
For any queries, leave a comment. And a thumbs up is always appreciated. Thanks !
.834 Region l is defined by x-y+2z > 5 with μ.-Yvwhile region 2 is defined by...
(2 points) Consider the following initial value problem, defined for t > 0: ' – 4y = f** (t – w) e4w dw, y(0) = -3. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} b. Obtain the solution y(t). yt) =
3. A medium I is defined by x=0, pr=5, while a medium? as defined by oc> O, as a free space (E=&o). Giren the magnetic vector intensity Coc, y, z) = 100 - 20 + 402, A/an] 3.1. Find the magnetic field density, B . 3.2. Determine the angle o, and , find H, and its make reopedinek with the normal to the surface? HINT: B in = B. But tan 6 = 1
Suppose that the Type I region defined by R = {(2,3)|a 5 x 5 b,g(x) < y = f(x)} has (Try) as its centroid. Let k > O be an arbitrary positive real number. Use the formulas for finding the centroid to show that if f(x) and g(x) are multiplied by k, then the resulting region, R' = {(2,y)|a < 5 b, kg(x) < y 5 kf (x)}, will have a centroid that is given by (T, ky).
Ler L: R4 → R3 be the linear transformation defined by (4p) L(z,y,z, t) = (x – y +t, 2x – 2, Y + 2z – t) a) Find the images of the standard basis of RA L(1,0,0,0) = L(0,1,0,0) = L(0,0,1,0) = L(0,0,0,1) = b) Find a basis and the dimension of the image of L c) Find a basis and the dimension of the kernel of L (8p) (8p)
5] (2) GIVEN: a> 0,0# {(x, y, z) z a"-x'-y") W is the solid region of R' that is below 2 and above the xy- plane. W has constant density,8 and the mass of W is M, m(W) M FIND: The moment of inertia, I, of W with respect to the z- axis, express 2 I in terms of M and a without 8
Ignore handwriting
(15 pts) Assume that SAT matkematcs scores of studeuts who attend s college are N(μ, σ2-8100). We shall test Ho : μ-530 against HA : μ > 530 Let the critical region be defined by C (x X 2 554.675}, where X is the sample meatu of a random sample of size n = 36 from this distribution. l arts (a) What is the value of the significance level of this test? a o S503 s 6 (b)...
Consider the region defined by the curves r = e, y=e, 2 = 0, and y = 0. HA pts Sketch the region defined above. HBS pts Find the exact volume of the solid generated by rotating the region about the y-axis. SOLUTION
Consider two regions separated by the plane defined by f(r,y, )-2r 3y -4z1 as described in the following Region l: f(z, y, z) > 1.Hr,-2. Hi = a,50-as,30 + a,20 (A/m). Region 2: f(x, y, z) < 1.42 = 5. (a) Find the normal component of Hi (b) Find the tangential component of Hi (e) Find the tangential component of H2. (d) Find the normal component of H2 (e) Determine the angle 1 between Hi and the unit normal vector...
6. (20 pts.) The plane y-0 separates region 1 (y 0), which is a dielectric materia with c, -3.5, from region 2 (y < 0), which is free space. If the electric flux density in region 1 is given by D,-15a, +22ay -20a, [nC/m'], find D..
5. we have two independent samples of n observations X1,X2, ,x, and Yi, ½, ,y, We want to test the hypothesis Ho M Hy versus the alternative Hi: Hr y (a) First, assume that the null hypothesis Ho is true and find the MLE for μ Ha-μυ (b) Then plug this estimate into the log likelihood along with the MLE's μ--x and μυ-D to calculate the LRT statistic (c) Is this likelihood ratio test equivalent to the test that rejects...