Sam has 480 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. As shown below, one of the sides has length x (in meters). Side along house x (a) Find a function that gives the area 4 (x) of the garden (in square meters) in terms of x. 4(x) = (b) What side length x gives the maximum area that the garden can have? Side length x : meters (c) What is the maximum area that the garden can have? Maximum area: square meters 4
Sam has 480 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. As shown below, one of the sides has length x (in meters). Side along house x (a) Find a function that gives the area 4 (x) of the garden (in square meters) in terms of x. 4(x) = (b) What side length x gives the maximum area that the garden can have? Side length x : meters (c) What is the maximum area that the garden can have? Maximum area: square meters 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Sam has 480 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing.
As shown below, one of the sides has length \( x \) (in meters).
[Diagram: A rectangular garden with one side labeled as “Side along house” and another side labeled with “x”.]
(a) Find a function that gives the area \( A(x) \) of the garden (in square meters) in terms of \( x \).
\[ A(x) = \, \]
(b) What side length \( x \) gives the maximum area that the garden can have?
Side length \( x \): \[ \] meters
(c) What is the maximum area that the garden can have?
Maximum area: \[ \] square meters](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd16b7a0c-3d0d-4ea9-8044-9d6208075991%2Fecf7970b-8594-41e8-a0ee-69debf0a6d74%2Flqh5bcv_processed.png&w=3840&q=75)
Transcribed Image Text:Sam has 480 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing.
As shown below, one of the sides has length \( x \) (in meters).
[Diagram: A rectangular garden with one side labeled as “Side along house” and another side labeled with “x”.]
(a) Find a function that gives the area \( A(x) \) of the garden (in square meters) in terms of \( x \).
\[ A(x) = \, \]
(b) What side length \( x \) gives the maximum area that the garden can have?
Side length \( x \): \[ \] meters
(c) What is the maximum area that the garden can have?
Maximum area: \[ \] square meters
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