Suppose that the x - and y -axes are rotated 45 ° about the origin to form the x ' - and y ' -axes . Given P − 4 , 2 in the x y -plane, find the coordinate of P in the x ' y ' -plane .
Suppose that the x - and y -axes are rotated 45 ° about the origin to form the x ' - and y ' -axes . Given P − 4 , 2 in the x y -plane, find the coordinate of P in the x ' y ' -plane .
Solution Summary: The author calculates the coordinate of P in the xprime y
Suppose that the
x
-
and
y
-axes
are rotated
45
°
about the origin to form the
x
'
-
and
y
'
-axes
. Given
P
−
4
,
2
in the
x
y
-plane,
find the coordinate of
P
in the
x
'
y
'
-plane
.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.