A plane flies at a speed of 370 mph on a bearing of S 45 ° E. Relative to the ground, the plane's speed is measured as 345 mph with a true bearing of S 40 ° E. Rounding to the nearest whole unit, a. Express the velocity of the plane v p relative to the air in terms of i and j. b. Express the true velocity of the plane v T in terms of i and j. c. Express the velocity of the wind v w in terms of i and j and find the speed of the wind.
A plane flies at a speed of 370 mph on a bearing of S 45 ° E. Relative to the ground, the plane's speed is measured as 345 mph with a true bearing of S 40 ° E. Rounding to the nearest whole unit, a. Express the velocity of the plane v p relative to the air in terms of i and j. b. Express the true velocity of the plane v T in terms of i and j. c. Express the velocity of the wind v w in terms of i and j and find the speed of the wind.
Solution Summary: The author explains how the plane's velocity can be expressed as v_p=262i-262j relative to the air.
A plane flies at a speed of
370
mph on a bearing of S
45
°
E. Relative to the ground, the plane's speed is measured as
345
mph with a true bearing of S
40
°
E. Rounding to the nearest whole unit,
a. Express the velocity of the plane
v
p
relative to the air in terms of i and j.
b. Express the true velocity of the plane
v
T
in terms of i and j.
c. Express the velocity of the wind
v
w
in terms of i and j and find the speed of the wind.
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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