Question

x(0) = -4, v(0) = 3, and a(0) = -0.5

the car changes its direction at the location x = 5.

a) if instead v(0) = 2.5, in which location does the car now change direction?

b) what v(0) will make the car change direction at x = 4?

Answer #1

Given a random variable X has the following pmf:
X
-1
0
1
P[X]
0.25
0.5
0.25
Define Y = X2 & W= Y+2.
Which one of the following statements is not true?
A) V[Y] = 0.25.
B) E[XY] = 0.
C) E[X3] = 0.
D) E[X+2] = 2.
E) E[Y+2] = 2.5.
F) E[W+2] = 4.5.
G) V[X+2] = 0.5.
H) V[W+2] = 0.25.
I) P[W=1] = 0.5
J) X and W are not independent.

Given a random variable X has the following pmf:
X
-1
0
1
P[X]
0.25
0.5
0.25
Define Y = X2 & W= Y+2.
Which one of the following statements is not true?
A) V[Y] = 0.25.
B) E[XY] = 0.
C) E[X3] = 0.
D) E[X+2] = 2.
E) E[Y+2] = 2.5.
F) E[W+2] = 4.5.
G) V[X+2] = 0.5.
H) V[W+2] = 0.25.
I) P[W=1] = 0.5
J) X and W are not independent.

Car A starts from rest and accelerates in the x-direction at 4
m/s^2 at the precise moment that it is passed by Car B traveling in
the same direction at a constant speed of 40 m/s. (Draw a free-body
diagram).
a) How long does it take Car A to catch Car B?
b) How far has Car A traveled when it catches Car B?
c) How fast is Car A traveling when it catches Car B?
...

4. (1 point) Consider the following pmf:
x = -2 0 3 5
P(X = x) 0.34 0.07 ? 0.21
What is the
E[
X 1 + X
]
5. (1 point) Screws produced by IKEA will be defective with
probability 0.01 independently of each other. What is the expected
number of screws to be defective in any given pack? Hint: you
should be able to recognize this distribution and use the result
from the Exercises at the end of...

Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and
?=3?+2?v=3i+2j.
A. Find the gradient of f.
∇?=∇f= ?+i+ ?j
Note: Your answers should be expressions of x and y; e.g. "3x -
4y"
B. Find the gradient of f at the point P.
(∇?)(?)=(∇f)(P)= ?+i+ ?j
Note: Your answers should be numbers
C. Find the directional derivative of f at P in the direction of
?v.
???=Duf=
D. Find the maximum rate of change of f at P.
E. Find the (unit) direction vector in which the maximum rate...

A uniform electric field of magnitude 260 V/m is directed in the
positive x direction. A +12.0 µC charge moves from the
origin to the point (x, y) = (20.0 cm, 50.0
cm).
(a) What is the change in the potential energy of the charge
field system?
______ J
(b) Through what potential difference does the charge move?
______ V
Full, detailed solutions please!

Given the set S = {(u,v): 0<= u<=4 and 0<= v<=3} and
the transformation T(u, v) = (x(u, v), y(u, v)) where x(u, v) = 4u
+ 5v and y(u, v) = 2u -3v,
graph the image R of S under the transformation T in the
xy-plan
and find the area of region R

Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5, −2, 8, 1).
Find the vector x that satisfies 2u − ||v||v = 3(w − 2x).

Consider the function:
f(x) = 0.5x if 0<x<1
f(x) = 0.5 if 1<x<2
f(x) =1.5-0.5x if 2<x<3
f(x) = 0 otherwise.
a. Show that this is a PDF.
b. Calculate P(x<2.5) and P(0.5<x<2).
c. Find the expected value and the median of this
distribution.

A car moves along a straight line with velocity, in feet/second,
given by
v(t)=35-5t for t≥0.
(a) With forward being the direction of positive
velocity, when is the car moving forward? Backward? Stopped?
The car is moving forward for
≤t<
.
The car is moving backward for t>
.
The car is not moving at the instant t=
.
(b) Does the car ever return to its starting
point? If so, when?
If the car never returns to its starting...

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