The solution is given below....
1. The density of a metal rod extending from (0,0,0) to (1,2,3) is d(x,y,z) = xyz....
1 A rod extending between x = 0 and x = 15.0 cm has uniform cross-sectional area A = 8.50 cm2. Its density increases steadily between its ends from 3.00 g/cm3 to 20.0 g/cm (a) Identify the constants B and C required in the expression pBCx to describe the variable density. B-3.00 C 1.133333 g/cm /cm4 (b) The mass of the rod is given by (B + cx)(8.50 cm2) dx all material Carry out the integration to find the mass...
Find dB,(0,0,0), the z component of the magnetic field at the point x =y=z=0 from the current I flowing over a short distance di = dl ſ located at the point 7c = x1 1 î. (Figure 3) Express your answer in terms of I, 21, MO, A, and dl. Recall that a component is a scalar, do not enter any unit vectors. View Available Hint(s) ΑΣΦ ? dB (0,0,0) =
дz дz 1. In the equation, x sin y - y cos z + xyz = 0, z is a function of x and y. Find and ду" дх D- 1) and o- (-11 1)
Consider the joint density function fX,Y,Z(x,y,z)=(x+y)e−zfX,Y,Z(x,y,z)=(x+y)e−z where 0<x<1,0<y<1,z>0. b) Find the marginal density of (x,z) : fX,Z(x,z). For your spot check, please report fX,Z(1/2,1/4)+fX,Z(1/4,1/2)+fX,Z(1/2,2) rounded to 3 decimal places.
Please answer 1 and 2! I'm very short on time and need immediate help on those problems! Would greatly appreciate the help! Thanks:) 1. A y = 0,2-0, z = 1, y Find its inass if the mass density is given by ơ(z, y, z)-xyz. 1-z. solid E is bounded by live plans ::: 0、 2. A solid E, is bounded by the cone z = 4VT21 and the plane z = 4. Find the mass of E if the...
The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...
Problem 2 - Three Continuous Random Variables Suppose X,Y,Z have joint pdf given by fx,YZ(xgz) = k xyz if 0 S$ 1,0 rS 1,0 25 1 ) and fxyZ(x,y,z) = 0, otherwise. (a) Find k so that fxyz(x.yz) is a genuine probability density function. (b) Are X,Y,Z independent? (c) Find PXs 1/2, Y s 1/3, Z s1/4). (d) Find the marginal pdf fxy(x.y). (e) Find the marginal pdf fx(x). Problem 2 - Three Continuous Random Variables Suppose X,Y,Z have joint...
6. (10 points) (a) (6 points) The gradient of the function o(x, y, z) at (1,2,3) is the vector (2, 1, 1) and g(1,2,3) = 1 (1) (2 points) Find the equation of the tangent plane of the level surface g(r, y, z) = 1 at (1,2,3) (ii) (2 points) Find the maximum rate of change of g(x, y, z) at (1, 2, 3). hax. rarte ot change: 23 14 (iii) (2 points) Find the rate of change of g...
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f : R3 +R be the function defined by f(x, y, z) = 1 - 2y + 3z. Using the change of variables theorem, rewrite Is f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
– 2, A solid E with density p(x, y, z) = y' is bounded by the planes x = 0, x = 1, y = y = 2,2 = – 2 and z = 2. Find the center of mass of E. Preview