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.
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
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