# A popular model of carry-on luggage has a length that is 10 inches greater than its

## Problem 119 Chapter 5.2

Intermediate Algebra for College Students | 6th Edition

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Intermediate Algebra for College Students | 6th Edition

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Problem 119

A popular model of carry-on luggage has a length that is 10 inches greater than its depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 40 inches. These conditions, with the assumption that this sum is 40 inches, can be modeled by a function that gives the volume of the luggage, V, in cubic inches, in terms of its depth, x, in inches. V(x) = x (x+10) [40-(x+x+10)] V(x) = x(x+10)(30-2x) V = olume depth length width: 40 (depth + length) a. Perform the multiplications in the formula for V(x) and express the formula in standard form. b. Use the functions formula from part (a) and the Leading Coefficient Test to determine the end behavior of its graph. c. Does the end behavior to the right make this function useful in modeling the volume of carry-on luggage as its depth continues to increase? d. Use the formula from part (a) to find V(10). Describe what this means in practical terms. e. The graph of the function modeling the volume of carry-on luggage is shown below. Identify your answer from part (d) as a point on the graph. x y 5 1 10 5 20 25 1000 2000 3000 1000 2000 25 20 15 10 5 y = V(x) f. Use the graph to describe a realistic domain, x, for the volume function, where x represents the depth of the carry-on luggage. Use interval notation to express this realistic domain.

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##### ISBN: 9780321758934

This full solution covers the following key subjects: . This expansive textbook survival guide covers 74 chapters, and 7519 solutions. Since the solution to 119 from 5.2 chapter was answered, more than 205 students have viewed the full step-by-step answer. The answer to “A popular model of carry-on luggage has a length that is 10 inches greater than its depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 40 inches. These conditions, with the assumption that this sum is 40 inches, can be modeled by a function that gives the volume of the luggage, V, in cubic inches, in terms of its depth, x, in inches. V(x) = x (x+10) [40-(x+x+10)] V(x) = x(x+10)(30-2x) V = olume depth length width: 40 (depth + length) a. Perform the multiplications in the formula for V(x) and express the formula in standard form. b. Use the functions formula from part (a) and the Leading Coefficient Test to determine the end behavior of its graph. c. Does the end behavior to the right make this function useful in modeling the volume of carry-on luggage as its depth continues to increase? d. Use the formula from part (a) to find V(10). Describe what this means in practical terms. e. The graph of the function modeling the volume of carry-on luggage is shown below. Identify your answer from part (d) as a point on the graph. x y 5 1 10 5 20 25 1000 2000 3000 1000 2000 25 20 15 10 5 y = V(x) f. Use the graph to describe a realistic domain, x, for the volume function, where x represents the depth of the carry-on luggage. Use interval notation to express this realistic domain.” is broken down into a number of easy to follow steps, and 245 words. Intermediate Algebra for College Students was written by Patricia and is associated to the ISBN: 9780321758934. The full step-by-step solution to problem: 119 from chapter: 5.2 was answered by Patricia, our top Math solution expert on 03/14/18, 07:37PM. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6.

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