Exam (elaborations)
Word Problems
- Course
- Institution
step by step solution with explanation
[Show more]
Seller
Follow
roneilalgara
Content preview
A piece of rope that is 18 feet long is cut into pieces. One piece is used to form a circle and theother used to form a square. Write a function f representing the area of the circle as a function
of the length of one side of the square s.
Hint : If C is the diameter of the circle and P is the perimeter of the square, then C + P = 18.
Answer
f(s) = (9-2s)2/π , the area of the circle as a function of the length of one side of the
square.
Explanation
Let
Length of the rope= 18 ft
C = circumference of circle
P = perimeter of square
s = side of the square
r = radius of the circle
Required
f(s) = ? , Area of circle as a function of the length of one side of the square
Solution
C = 2πr , circumference of a circle
P = 4s , perimeter of a square
C+P = 18 ; substitute the formulas
2πr + 4s = 18 ; get the expression for radius,r ;
2πr = 18-4s
r = (18-4s)/2π ; simplifying by dividing by 2
r = (9-2s)/π >>equation 1
Solve for the area of circle as a function of the length of one side of the square, f(s) ;
f(s) = πr2 ; substitute equation 1 to the r
= π((9-2s)/π))2
= π (9-2s)2/π2
= π (81-36s+4s2)/π2
f(s) = (81-36s+4s2)/π
f(s) = (9-2s)2/π , the area of the circle as a function of the length of one side of the
square.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller roneilalgara. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75323 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now