Question: A closed box with a square base is required to have a volume of 10 cubic feet. (a) Build a model that expresses the amount

A closed box with a square base is required to have a volume of 10 cubic feet.

(a) Build a model that expresses the amount A of material used to make such a box as a function of the length x of a side of the square base.

(b) How much material is required for a base 1 foot by 1 foot?

(c) How much material is required for a base 2 feet by 2 feet?

(d) Graph A = A(x). For what value of x is A smallest?

Step by Step Solution

★★★★★

3.56 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b c d Graphing The ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000 cubic inches. See the illustration. (a) Express the surface area S of the box as a...

Q:

An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. (a) Express the...

Q:

A rectangular box with a square base is to be formed from a square piece of metal with 12-inch sides. If a square piece with side x is cut from each corner of the metal and the sides are folded up to...

Q:

An open box with a square base is required to have a volume of 10 cubic feet. (a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base....

Q:

1. Two triangular pens are built against a barn. Four hundred forty meters of fencing are to be used for the Barn three sides and the diagonal dividing fence (see figure). What dimensions maximize...

Q:

A rectangle is constructed with its base on the xaxis and its upper two vertices on the parabola y = 36 - x2. What are the dimensions of the rectangle with the maximum area? What is the area? The...

Q:

Complete parts a through c for the given function. 2 f(x)=x3(x1)on[1,1] (E a. Locate the critical point(s) of f. Select the correct choice below and. if necessary, fill in the answer box to complete...

Q:

\fa. A rectangular pen is built with one side against a barn If 1600 rn of fencing are used forthe other three sides ofthe pen, what dimensions maXimize the area ofthe pen? b. A rancher plans to make...

Q:

Can someone please help me with these questions. A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 490 cubic feet. The concrete for the base costs $8...

Q:

NYC College of Technology, CUNY Mathematics Department Spring 2023 MAT 1475 Final Exam Review Problems Revised by Prof. Kostadinov, Prof Africk and Prof Colucci: Fall 2010 through Fall 2015 Revised...

Q:

Laci Satterfield received a text message from Simon & Schuster, a publishing company, advertising a new Stephen King novel that it was publishing. Satterfield filed suit against Simon & Schuster for...

Q:

4. Determine whether or not each of the following statements is true or false, and justify your answer with a proof or a counterexample (a) (3 points) Srzdz (b) (3 points) If f is analytic at every...

Q:

In 1 9 6 0 the world s population was 3 . 0 4 billion people and was growing at the rate of 1 . 8 % per year. How many people were added to the world population that year?

Q:

=+8. Why is oligopolistic collusion more difficult when there is product variation than when the products of all firms are identical?

Q:

Assume that the random variable X is normally distributed, with mean = 50 and standard deviation = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding...

Q:

Assume that the random variable X is normally distributed, with mean = 50 and standard deviation = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding...

Q:

Assume that the random variable X is normally distributed, with mean = 50 and standard deviation = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding...

Q:

A corporation in a 40% tax bracket invests in the preferred stock of another company and earns a 5% pretax rate of return. An individual investor in a 20% tax bracket invests in the same preferred...

Q:

Notice this study used the verbal answer from each subject to measure the cocaine use status after six weeks of treatment. It has been argued that verbal reporting of cocaine use will cause subjects...

Q:

You have the following expectations about market returns and interest rates on T-bills: T-Bill Rate Market Rate Probability RF Probability MR 0.1 0.02 0.1 -0.1 0.2 0.03 0.3 0.15 0.4 0.06 0.3 0.33 0.2...