9) Find the flux of the field =< 3x, -y, -z > through the surface of the box in the first octant bounded by the coordinate axis and the planes x = 1, y = 2, z = 3
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
Let F(x,y,z) = <7x, 5y, 2z > be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 72 = 9 in the first octant. Answer: Finish attempt
2. Let I be the surface of the cone z = V x2 + y2 (without the top) between planes z = 0 and z = 2. Let F =< x,y,z2 >. Calculate the upward directed flux SS FdS (a) Using the Divergence Theorem. (10 points) (b) Without using the Divergence Theorem. (20 points)
(8) The Divergence Theorem for Flux in Space F(x, y, z) =< P, Q, R >=< xz, yz, 222 > S: Bounded by z = 4 – x² - y2 and z = 0 Flux =S} F înds S (8a) Find the Flux of the vector field F through this closed surface. (8) The Divergence Theorem for Flux in Space F(x,y,z) =< P,Q,R >=< xz, yz, 222 > S: Bounded by z = 4 – x2 - y2 and z...
Let F(x,y,z) = <7x, 5y, 2z> be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 7z = 8 in the first octant. Answer:
How to solve it? Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
Calculate the flux of the vector field out of the ball x² + y² =²<4 if vfx, y, z) = (y2); +(2+yJj+ft+422)z a) none 6) 128 T 8160 d) 32T e) 647
6. Find the flux of F(x, y, z) (ax, by, cz) a > 0, b > 0, c> 0, through the surface S, where S is the part of the cone z = Vax)2 + (by)2 that lies between the planes z = 0 and z = 2, oriented upwards. [10]
2. Let R be the region R = {(X,Y)|X2 + y2 < 2} and let (X,Y) be a pair of random variables that is distributed uniformly on this region. That is fx,y(x, y) is constant in this region and 0 elsewhere. State the sample space and find the probability that the random variable x2 + y2 is less than 1, P[X2 +Y? < 1].