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 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.
Solution Summary: The author explains how to determine the maximum volume of a square box for various heights using the table given below.
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.
A research study in the year 2009 found that there were 2760 coyotes
in a given region. The coyote population declined at a rate of 5.8%
each year.
How many fewer coyotes were there in 2024 than in 2015?
Explain in at least one sentence how you solved the problem. Show
your work. Round your answer to the nearest whole number.
Answer the following questions related to the following matrix
A =
3
³).
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY