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39. An open top rectangular box with a square bottom has a volume of 120 cubic meters. Its bottom and sides are made from two different materials. It costs 10 dollars per square meter for the bottom material and 12 dollars per square meter for the sides. Determine a model for cost of materials as a function of w. 5760 11520 C(w)=10w² + (A) (C) C(w) = 20w² + C(w) = 10w² + W 5760 W (B) (D) C(w) = 20w² + W 1440 W (E) C(w)=10w² + W 1440 W h W

39. An open top rectangular box with a square bottom has a volume of 120 cubic meters. Its bottom and sides are made from two different materials. It costs 10 dollars per square meter for the bottom material and 12 dollars per square meter for the sides. Determine a model for cost of materials as a function of w. 5760 11520 C(w)=10w² + (A) (C) C(w) = 20w² + C(w) = 10w² + W 5760 W (B) (D) C(w) = 20w² + W 1440 W (E) C(w)=10w² + W 1440 W h W

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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**Problem 39.** **Text:** An open-top rectangular box with a square bottom has a volume of 120 cubic meters. Its bottom and sides are made from two different materials. It costs 10 dollars per square meter for the bottom material and 12 dollars per square meter for the sides. Determine a model for the cost of materials as a function of \( w \). **Multiple Choice Options:** - (A) \( C(w) = 20w^2 + \frac{5760}{w} \) - (B) \( C(w) = 10w^2 + \frac{11520}{w} \) - (C) \( C(w) = 10w^2 + \frac{5760}{w} \) - (D) \( C(w) = 20w^2 + \frac{1440}{w} \) - (E) \( C(w) = 10w^2 + \frac{1440}{w} \) **Diagram Explanation:** The diagram accompanying the problem shows an open-top rectangular box. The base of the box is square with side length \( w \). The height of the box is denoted by \( h \). To summarize: 1. The box is rectangular with a square bottom (width and breadth both are \( w \)). 2. The volume of the box is 120 cubic meters. 3. Material costs: - Bottom: 10 dollars per square meter. - Sides: 12 dollars per square meter.
Transcribed Image Text:**Problem 39.** **Text:** An open-top rectangular box with a square bottom has a volume of 120 cubic meters. Its bottom and sides are made from two different materials. It costs 10 dollars per square meter for the bottom material and 12 dollars per square meter for the sides. Determine a model for the cost of materials as a function of \( w \). **Multiple Choice Options:** - (A) \( C(w) = 20w^2 + \frac{5760}{w} \) - (B) \( C(w) = 10w^2 + \frac{11520}{w} \) - (C) \( C(w) = 10w^2 + \frac{5760}{w} \) - (D) \( C(w) = 20w^2 + \frac{1440}{w} \) - (E) \( C(w) = 10w^2 + \frac{1440}{w} \) **Diagram Explanation:** The diagram accompanying the problem shows an open-top rectangular box. The base of the box is square with side length \( w \). The height of the box is denoted by \( h \). To summarize: 1. The box is rectangular with a square bottom (width and breadth both are \( w \)). 2. The volume of the box is 120 cubic meters. 3. Material costs: - Bottom: 10 dollars per square meter. - Sides: 12 dollars per square meter.
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