1) is already done in the second photo
2) a)
F = (G*m1*m2)*(1/r2)
F is y
(G*m1*m2) is m
and (1/r2) is x
b) F = (G*m2/r)*(m1)
F is y
(Gm2/r) is m
and (m1) is x
3)
linearize such that ‘ ‘ is the x in y=mx+c. For example look at photo 2. this is for graphing data F:mu wrt '...
2. Let Mx(t) = 1c' + 2t?c". Find the following: (b) Var(X). (c) If Y = X-2, show that the moment-generating function of Y is e-2tMx(t). (d) If W = 3X, show that the moment-generating function of W is MX(3). 7/3,5/9
help pleasee
ignore the first photo, i need help with number
2
4. Let F(x, y, z) = (e" cos(y) + yz, xz - e" sin(y),ry+z). Compute 5.F-ds , where c: [0, 1] → R is given by c(t) = (tet, arcsin(t),t +1) 4. Let F(x, y, z) = (e" cos(y) + yz, xz - e" sin(y),ry+z). Compute 5.F-ds , where c: [0, 1] → R is given by c(t) = (tet, arcsin(t),t +1)
28, 30, 36.
pi DIFFERENTIAL EQUATIONS CHAPTER 2 FIRST-ORDER DIFFERE dx - x = 2y2 y(t) = 5 RE Ri = E, i(0) = in. L. R. E, i, constants a = k(T – T.). TO) = To, k, Tm, T, constants 31. x + y = 4x + 1, y(1) = 8 32. y' + 4xy = rer? y(0) = -1 dy + y = ln x, y(1) = 10 dx 34. x(x + 1) + xy = 1,...
1. Suppose m,b,c E R. Prove: f(1) = mx + b is continuous at c. 2. Prove: f(x) = x3 is continuous at 5.
2, define m EXERCISE 3.32. For an arbitrary integer S.m = {(x,y, z) e R m y zm = 1}. (1) Prove that Sm is a regular surface. (2) Use a computer graphing application to plot Sm for several choics of m. What does Sm look like for large m?
2, define m EXERCISE 3.32. For an arbitrary integer S.m = {(x,y, z) e R m y zm = 1}. (1) Prove that Sm is a regular surface. (2) Use...
For the illustrative example discussed in Section C.10 the X
X and X
y
using the data in the deviation form are as follows:
X
X =
1,103,111.333 16,984
16,984 280
X
y =
955,099.333
14,854.000
a. Estimate β2 and β3.
b. How would you estimate β1?
c. Obtain the variance of βˆ
2 and βˆ
3 and their covariances.
d. Obtain R2 and R¯ 2 .
e. Comparing your results with those given in Section...
Use the given moment-generating function, Mx(t), to identify the distribution of the random variable, X in each of the following cases. (Specify the exact type of distribution and the value(s) of any relevant parameters(s): 1. (a) M(-3 (b) M() exp(2e -2) Ce) M T112t)3 (f) Mx(t) = ( 1-3t 10 ) (d) Mx(t)= exp(2t2_t) (e) Mx(t)= - m01 -2t)!
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
Example A.3 Surface normal vector. Let S be a surface that is represented by f(x, y, z) -c, where f is defined and differentiable in a space. Then, let C be a curve on S through a point P-Go, yo,Zo) on S, where C is represented by rt)[x(t), y(t), z(t)] with r(to) -[xo. Vo, zol. Since C lies on S, r(t) must satisfy f(x, y. z)-c, or f(x(t), y(t), z(t))-c. Show that vf is orthogonal to any tangent vector r'(t)...