A crossed belt connects a 16-centimeter pulley (x = 8-cm radius) on an electric motor with a 32-centimeter pulley (y = 16-cm radius) on a saw arbor, as shown in the figure below. The electric motor runs at 1,900 revolutions per minute. (a) Determine the number of revolutions per minute of the saw. rpm (b) How does crossing the belt affect the saw in relation to the motor? Crossing the belt ensures the direction of the saw and that of the motor are the same. Crossing the belt reverses the direction of the saw from that of the motor. 4 (c) Let L be the total length of the belt. Write L as a function of p, where is measured in radians. (Hint: Add the lengths of the straight sections of the belt and the length of the belt around each pulley.) L= What is the domain of the function? (Enter your answer using interval notation.) (d) Use a graphing utility to complete the table. (Round your answers to one decimal place.) 4 0.3 0.6 0.9 1.2 1.5 L (e) Use a graphing utility to graph the function over the appropriate domain. L 500 450 400 350 300 250 200 150 100 50 L 500 450 400 350 300 250 200 150 100 50 2/4 2/4 500 450 400 350 300 250 200 150 100 50 L 500 450 400 330 300 250 200 150 100 50 2/4 n/4 x/2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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A crossed belt connects a 16-centimeter pulley (x = 8-cm radius) on an electric motor with a 32-centimeter pulley (y = 16-cm radius) on a saw arbor, as shown in the figure below. The electric motor runs at 1,900 revolutions per minute.
(a) Determine the number of revolutions per minute of the saw.
rom
грm
(b) How does crossing the belt affect the saw in relation to the motor?
Crossing the belt ensures the direction of the saw and that of the motor are the same.
Crossing the belt reverses the direction of the saw from that of the motor.
(c) Let L be the total length of the belt. Write Las a function of , where e is measured in radians. (Hint: Add the lengths of the straight sections of the belt and the length of the belt around each pulley.)
L=
What is the domain of the function? (Enter your answer using interval notation.)
(d) Use a graphing utility to complete the table. (Round your answers to one decimal place.)
0.3
0.6
0.9
1.2
1.5
L
(e) Use a graphing utility to graph the function over the appropriate domain.
so0f
5o0
450
450
400
400
350
350
300
300
250
250
200
200
150
150
100
100
50
50
/2
5o0
500
450
450
400
400
350
350
300
300
250
250
200
200
150
150
100-
100
50
50
/2
Transcribed Image Text:A crossed belt connects a 16-centimeter pulley (x = 8-cm radius) on an electric motor with a 32-centimeter pulley (y = 16-cm radius) on a saw arbor, as shown in the figure below. The electric motor runs at 1,900 revolutions per minute. (a) Determine the number of revolutions per minute of the saw. rom грm (b) How does crossing the belt affect the saw in relation to the motor? Crossing the belt ensures the direction of the saw and that of the motor are the same. Crossing the belt reverses the direction of the saw from that of the motor. (c) Let L be the total length of the belt. Write Las a function of , where e is measured in radians. (Hint: Add the lengths of the straight sections of the belt and the length of the belt around each pulley.) L= What is the domain of the function? (Enter your answer using interval notation.) (d) Use a graphing utility to complete the table. (Round your answers to one decimal place.) 0.3 0.6 0.9 1.2 1.5 L (e) Use a graphing utility to graph the function over the appropriate domain. so0f 5o0 450 450 400 400 350 350 300 300 250 250 200 200 150 150 100 100 50 50 /2 5o0 500 450 450 400 400 350 350 300 300 250 250 200 200 150 150 100- 100 50 50 /2
(f) Find
lim
L.
9-(x/2)
(9) Use a geometric argument as the basis of a second method of finding this limit in part (f).
the length of the belt can be computed from the triangles formed.
As e
As - the entire length of the belt is wrapped completely around the pulleys with no straight sections.
As e-
the the belt is only connected to the larger pulley.
As e - the distance between the pulleys approaches o.
2
the the belt is only connected to the smaller pulley.
2
As e
(h) Find
lim
L.
Transcribed Image Text:(f) Find lim L. 9-(x/2) (9) Use a geometric argument as the basis of a second method of finding this limit in part (f). the length of the belt can be computed from the triangles formed. As e As - the entire length of the belt is wrapped completely around the pulleys with no straight sections. As e- the the belt is only connected to the larger pulley. As e - the distance between the pulleys approaches o. 2 the the belt is only connected to the smaller pulley. 2 As e (h) Find lim L.
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