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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. (a) 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. Explore rectangular tinplate with sides in at least two other ratios. (c) Hint: Change the value of both p and q, and determine exact solutions for x. (d) Develop a coniecture 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.

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. (a) 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. Explore rectangular tinplate with sides in at least two other ratios. (c) Hint: Change the value of both p and q, and determine exact solutions for x. (d) Develop a coniecture 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.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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part c question b and c pls

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.
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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