Question

In a process with continuous paper, the paper passes across three rollers of radii 3 inches, 4 inches, and 6 inches.

Diagram: https://imgur.com/a/VptgN

The centers of the three inch and six inch rollers are d inches apart, and the length of the arc in contact with the paper on the four inch roller is s inches.

a. use the law of cosines to write an equation giving the relationship betweeen d and theta

b. Write theta as a function of d

c. Complete the table (view the table in this link https://imgur.com/a/Fccd5

Answer 1

a) d²=(3+4)²+(4+6)²-2(3+4)(4+6)cosθ=49+100-140cosθ=149-140cosθ.

b) θ=arccos((149-d²)/140)

c) arc/circumference=angle/360; s/8π=(360-θ)/360 so s=(360-θ)π/45.

d (inches)	θ (degrees)	s (inches)
9	60.94	20.88
10	69.51	20.28
12	87.95	18.99
13	98.21	18.28
14	109.62	17.48
15	122.88	16.55
16	139.84	15.37