3. The diagram on the right shows an open box with a squarebase of side x cm and a height of h cm. The box is madefrom a piece of cardboard with an area of 75 cm².(a) Show that the volume of the box, V cm², is given byV= (75x – x).h cmx cmx cm(b) Find the value of x such that the volume, V is maximumand also the maximum volume of the box.

a)Area of the box (A)=x.x+2xh+2xhA=x2+4xh75=x2+4xh [Since A=75 cm2]75-x2=4xhh=14x75-x2Volume of the…

Answered: 3. The diagram on the right shows an…

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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Similar questions

Your company are designing metal trays. They will be made out of a sheet of metal which has a perimeter of 80 cm. The box is made by removing squares of side y = 2 cm from each corner of the rectangle and then folding in the sides. A net is shown below. Your company wants to maximise the capacity of these trays and wants you to investigate what value of x will give you the maximum volume. Investigate how changing the size of the square at each corner would affect the capacity of the tray and investigate the value of y which would give you maximum volume. Y cm x cm
The total revenue for a product can be calculated as the area under the demand curve. Suppose that the demand curve for a certain wine (in dollars per liter) is given by the following, where is the demand in liters. Estimate the total revenue using rectangles of width 10 ters D(4) = ² -10q+267 for 0 sqs50 The approximate revenue using left endpoints is The approximate revenue using right endpoints is $ The approximate revenue using the average is $
The cost of toducing X units of a Product is modeled by C= 240+ 75X-360 Inx, xz\. Find the minimum auerage cost.
2. A closed box has a square base with side length l feet and height h feet. Given that the volume of the box is 29 cubic feet, express the surface area of the box in terms of l only. S(1) = 212 + 1161³ 116 S(1) = 212 + S(1) = 212 + 1161 S(1) = 612 None of the above.
Your company are designing metal trays. They will be made out of a sheet of metalwhich has a perimeter of 80 cm. The box is made by removing squares of side y = 2cm from each corner of the rectangle and then folding in the sides. A net is shownbelow.● Your company wants to maximise the capacity of these trays and wants you toinvestigate what value of x will give you the maximum volume.● Investigate how changing the size of the square at each corner would affect thecapacity of the tray and investigate the value of y which would give youmaximum volume.

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