Prove that there are no natural number solutions to the equation where x, y ≥ 2 ... (See Picture Below)
Prove that there are no natural number solutions to the equation where x, y ≥ 2...
PROBLEM 2 Consider the family of circles P = {C, TER>0}, where Cr = {(x, y) R2 | x2 + y2 = p2} is a circle of radius r > 0. Prove that P is a partition of R2. State an equivalence relation induced by this partition. Hint: What is a property that is True for all points in a fixed circle?
[10] 1. Solve the first-order equation Tư + (x – 2) = -xe-3, > 0.
Let z=5 where x, y, z E R. Prove that z? +z2+z?>
How to solve it? Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
using this formula 2. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over the paraboloid z=1 – x2 - y2, z > 0. SA errom bove de SS (-P (- Puerto Q + R) dA dy
Let X, Y ~ 10,11 independently. Find P(max(X, Y} > 0.8 1 min(X, Y} = 0.5)
3. (10 pts.) X is a Gaussian random variable with E{X} = 2 and Var(X) = 16. Let Y = 3X +1. Determine the probability: Pr(Y > 2)
Prove X, Y, Z, JER. XKY Prove Z <# X AND Y<j, if and only if (x,y) [z,j]
The Bessel equation of order one-half is X .2 dy d.2 + X dy dar +(x2 - :) y = 0, X > 0 4 a) Verify that yı(x) = x-1/2 sin x is a solution to the equation b) Use reduction of order to find a second linearly independent solution. (Hint: one possibility is y2(x) = x-1/2 cos x.] c) Compute the Wronskian of these two solutions explicitly and verify that it is equal to the solution we computed...
Find a polar equation of the form r = f(@), where r > 0, for the curve represented by the Cartesian equation x2 + y2 = 9. Note: Since is not a symbol on your keyboard, use t in place of 0 in your answer. =