Using Stoke's Thm, find the work done by the vector field F(x,
y, z) = 〈z,...
Using Stoke's Thm, find the work done by the vector field F(x,
y, z) = 〈z, x, y〉, that moves an object along the triangle with
vertices P(1, 0, 0), Q(0, 1, 0), R(0, 0, 1), in a counterclockwise
manner, starting and ending at P.
1 point) Find the work done by F along different paths between
(1,0,1) and (1,1,0).
You...
1 point) Find the work done by F along different paths between
(1,0,1) and (1,1,0).
You might simplify your computation by writing F=G+H=∇g+H, so
that you have a decomposition ofFF into a conservative vector field
and a simpler non-conservative vector field.
F=〈e^(yz)+2y, xze^(yz)+zcos(y)−3z, xye^(yz)+sin(y)−2x〉
(a) The path is the straight line path between those two points.
(Hint: the answer is not 2, 4, or 0.)
Work is .
(b) The path consists of the line segment from (1,0,1) to the
origin,...
For each of the following vector fields F , decide whether it is
conservative or not...
For each of the following vector fields F , decide whether it is
conservative or not by computing the appropriate first order
partial derivatives. Type in a potential function f (that is, ∇?=?)
with ?(0,0)=0. If it is not conservative, type N. A.
?(?,?)=(6?−6?)?+(−6?+12?)? ?(?,?)= -6xsiny + y^2 B. ?(?,?)=3??+4??
?(?,?)= N C. ?(?,?)=(3sin?)?+(−12?+3?cos?)? ?(?,?)= 0 Note: Your
answers should be either expressions of x and y (e.g. "3xy + 2y"),
or the letter "N"
using matlab Write your own routine for Gaussian elimination
without any pivoting. Input for the routine...
using matlab Write your own routine for Gaussian elimination
without any pivoting. Input for the routine should consist of the
number (n) of equations and the augmented matrix. Output should be
the vector solution of the system. Test your code by using it to
solve the following two problems: a) x + y + w + z = 10, 2x + 3y +
w + 5z = 31, −x + y − 5w + 3z = −2, 3x + y...
For each of the
following vector fields F , decide whether it is
conservative or not...
For each of the
following vector fields F , decide whether it is
conservative or not by computing curl F . Type in
a potential function f (that is, ∇f=F∇f=F
). If it is not conservative, type N.
A.
F(x,y)=(−10x+3y)i+(3x+10y)jF(x,y)=(−10x+3y)i+(3x+10y)j
f(x,y)=f(x,y)=
B.
F(x,y)=−5yi−4xjF(x,y)=−5yi−4xj
f(x,y)=f(x,y)=
C.
F(x,y,z)=−5xi−4yj+kF(x,y,z)=−5xi−4yj+k
f(x,y,z)=f(x,y,z)=
D.
F(x,y)=(−5siny)i+(6y−5xcosy)jF(x,y)=(−5siny)i+(6y−5xcosy)j
f(x,y)=f(x,y)=
E.
F(x,y,z)=−5x2i+3y2j+5z2kF(x,y,z)=−5x2i+3y2j+5z2k
f(x,y,z)=f(x,y,z)=
Note: Your answers should be either expressions of x, y and z
(e.g. "3xy + 2yz"), or the letter "N"
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that...
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x,
y) ≥ 0 for all (x, y). Hint: find the minimum value of H.
(4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin
is a critical point for f which is a saddle point, even though on
any line through the origin, f has a local minimum at (0, 0)
Show work/reason for answer if possible
Q4. An insurance company offers its policyholders a number of...
Show work/reason for answer if possible
Q4. An insurance company offers its policyholders a number of
different premium payment options. For a randomly selected
policyholder, let X = the number of months between successive
payments. The CDF of X is given as follows:
F[x]=
0 x<2
0,2 2<=x<4
0,4 4<=x<=6
1 x>=6
Also let Y = Min [2X+1, 6]
Which one of the following is not true? Hint: Find the PMF of X
first, then PMF of Y....
Let f(x)=5−log(x+1), g(x)=x2−2x−4 and k(x)=5/(x−4).
(a) Find (fog)(x)(fog)(x) and its domain using the interval
notation.
(b)...
Let f(x)=5−log(x+1), g(x)=x2−2x−4 and k(x)=5/(x−4).
(a) Find (fog)(x)(fog)(x) and its domain using the interval
notation.
(b) Find the inverse of the function ff.
(c) Find the function g/kg/k and its domain using the interval
notation.
(d) Simplify the expression
[k(x+h)−k(x)]/h[k(x+h)−k(x)]/h.
Show work/reason for answer if possible
5. Consider X~ Normal (7, 32) independent of Y~ Normal...
Show work/reason for answer if possible
5. Consider X~ Normal (7, 32) independent of Y~ Normal (5, 22).
Which one of the following statements is not true?
A) E(X -Y) = 2
B) E(2X –Y+3) = 12
C) V(X +Y) = 32 +22
D) V(X -Y) = 32 +22
E) X+Y still a normal random variable
F) X -Y still a normal random variable
G) 3X is still a normal random variable
H) 3X+5 is still a normal random variable...