Volume A small shelter for delicate plants is to be con-structed of thin plastic material. It will have square ends and arectangular top and back, with an open bottom and front, asshown in the figure. The total area of the four plastic sides is tobe 1200 in?.(a) Express the volume V of the shelter as a function of thedepth x.(b) Draw a graph of V.(c) What dimensions will maximize the volume of theshelter?y

a) Given The total area of the four plastic side is to be 1200in2 To express the volume V of the…

Answered: Volume A small shelter for delicate…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.CR: Chapter Review

Problem 26E

See similar textbooks

Similar questions

Volume of a Box An open box is to constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shownin figure. (a) Express the volume V of the box as a function of x. (b) What is the domain of V? (Use the fact that length and volume must be positive.) (c) Draw a graph of the function V, and use it to estimate the maximum volume for such a box.
Fluid Flow The intake pipe of a 100-gallon tank has a flow rate of 10 gallons per minute, and two drainpipes have flow rates of 5 gallons per minute each. The figure shows the volume V of fluid in the tank as a function of time t. Determine whether the input pipe and each drainpipe are open or closed in specific subintervals of the 1 hour of time shown in the graph. (There are many correct answers.)
Geometry You want to make an open box from a rectangular piece of material, 15 centimeters by 9 centimeters, by cutting equal squares from the corners and turning up the sides. (a) Let x represent the side length of each of the squares removed. Draw a diagram showing the squares removed from the original piece of material and the resulting dimensions of the open box. (b) Use the diagram to write the volume V of the box as a function of x. Determine the domain of the function. (c) Sketch the graph of the function and approximate the dimensions of the box that yield a maximum volume. (d) Find values of x such that V=56. Which of these values is a physical impossibility in the construction of the box? Explain.
Geometry The perimeter of a rectangle is 200meters. (a) Draw a diagram that gives a visual representation of the problem. Let x and y represent the length and width of the rectangle, respectively. (b) Write yas a function of x.Use the result to write the area A as a function of x. (c) Of all possible rectangles with perimeters of 200meters, find the dimensions of the one with the maximum area.
Maximum Volume An open box of maximum volume is made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). (a) The table shows the volumes V (in cubic centimeters) of the box for various heights x (in centimeters). Use the table to estimate the maximum volume. (b) Plot the points (x,V) from the table in part (a). Does the relation defined by the ordered pairs represent V as a function of x ? (c) Given that V is a function of x, write the function and determine its domain.
Maximum Area A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals (see figure). (a) Write the area A of the corrals as a function of x. (b) What dimensions produce a maximum enclosed area?
Geometry A rectangular package to be sent by a delivery service (see figure) has a combined length and girth (perimeter of a cross section) of 120 inches. (a) Use the diagram to write the volume V of the package as a function of x. (b) Use a graphing utility to graph the function and approximate the dimensions of the package that yield a maximum volume. (c) Find values of x such that V=13,500. Which of these values is a physical impossibility in the construction of the package? Explain.
Volume of a box A cardboard box has a square base, with each edge of the base having length x inches, as shown in the figure. The total length of all 12 edges of the box is 144 in. (a) Show that the volume of the box is given by the function V(x)=2x2(18x). (b) What is the domain of V? Use the fact that length and volume must be positive. (c) Draw a graph of the function V and use it to estimate the maxim volume for such a box.
Population Growth and Decline The graph shows the population P in a small industrial city from 1950 to 2000. Thevariable x represents the number of year since 1950. (a) Determine the intervals on which the function P isincreasing and on which it is decreasing. (b) What as the maximum population, and in what yearwas it attained? (c) Find the net change in the population P from 1970 to 1990.
Maximum Volume You construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). (a) Write a function V that represents the volume of the box. (b) Determine the domain of the function V . (c) Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V(x) . Use the table to estimate the dimensions that produce a maximum volume. (d) Use the graphing utility to graph V and use the graph to estimate the value of x for which V(x) is a maximum. Compare your result with that of part (c).

Recommended textbooks for you

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS