 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) + [Ī£(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 Ā· Science & Mathematics Ā· 27/05/2017

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

By Stokes ā«[C] ā¢ = ā¬[S] curl()ā¢ where S is the enclosed area with upwards normal curl() = (1āx,ā1,zā6) Applying polars x=rcosĪø, y=rsinĪø gives S as = (rcosĪø, rsinĪø,rsinĪø+8), rā[0,1], Īøā[0,2Ļ...

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

5. ### Use Stokes' Theorem to evaluate ā«F Ā· dr?

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

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

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

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

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

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

...ākĀ²) dy = ā« Ā±1/k dx ln(ā(yĀ²ākĀ²) + y) = Ā±x/k + c Solve for y: ā(yĀ²ākĀ²) + y = Ce^(Ā±x/k) ā(yĀ²...

1 Answers Ā· Science & Mathematics Ā· 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 = ā« 1/(xāk) dx tanā»Ā¹(u) ā 1/2 ln(uĀ²+1) = ln|xāk| + C tanā»Ā¹((yāk)/(xāk)) ā 1/2 ln((yāk)Ā²/(xāk)Ā²+1...

2 Answers Ā· Science & Mathematics Ā· 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 Ā· Science & Mathematics Ā· 10/04/2017