0 4 From a square piece of metal of side length 6 m, four squares are removed as shown in the diagram. The metal is folded along the dashed lines to form an open box with height x m. a Show that the volume of the box, V m³, is given by V = 4x³ - 24x² + 36x. b Find the value of x that gives the box its maximum volume and find the maximum volume. Exa
0 4 From a square piece of metal of side length 6 m, four squares are removed as shown in the diagram. The metal is folded along the dashed lines to form an open box with height x m. a Show that the volume of the box, V m³, is given by V = 4x³ - 24x² + 36x. b Find the value of x that gives the box its maximum volume and find the maximum volume. Exa
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.CR: Review Problem Set
Problem 24CR: An outpatient operating room charges each patient a fixed amount per surgery plus an amount per...
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Question 4
![Skillsheet
Example 8
Example 9
Example 10
the function y = f(x) is defined on an interval, such as [a, b] or [0, 0o), check the
values of the function at the endpoints.
Exercise 18E
1
A loop of string of length 200 cm is to be formed into a rectangle. Find the maximun
area of this rectangle.
2
Find the maximum value of the product of two numbers x and 10 - x.
3
Given that x + y = 2, calculate the minimum value of x² + y².
4 From a square piece of metal of side length 6 m,
four
squares
are removed as shown in the diagram. The metal is folded
along the dashed lines to form an open box with height x m.
a Show that the volume of the box, V m³, is given by
V = 4x³ - 24x² + 36x.
5
b Find the value of x that gives the box its maximum
volume and find the maximum volume.
A bank of earth has cross-section
as shown in the diagram. The curve
defining the bank has equation
1²
400
y =
(20-x) for x = [0, 20]
y (m) A
Example 12
9
Example 13 10
Example 14](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07afc3d5-1c08-4021-bc0e-c926bd50f7fc%2F9ab4b136-e8f6-451b-bb3a-f4900ca026de%2Fedwf4j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Skillsheet
Example 8
Example 9
Example 10
the function y = f(x) is defined on an interval, such as [a, b] or [0, 0o), check the
values of the function at the endpoints.
Exercise 18E
1
A loop of string of length 200 cm is to be formed into a rectangle. Find the maximun
area of this rectangle.
2
Find the maximum value of the product of two numbers x and 10 - x.
3
Given that x + y = 2, calculate the minimum value of x² + y².
4 From a square piece of metal of side length 6 m,
four
squares
are removed as shown in the diagram. The metal is folded
along the dashed lines to form an open box with height x m.
a Show that the volume of the box, V m³, is given by
V = 4x³ - 24x² + 36x.
5
b Find the value of x that gives the box its maximum
volume and find the maximum volume.
A bank of earth has cross-section
as shown in the diagram. The curve
defining the bank has equation
1²
400
y =
(20-x) for x = [0, 20]
y (m) A
Example 12
9
Example 13 10
Example 14
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