Inbox X Secti X O (26) X webassign.net/web/Student/Assignment-Responses/submit?dep-23623652&tags=Dautosave#question4056429 6 An open box of maximum volume is to be made from a square piece of material, s = 36 inches on a side, by cutting equal squares fr s- 2r- х х (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Height, x Volume, V 36 – 2(1) 1[36 – 2(1)]² = 1156 2 36 – 2(2) 2[36 – 2(2)]² = 2048 %3D 36 – 2(3) 3[36 – 2(3)]² = 2700 36 – 2(4) 4[36 – 2(4)]? = 3136 %3D 36 – 2(5) 5[36 – 2(5)]² = 3380 6. 36 – 2(6) 6[36 – 2(6)]² = 3456 Use the table to guess the maximum volume. V = x (36-2x) ^2 X Your answer cannot be understood or graded. More Information %3D Enter a number. (b) Write the volume V as a function of x. V= 0 < x < 18 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = 24,24,6 X Your answer cannot be understood or graded. More Information %3D (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. Section 4.3 - In..pdf MAC 2311 - Q1...pdf Section 4.4 -C....pdf Section 4.6 - A....pdf Section 4.7 - O MacBook Pro DII F1 F2 F3 F4 F5 F6 F7 F8 F9 2$ & 4 8. Q т 1. 3. 4, -s-2r-
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Did I do the Volume right and what does it mean to be a function of x
![Inbox X
Secti X
O (26) X
webassign.net/web/Student/Assignment-Responses/submit?dep-23623652&tags=Dautosave#question4056429 6
An open box of maximum volume is to be made from a square piece of material, s = 36 inches on a side, by cutting equal squares fr
s- 2r-
х
х
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
Height, x
Volume, V
36 – 2(1)
1[36 – 2(1)]² = 1156
2
36 – 2(2)
2[36 – 2(2)]² = 2048
%3D
36 – 2(3) 3[36 – 2(3)]² = 2700
36 – 2(4) 4[36 – 2(4)]? = 3136
%3D
36 – 2(5) 5[36 – 2(5)]² = 3380
6.
36 – 2(6) 6[36 – 2(6)]² = 3456
Use the table to guess the maximum volume.
V = x (36-2x) ^2 X Your answer cannot be understood or graded. More Information
%3D
Enter a number.
(b) Write the volume V as a function of x.
V=
0 < x < 18
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
V = 24,24,6
X Your answer cannot be understood or graded. More Information
%3D
(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
Section 4.3 - In..pdf
MAC 2311 - Q1...pdf
Section 4.4 -C....pdf
Section 4.6 - A....pdf
Section 4.7 - O
MacBook Pro
DII
F1
F2
F3
F4
F5
F6
F7
F8
F9
2$
&
4
8.
Q
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1.
3.
4,
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