30. Shipping Packages The U.S. Postal Service will accept abox for domestic shipment only if the sum of its length and girth(distance around), as shown in the figure, does not exceed 108 in.What dimensions will give a box with a square end the largestpossible volume?Girth = Distancearound hereLengthSquare end

Let b be length of the box and a be the length of the side of the square. We know that :…

Answered: 30. Shipping Packages The U.S. Postal…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section1.4: Quadratic Equations And Applications

Problem 106E: Dimensions of a Garden A gardener has 100 meters of fencing to enclose two adjacent rectangular...

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Similar questions

Determine dimensions A, B, C, D, E, F, and G of the plate in Figure 2-5. Reduce to lowest terms where necessary. All dimensions are in inches. A = ______. B = ______. C = ______. D = ______. E = ______. F = ______. G = ______.
Enclosing a field You have 16 miles of fence that you will use to enclose a rectangle field. a.Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 3 miles and length 5 miles. What is the area of this rectangle? b.Draw a picture to show that you can arrange the 16 miles fence into a rectangle of width 2 miles and length 6 miles. What is the area of this rectangle? c.The first two parts of this exercise are designed to show you that you can get different areas for the rectangle of the sane perimeter, 16 miles. In general, if you arrange the 16 miles of fence into a rectangle of width w miles, then it will enclose an area of A=w8-w square miles. iMake a graph of the area enclosed as a function of w, and explain what the graph is showing. iiWhat width w should you use to enclose the most area? iiiWhat is the length of the maximum-area rectangle that you made, and what kind of figure do you have?
Width of a Lawn A factory is to be built on a lot measuring 180 ft by 240 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be, and what are the dimensions of the factory?
Dimensions of a Garden A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens (see figure). The gardener wants the enclosed area to be 350 square meters. What dimensions should the gardener use to obtain this area ?
Forming a pen We want to form a rectangle pen of area 100 square feet. One side of the pen is to be formed by an existing buliding and the other three sides by a fence see Figure 2.106. Let W be the length, in feet, of the sides of the rectangle perpendicular to the buliding, and let L be the length, in feet, of the other side. Figure 2.106 a.Find a formula for the total amount of fence needed in terms of W and L b. Express, as an equation involving W and L, the requirement that the area be 100 square feet. c.Solve the equation you found in part b for L. d.Use your answers to parts a and c to find a formula for F, the total amount, in feet, of fence needed, as a function of W alone. e.Make a graph of F versus W. f.Determine the dimension of the rectangle that requires a minimum amount of fence.

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