Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.
Using the Laplace transform, solve the initial value problem 8. y(0)-0. y" + 4y-sint-u2" sin(t-2r), y(0)-0,
5. (50pt) X and Y are continuous random variables with pdf f(x, y) 2r for 0 < x y < 1, and f(x,y) = 0 otherwise. Find the conditional expectation of Y given X = z.
Find the area of the region enclosed by the curves: x = -sec^2 y, x = sec^2 y, y = 0, y = pi/4 Using the method of cylindrical shells to find the volume of the solid that results when the region enclosed by the curves is revolved around the y axis. y = sqrt (x+1), y = 1, x = 1 y = 3 sqrt x, y =0, x =1 Find the volume of the solid that results when...
A particle travels along the circular path x2 +y-r, when the time t = 0 the particle it's at-r meter and y =0 m. If the y components of the particle's velocity is Vy 2r cos2t, determine: (a) the x and y components of its acceleration at any instant. (b) Draw the trajectory with the vector velocity and acceleration at t = π/4 sec. (c) calculate the average vector velocity between 0 and t/4 sec. (d) the distance travelled when...
1.Find the general solution to the following ODE's a). y'' +y= sec^2t b). x^2y'' +3xy'+3y=0
aercise 6.43. Let the random variables X, Y have joint density function 2r y + vy, ifo<r< 1 and 0< fx,y(x, y) 0, else. Let T = min(X, Y) and V max(X,Y). Assuming that T, V are jointly ontinuous, find their joint density function. Hint. Look at Example 6.40.
aercise 6.43. Let the random variables X, Y have joint density function 2r y + vy, ifo
2. For this differential equation y"(t) - 6y'(t) + 15y(t) = 2r(t), determine (4 points) a) Transfer function b) The poles and zeros of the transfer function c) Given that r(t) = sin(3t),y(0) = -1, y'(0) = -4, find y(t) using partial fraction expansion
Solve e^x dy/dx = x sec (y) y (0) = pi
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0 < z < i, zero elsewhere, be the pdf of X. (a) Compute E(1/X). (b) Find the edf and the pdf of Y 1/X c) Compute E(Y) and compare this result with the answer obtained in Part (a).
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0