show complete solutions
A 1 4 - 2 3 8 o $ = 1 1 2 1o OB solve For AB
22. Suppose that (ab, p)- 1 and that p> 2. Show that the number of solutions (x, y) of the congruence ax2 + by 1 (mod p) is -ab
22. Suppose that (ab, p)- 1 and that p> 2. Show that the number of solutions (x, y) of the congruence ax2 + by 1 (mod p) is -ab
show complete solutions
4. 4 l А 1 2 3 3 8 0 BE -1 sowe For AB
perawan | ES | POR TU FERT Solve the system by the method of elimination and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY) (x, y) = (1 Need Help? Read It Watch!
Question 1 - 16 Consider the following intial-boundary value problem. au au 0<x< 1, 10, at2 ax?' u(0,t) = u(11,t) = 0, 7>0, u(x,0) = 1, 34(x,0) = sin10x + 7sin50x. (show all your works). A) Find the two ordinary differential equations (ODES). B) Solve these two ODES. Show all cases 1 <0, 1 = 0, and > 0 C) Write the complete solution of this initial - boundary value problem.
6 & 7
5 points. Solve the equation for solutions in the interval (0,271). 1 6) sin x cos X= 5 points. Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary. 7) sin2e - sin 0 - 12 = 0 7
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A = [1 4 6 Ba [-] sowe for (TA)
5. Solve Au=0, r>1, 0 < θ < 2π, a(1,0) cos θ, 0 < θ < 2π.
5. Solve Au=0, r>1, 0
5. Solve Au=0, r>1, 0 < θ < 2π, u(1.0) = cos θ, 0 < θ < 2π.
5. Solve Au=0, r>1, 0
Problem 2. (15 points) Solve the following Laplace's equation in a cube as outlined below. au au au 2,2 + a2 + a2 = 0, on 0<x<1, 0<y<1, 0<?<1, (0, y, z) = (1, y, z) = 0, (x, 0, 2) = u(x, 1, ) = 0, (x, y,0) = 0, u(x,y, 1) = x. (a) Seek a solution of the form u(x, y, z) = F(x) G(v) H(-). Show that with the appropriate choice of separation constants, you can...