Consider the following set of points (1,0), (2, 2), (0,2), (0,0) and let 1 2 0...
dA, where R is the trapezoidal region cos yt x with vertices (1,0), (2, 0), (0,2), and (0, 1)
dA, where R is the trapezoidal region cos yt x with vertices (1,0), (2, 0), (0,2), and (0, 1)
3. The pair of random variables X and Y is uniformly distributed on the interior of the triangle with the vertices whose coordinates are (0,0), (0,2), and (2,0) (i.e., the joint density is equal to a constant inside the triangle and zero outside). (a) (10 points) Find P(Y+X< 1). (b) (10 points) Find P(X = Y). (c) (10 points) Find P(Y > 1X = 1/2).
3. The pair of random variables X and Y is uniformly distributed on the interior...
Find an equation for the plane through the points (4,3,5), (1,0,-1), (0,2,-2). The Plane is?
Input: a directed grid graph G, a set of target points S, and an integer k Output: true if there is a path through G that visits all points in S using at most k left turns A grid graph is a graph where the vertices are at integer coordinates from 0,0 to n,n. (So 0,0, 0,1, 0,2, ...0,n, 1,0, etc.) Also, all edges are between vertices at distance 1. (So 00->01, 00->10, but not 00 to any other vertex....
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
5 ve 6. Soru
Dry - xdA over the triangle with vertices ( -1,0), (0,0) and (0,1) changing the variables by u = y - x and v = y + x. (DONOTEVALUATE INTEGRAL) 1 w 5. (15 points) Write the integral representing the area of the region al < x2 + y2 < band below the line y = x in polar coordinates.(DONOT EVALUATE INTEGRAL) ,y,z) as an iterated integral in cartesian coor- dinates. E is the region inside...
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
5,6 please
5. Parametrize the plane P in R3 containing the points x (1,0, ), x (2,0, 1) and x3 (1,3, 1). Does the plane P contain the point (-1,3,2)? 6. Sketch and parametrize the triangle in the plane with vertices x! = (-1,-2), x2 = (2, and x3 (1,3). Does this triangle contain the origin (0, 0,0)
2. Consider the set of curved coordinates t(t, s) in the plane R2(0,0) related to the Euclidian coordinates (r, y) by the transformations: 2 s2+ t . . t t ys , . (a) (10 points) Find Dx(t) := = (b) (5 points) Find the volume element dx dy expressed in the coordinates (s, t). Use that da dy detds dt 0(t,s) (c) bonus (10 points) Express the vector of first partial derivatives [, using the formula [a,,%) . via...
45 points) Consider the following vectors in R3 2 0 0 2 2 Vi = 1 ;02 31; V3 = 11:04 = -1 ; Us = 4 2 2 3 (c) Find a basis of R3 among V1, V2, V3, V4, V5, and call it basis V. (d) Is vs Espan{V1, V2, 03, 04}? Explain. (e) Find the coordinates of us with respect to the basis V.