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.
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter8: Rational Expressions And Equations
Section8.9: Use Direct And Inverse Variation
Problem 8.175TI: The distance that Brad travels varies directly with the time spent traveling. Brad travelled 660...
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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?
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