You are designing a poster which has a border around the printed portion. The border is 2 inches wide on the left and right sides, and 3 inches wide on the top and bottom. The entire poster will be a total of 300 square inches, including the borders and printed portion combined. B Write an equation relating the dimensions x (the length of the left and right sides of the poster) and y (the width of the top and bottom sides of the poster) to the area A of the printed portion inside the border, using the fact that the whole area of the entire poster is a total of 300 square inches and the dimensions of the border are as described. The equation should have the form A = f (x, y), so the right side will have both x and y in it. Find A in terms of x, y, and dy using implicit differentiation. dy ? ● Solve for y in terms of using the area of the entire poster. What is da dA d.A . 4. What is the interpretation of in Replace y and in your expression for context? da da da • Now go back to your equation A = f (x, y) and replace y with the expression you found for it, to get A (x). dA Is the same when you differentiate A (x) as it was when you used the implicit da version? Reflect on this process. Find the values of x and y which maximize the printed area of the poster using the optimization process.
You are designing a poster which has a border around the printed portion. The border is 2 inches wide on the left and right sides, and 3 inches wide on the top and bottom. The entire poster will be a total of 300 square inches, including the borders and printed portion combined. B Write an equation relating the dimensions x (the length of the left and right sides of the poster) and y (the width of the top and bottom sides of the poster) to the area A of the printed portion inside the border, using the fact that the whole area of the entire poster is a total of 300 square inches and the dimensions of the border are as described. The equation should have the form A = f (x, y), so the right side will have both x and y in it. Find A in terms of x, y, and dy using implicit differentiation. dy ? ● Solve for y in terms of using the area of the entire poster. What is da dA d.A . 4. What is the interpretation of in Replace y and in your expression for context? da da da • Now go back to your equation A = f (x, y) and replace y with the expression you found for it, to get A (x). dA Is the same when you differentiate A (x) as it was when you used the implicit da version? Reflect on this process. Find the values of x and y which maximize the printed area of the poster using the optimization process.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 1ST
Related questions
Question
![You are designing a poster which has a border around the printed portion. The border is 2
inches wide on the left and right sides, and 3 inches wide on the top and bottom. The
entire poster will be a total of 300 square inches, including the borders and printed
portion combined.
Write an equation relating the dimensions (the length of the left and right sides of
the poster) and y (the width of the top and bottom sides of the poster) to the area A
of the printed portion inside the border, using the fact that the whole area of the
entire poster is a total of 300 square inches and the dimensions of the border are as
described. The equation should have the form A = f (x, y), so the right side will
have both and y in it.
dy
Find
in terms of x, y, and using implicit differentiation.
Solve for y in terms of using the area of the entire poster. What is
Replace y and in your expression for A. What is the interpretation of di
in
context?
Now go back to your equation A = f (x, y) and replace y with the expression you
found for it, to get A (x).
dA
Is the same when you differentiate A (x) as it was when you used the implicit
dr
version? Reflect on this process.
Find the values of x and y which maximize the printed area of the poster using the
optimization process.
DELL
FP
WA
dy?
Sign out](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2F7d120217-3a97-43b9-ad39-b78f57387c51%2Frfitvqg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:You are designing a poster which has a border around the printed portion. The border is 2
inches wide on the left and right sides, and 3 inches wide on the top and bottom. The
entire poster will be a total of 300 square inches, including the borders and printed
portion combined.
Write an equation relating the dimensions (the length of the left and right sides of
the poster) and y (the width of the top and bottom sides of the poster) to the area A
of the printed portion inside the border, using the fact that the whole area of the
entire poster is a total of 300 square inches and the dimensions of the border are as
described. The equation should have the form A = f (x, y), so the right side will
have both and y in it.
dy
Find
in terms of x, y, and using implicit differentiation.
Solve for y in terms of using the area of the entire poster. What is
Replace y and in your expression for A. What is the interpretation of di
in
context?
Now go back to your equation A = f (x, y) and replace y with the expression you
found for it, to get A (x).
dA
Is the same when you differentiate A (x) as it was when you used the implicit
dr
version? Reflect on this process.
Find the values of x and y which maximize the printed area of the poster using the
optimization process.
DELL
FP
WA
dy?
Sign out
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