A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at an angle of 38 ° at point B The distance from A to B is 18 mi , and the distance from B to C is 12 mi (see the figure), if the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.
A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at an angle of 38 ° at point B The distance from A to B is 18 mi , and the distance from B to C is 12 mi (see the figure), if the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.
Solution Summary: The author calculates the distance travelled by the bicyclist from point A and C on off road by applying the cosine.
A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at an angle of
38
°
at point
B
The distance from
A
to
B
is
18
mi
, and the distance from
B
to
C
is
12
mi
(see the figure), if the bicyclist can ride
22
mph
on the paved roads and
6.8
mph
off-road, would it be faster for the bicyclist to ride from
A
to
C
on the paved roads or to ride a direct line from
A
to
C
off-road? Explain.
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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