3. You wish to fence in a rectangular garden in your back yard, with one side of the garden against the house and that side unfenced (see the figure below). (a) Suppose you have 20 feet of fencing for the garden. Find the dimensions of the garden that yield the largest possible area A of the garden, as follows: i. For half of your group, write A as a function of x alone (without any y's), and note the domain of A. Then find the maximum value of the area A of the garden. ii. For the other half of your group, write A as a function of Y alone (without any r's), and note the domain of A. Then find the maximum value of the area A of the garden. iii. In a complete sentence, tell why the answer in i should be, or should not be, the same as the answer in (ii).
3. You wish to fence in a rectangular garden in your back yard, with one side of the garden against the house and that side unfenced (see the figure below). (a) Suppose you have 20 feet of fencing for the garden. Find the dimensions of the garden that yield the largest possible area A of the garden, as follows: i. For half of your group, write A as a function of x alone (without any y's), and note the domain of A. Then find the maximum value of the area A of the garden. ii. For the other half of your group, write A as a function of Y alone (without any r's), and note the domain of A. Then find the maximum value of the area A of the garden. iii. In a complete sentence, tell why the answer in i should be, or should not be, the same as the answer in (ii).
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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Transcribed Image Text:3. You wish to fence in a rectangular garden in your back yard, with one side of the garden against the
house and that side unfenced (see the figure below).
(a) Suppose you have 20 feet of fencing for the garden. Find the dimensions of the garden that yield
the largest possible area A of the garden, as follows:
i. For half of your group, write A as a function of x alone (without any y's), and note the domain
of A. Then find the maximum value of the area A of the garden.
ii. For the other half of your group, write A as a function of Y alone (without any x's), and note
the domain of A. Then find the maximum value of the area A of the garden.
iii. In a complete sentence, tell why the answer in i should be, or should not be, the same as the
answer in (ii).
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