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.
Listen
A falling object travels a distance given by the formula d = 6t + 9t2 where d is in feet
and t is the time in seconds. How many seconds will it take for the object to travel
112 feet? Round answer to 2 decimal places. (Write the number, not the units).
Your Answer:
Solve by the quadratic formula or completing the square to obtain exact solutions.
2
e
104
OA) -16±3√6
B) 8±√10
O c) -8±√10
OD) 8±3√√6
U
Question 14 (1 point)
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The frame on a picture is 18 in by 22 in outside and is of uniform width. Using
algebraic methods, what is the width of the frame if the inner area of the picture
shown is 250 in²2? Write answer to 2 decimal places. (Write the number with no
units).
18 in
Your Answer:
22 in
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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