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).
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).
Solution Summary: The author explains the function V that represents the volume of the box, made from a square piece of material, 36 inches, by cutting equal squares with sides of length x from the corners.
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).
Solve questions by Course Name (Ordinary Differential Equations II 2)
please Solve questions by Course Name( Ordinary Differential Equations II 2)
InThe Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth.
Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth
from which the flash is visible? (Earth’s radius is approximately 4000 miles.)
Chapter 3 Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.