Solve this equation for y in terms of ï.
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
![Equation:
Solve this equation for y in terms of x.
y =
=
Find a formula for the volume V(x) in terms of ï.
V(x) = cubic inches
What is the domain of the function V? Note that must
be positive and y > x; consider how these facts, and
the constraint that girth plus length is 108 inches, limit
the possible values for x. Give your answer using
interval notation.
Domain:
Find the absolute maximum of the volume of the parcel
on the domain you established above and hence also
determine the dimensions of the box of greatest
volume.
Maximum Volume =
Optimal dimensions: x =
cubic inches
and y=
0
inches](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedffb35b-fe6b-47d0-af22-c8dea69753fa%2Fd785ec4e-8c37-4403-b1e4-980b57dc9410%2Fncsfmso_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Equation:
Solve this equation for y in terms of x.
y =
=
Find a formula for the volume V(x) in terms of ï.
V(x) = cubic inches
What is the domain of the function V? Note that must
be positive and y > x; consider how these facts, and
the constraint that girth plus length is 108 inches, limit
the possible values for x. Give your answer using
interval notation.
Domain:
Find the absolute maximum of the volume of the parcel
on the domain you established above and hence also
determine the dimensions of the box of greatest
volume.
Maximum Volume =
Optimal dimensions: x =
cubic inches
and y=
0
inches
![According to U.S. postal regulations, the girth plus the
length of a parcel sent by mail may not exceed 108
inches, where by "girth" we mean the perimeter of the
smallest end. What is the largest possible volume of a
rectangular parcel with a square end that can be sent
by mail? Such a package is shown below, with and
measured in inches. Assume . What are the dimensions
of the package of largest volume?
X
y
X
Find a formula for the volume of the parcel in terms of
and .
Volume =
cubic inches
The problem statement tells us that the parcel's girth
plus length may not exceed 108 inches. In order to
maximize volume, we assume that we will actually need
the girth plus length to equal 108 inches. What
equation does this produce involving and ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedffb35b-fe6b-47d0-af22-c8dea69753fa%2Fd785ec4e-8c37-4403-b1e4-980b57dc9410%2Fp5f3oz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:According to U.S. postal regulations, the girth plus the
length of a parcel sent by mail may not exceed 108
inches, where by "girth" we mean the perimeter of the
smallest end. What is the largest possible volume of a
rectangular parcel with a square end that can be sent
by mail? Such a package is shown below, with and
measured in inches. Assume . What are the dimensions
of the package of largest volume?
X
y
X
Find a formula for the volume of the parcel in terms of
and .
Volume =
cubic inches
The problem statement tells us that the parcel's girth
plus length may not exceed 108 inches. In order to
maximize volume, we assume that we will actually need
the girth plus length to equal 108 inches. What
equation does this produce involving and ?
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