SIUES). r= radius Areas = ar h = height Area = h(2ar) Circumference 2nr Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can write that as A (r) = 2 rr² + 12 ar. 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 6 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 rr2 + 12 Tr. This equation is the same as 2 rr2 + 12 ar- 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 T+1 r+1 more information in the Introduction to Mobius unit. • If you want to type in in Mobius, in text mode you can type in (3*pi+1)(x+1). There is Part c: If the surface area is 125 square inches, then what is the radius r? In other words, evaluate r(125). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as v17.3, you could • Use a spreadsheet such as Microsoft Excel or OpenOffice Cale and type in =sqrt(17.3) • Use a browser to connect to the Internet and type in sqrt(17.3) into a search field • Use a calculator The radius is Number inches if the surface area is 125 square inches.
SIUES). r= radius Areas = ar h = height Area = h(2ar) Circumference 2nr Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can write that as A (r) = 2 rr² + 12 ar. 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 6 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 rr2 + 12 Tr. This equation is the same as 2 rr2 + 12 ar- 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 T+1 r+1 more information in the Introduction to Mobius unit. • If you want to type in in Mobius, in text mode you can type in (3*pi+1)(x+1). There is Part c: If the surface area is 125 square inches, then what is the radius r? In other words, evaluate r(125). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as v17.3, you could • Use a spreadsheet such as Microsoft Excel or OpenOffice Cale and type in =sqrt(17.3) • Use a browser to connect to the Internet and type in sqrt(17.3) into a search field • Use a calculator The radius is Number inches if the surface area is 125 square inches.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:SIdes).
r radius
Areas = nr
h height
Area = h(2xr)
Circumference
2ar
Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can
write that as A (r) = 2 rr² + 12 ar. 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 6 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 Tr2 + 12 Tr. This equation is the same as 2 rr2 + 12 rr - 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 п+1
r+1
• If you want to type in
in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is
more information in the Introduction to Mobius unit.
Part c: If the surface area is 125 square inches, then what is the radius r? In other words, eväluate
r (125). Round your answer to 2 decimal places.
Hint: To compute a numeric square root such as v17.3, you could
• Use a spreadsheet such as Microsoft Excel or OpenOffice Cale and type in =sqrt(17.3)
• Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
• Use a calculator
The radius is Number
inches if the surface area is 125 square inches.
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