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A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. a) Give the restrictions on x. 0

A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. a) Give the restrictions on x. 0

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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I do not have a graphing calculator and have no idea how to finish part C of this problem. If someone could help me out that would be great! The second attachment is the instructions but I am a little lost. Any help appreciated.

Part C: For what value of x will volume be a maximum?

 

Homework: Sections 1.7, 1.8, 3.1, & 3.4 Homework - Applicati A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. a) Give the restrictions on x. 0<x< 5 (Simplify your answer.) b) Determine a function V that gives the volume of the box as a function of x. V(x) = 4x³-48x² +140x Question 6, 3.4.91-GC Part 3 of 5 c) For what value of x will the volume be a maximum? X≈ inches (Round to the nearest hundredth.) 14 LECHUS 10 inches
Transcribed Image Text:Homework: Sections 1.7, 1.8, 3.1, & 3.4 Homework - Applicati A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. a) Give the restrictions on x. 0<x< 5 (Simplify your answer.) b) Determine a function V that gives the volume of the box as a function of x. V(x) = 4x³-48x² +140x Question 6, 3.4.91-GC Part 3 of 5 c) For what value of x will the volume be a maximum? X≈ inches (Round to the nearest hundredth.) 14 LECHUS 10 inches
ctions 1.7, 1.8, 3.1, & 3.4 pplicati oard measur the sides. Let volume be t gives the Multiply the factors. dth.) View an example | 2 parts remaining A rectangular piece of cardboard measuring 14 in by 20 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. V(x) = (20-2x)(14-2x)(x) Question 6. 3.4.91-GC Print (...) View an example Get more help . Done GLECHES 20 ** V(x) = 4x³ - 68x²+280x c) For what value of x will the volume be a maximum? What is this maximum volume? To determine the maximum volume and the corresponding value for x, use a graphing calculator to graph V(x). Remember to set the window to show the restrictions on x. Use the 'calculate maximum' feature of your calculator to calculate the maximum value of the function. The maximum volume occurs when x is about 2.70 inches (rounded to the nearest hundredth). The maximum volume is approximately 339.01 cubic inches (rounded to the nearest hundredth). d) For what values of x will the volume be greater than 200 cubic inches? To determine the values of x for which the volume will be greater than 200 cubic inches, set V(x) > 200. 14 inches. MacBook Air A HW Score: 35.71%, 5 of 14 poi Continu Continue
Transcribed Image Text:ctions 1.7, 1.8, 3.1, & 3.4 pplicati oard measur the sides. Let volume be t gives the Multiply the factors. dth.) View an example | 2 parts remaining A rectangular piece of cardboard measuring 14 in by 20 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. V(x) = (20-2x)(14-2x)(x) Question 6. 3.4.91-GC Print (...) View an example Get more help . Done GLECHES 20 ** V(x) = 4x³ - 68x²+280x c) For what value of x will the volume be a maximum? What is this maximum volume? To determine the maximum volume and the corresponding value for x, use a graphing calculator to graph V(x). Remember to set the window to show the restrictions on x. Use the 'calculate maximum' feature of your calculator to calculate the maximum value of the function. The maximum volume occurs when x is about 2.70 inches (rounded to the nearest hundredth). The maximum volume is approximately 339.01 cubic inches (rounded to the nearest hundredth). d) For what values of x will the volume be greater than 200 cubic inches? To determine the values of x for which the volume will be greater than 200 cubic inches, set V(x) > 200. 14 inches. MacBook Air A HW Score: 35.71%, 5 of 14 poi Continu Continue
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