Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting a square from each corner. The sides of the rectangular tinplate are in a ratio p:q. Consider a rectangle where one side is twice the length of the other (i.e. p: q = 2:1). Using your (a) process and findings from Part B, determine the exact value of x that gives the maximum volume for this cake tin. (b) Repeat this process for a rectangular tinplate in the ratio 3:1. (c) Explore rectangular tinplate with sides in at least two other ratios. Hint: Change the value of both p and q, and determine exact solutions for x.
Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting a square from each corner. The sides of the rectangular tinplate are in a ratio p:q. Consider a rectangle where one side is twice the length of the other (i.e. p: q = 2:1). Using your (a) process and findings from Part B, determine the exact value of x that gives the maximum volume for this cake tin. (b) Repeat this process for a rectangular tinplate in the ratio 3:1. (c) Explore rectangular tinplate with sides in at least two other ratios. Hint: Change the value of both p and q, and determine exact solutions for x.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.3: Modeling Data With Linear Functions
Problem 21E
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Transcribed Image Text:Part C (Rectangular Cake Tins):
Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting a square
from each corner. The sides of the rectangular tinplate are in a ratio p:q.
(а)
Consider a rectangle where one side is twice the length of the other (i.e. p: q = 2:1). Using your
process and findings from Part B, determine the exact value of x that gives the maximum volume for
this cake tin.
(b)
Repeat this process for a rectangular tinplate in the ratio 3:1.
(c)
Explore rectangular tinplate with sides in at least two other ratios.
Hint: Change the value of both p and q, and determine exact solutions for x.
(d)
Develop a conjecture about the relationship between x (the cut to be made for the square) and the
length of each side of the rectangle tinplate (p and q) such that the cake tin has a maximum volume.
Show sufficient working to support your conjecture.
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