Software used to program video games often uses an origin at the top left of the display canvas. The positive x -axis is to the right and the positive y -axis is downward. Suppose that a player moves on a direct path from the origin to a point P with pixel location 135 , 200 . Then the player moves directly to point Q at a pixel location of 420 , 150 . a. Find the player's bearing from the origin to point P . Round to one-hundredth of a degree. b. Find the player's bearing from point P to point Q . Round to one-hundredth of a degree.
Software used to program video games often uses an origin at the top left of the display canvas. The positive x -axis is to the right and the positive y -axis is downward. Suppose that a player moves on a direct path from the origin to a point P with pixel location 135 , 200 . Then the player moves directly to point Q at a pixel location of 420 , 150 . a. Find the player's bearing from the origin to point P . Round to one-hundredth of a degree. b. Find the player's bearing from point P to point Q . Round to one-hundredth of a degree.
Solution Summary: The author calculates the bearing of the player at point P if the software that is used to program video game often uses an origin at the top left
Software used to program video games often uses an origin at the top left of the display canvas. The positive
x
-axis
is to the right and the positive
y
-axis
is downward. Suppose that a player moves on a direct path from the origin to a point
P
with pixel location
135
,
200
. Then the player moves directly to point
Q
at a pixel location of
420
,
150
.
a. Find the player's bearing from the origin to point
P
. Round to one-hundredth of a degree.
b. Find the player's bearing from point
P
to point
Q
. Round to one-hundredth of a degree.
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?
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