An open box of maximum volume is to be made from a square piece of material, s = 18 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). s- 2x– х (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height x Length and Width Volume V 18 – 2(1) 1[18 – 2(1)]2 = 256 2 18 – 2(2) 2[18 – 2(2)]2 = 392 18 – 2(3) 3[18 – 2(3)]2 = 432 4 18 – 2(4) 4[18 – 2(4)]? = 400 %3D 18 – 2(5) 5[18 – 2(5)]? = = 320 18 – 2(6) 6[18 – 2(6)]? = 216 Use the table to guess the maximum volume. V = 432 (b) Write the volume V as a function of x. 0 < x < 9 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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![An open box of maximum volume is to be made from a square piece of material, s = 18 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
s- 2x–
х
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Height x
Length and Width
Volume V
18 – 2(1)
1[18 – 2(1)]2 = 256
2
18 – 2(2)
2[18 – 2(2)]2 = 392
18 – 2(3)
3[18 – 2(3)]2 = 432
4
18 – 2(4)
4[18 – 2(4)]? = 400
%3D
18 – 2(5)
5[18 – 2(5)]? =
= 320
18 – 2(6)
6[18 – 2(6)]? = 216
Use the table to guess the maximum volume.
V = 432
(b) Write the volume V as a function of x.
0 < x < 9
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F105a6b10-1479-49f6-854d-b98a0aa319bf%2F71d15337-5bed-49b7-90b8-f2f19bae3079%2F9ck6zd9.png&w=3840&q=75)
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