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Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A (r) = 2 2 + 16 r. What is the domain of A (r)? In other words, for which values of ris A (r) defined? Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e., to turn A as a function of r into r as a function of A. r(A) = Hints: . To calculate an inverse function, you need to solve for r. Here, you would start with A = 2 ² + 16 πr. This equation is the same as 2 r² + 16 πr – A = 0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula. 3 π+1 If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is x+1 more information in the Introduction to Mobius unit. ● Part c: If the surface area is 250 square inches, then what is the radius r? In other words, evaluate r (250). Round your answer to 2 decimal places.

Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A (r) = 2 2 + 16 r. What is the domain of A (r)? In other words, for which values of ris A (r) defined? Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e., to turn A as a function of r into r as a function of A. r(A) = Hints: . To calculate an inverse function, you need to solve for r. Here, you would start with A = 2 ² + 16 πr. This equation is the same as 2 r² + 16 πr – A = 0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula. 3 π+1 If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is x+1 more information in the Introduction to Mobius unit. ● Part c: If the surface area is 250 square inches, then what is the radius r? In other words, evaluate r (250). Round your answer to 2 decimal places.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.7: Inverse Functions
Problem 46SE: The circumference C of a circle is a function of its radius given by C(r)=2r. Express the radius of...
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Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A (r) = 2 77² +16 7r. What is the domain of A (r)? In other words, for which values of r is A (r) defined? Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e., to turn A as a function of r into r as a function of A. r (A) = Hints: • To calculate an inverse function, you need to solve for r. Here, you would start with A = 2 ² + 16 Tr. This equation is the same as 2 2 + 16 πr - A=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula. 3 π+1 If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is x+1 more information in the Introduction to Mobius unit. ● Part c: If the surface area is 250 square inches, then what is the radius r? In other words, evaluate r (250). Round your answer to 2 decimal places.
Transcribed Image Text:Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A (r) = 2 77² +16 7r. What is the domain of A (r)? In other words, for which values of r is A (r) defined? Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e., to turn A as a function of r into r as a function of A. r (A) = Hints: • To calculate an inverse function, you need to solve for r. Here, you would start with A = 2 ² + 16 Tr. This equation is the same as 2 2 + 16 πr - A=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula. 3 π+1 If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is x+1 more information in the Introduction to Mobius unit. ● Part c: If the surface area is 250 square inches, then what is the radius r? In other words, evaluate r (250). Round your answer to 2 decimal places.
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