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
in Word Problem Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

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

 

by Top Rated User (651k points)

Related questions

1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
83,029 questions
87,742 answers
1,973 comments
4,553 users