Homework Help is Here – Start Your Trial Now!
Math
Calculus
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. (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. Develop a conjecture about the relationship between x (the cut to be made for the square) and the (d) length of each side of the rectangle tinplate Show sufficient working to support your conjecture. 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. (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. Develop a conjecture about the relationship between x (the cut to be made for the square) and the (d) length of each side of the rectangle tinplate Show sufficient working to support your conjecture. 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...
See similar textbooks
icon
Related questions
Question

part d 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.
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS