A box is formed by cutting squares from the four corners of a 7"-wide by 9"-long sheet of paper and folding up the sides. Let a represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches). a. Write a formula that expresses V in terms of x. V = 4x^3-32x^2+63x Preview %3D b. Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula for f. f(x) = 4x^3-32x^2+63x Preview

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 84E
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Reasoning IMathAS A X
O Rational Reasoning IMathAS A X
athas.rationalreasoning.net/assessment/showtest.php
A box is formed by cutting squares from the four corners of a 7"-wide by 9"-long sheet of paper and folding up the sides.
Let x represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches).
a. Write a formula that expresses V in terms of x.
V = 4x^3-32x^2+63x
Preview
b. Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula for
f.
(2)f
= 4x^3-32x^2+63x
Preview
c. What is the domain of f? Enter your answer as an interval. Hint.
(0,7/2)
Preview
d. What is the range of f? Enter your answer as an interval. Hint.
Tip: Use a graphing tool like www.Desmos.com to find the maximum volume possible.
Preview
no answer given
Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
Box 2: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
Box 3: Enter vour answer using interval notation. Example: [2.5).
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Transcribed Image Text:イ * 00 .3 Tab Window Help Edit View History Bookmarks People Reasoning IMathAS A X O Rational Reasoning IMathAS A X athas.rationalreasoning.net/assessment/showtest.php A box is formed by cutting squares from the four corners of a 7"-wide by 9"-long sheet of paper and folding up the sides. Let x represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches). a. Write a formula that expresses V in terms of x. V = 4x^3-32x^2+63x Preview b. Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula for f. (2)f = 4x^3-32x^2+63x Preview c. What is the domain of f? Enter your answer as an interval. Hint. (0,7/2) Preview d. What is the range of f? Enter your answer as an interval. Hint. Tip: Use a graphing tool like www.Desmos.com to find the maximum volume possible. Preview no answer given Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 2: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 3: Enter vour answer using interval notation. Example: [2.5). tv MacBook Pro G Search or type URL ( 23 & 2$ V ) 4. 5. 9. R M P.
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