An open box is to be made from a square piece of material, 36 centimeters on a side by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). 36 - 2x (a) Determine which of the following functions V(x) represents the volume of the box. Ov(x) = x(36 - 2x)² Ov(x) = x²(36 - 2x)² Ov(x) = x²(36 - 2x) Ov(x) = (36 - 2x)² O v(x) = x(36 - 2x) (b) Determine the domain of the function V. 0 cm < x < 6 cm O x > 36 cm 0 cm < x < 18 cm. O x < 18 cm O 0 cm < x < 36 cm (c) Use the table feature of a graphing utility to create a table that shows various box heights x and the corresponding volumes V. (Fill in the table below.) Box Height, x Box Volume, V 1 cm cm³ cm3 cm3 2 cm 3 cm 4 cm 5 cm 6 cm 7 cm cm3 cm3 cm³ cm³ Use the table to estimate a range of dimensions within which the maximum volume is produced. The x-value is between 1 cm and 3 cm. The x-value is between 3 cm and 5 cm. The x-value is between 5 cm and 7 cm.
An open box is to be made from a square piece of material, 36 centimeters on a side by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). 36 - 2x (a) Determine which of the following functions V(x) represents the volume of the box. Ov(x) = x(36 - 2x)² Ov(x) = x²(36 - 2x)² Ov(x) = x²(36 - 2x) Ov(x) = (36 - 2x)² O v(x) = x(36 - 2x) (b) Determine the domain of the function V. 0 cm < x < 6 cm O x > 36 cm 0 cm < x < 18 cm. O x < 18 cm O 0 cm < x < 36 cm (c) Use the table feature of a graphing utility to create a table that shows various box heights x and the corresponding volumes V. (Fill in the table below.) Box Height, x Box Volume, V 1 cm cm³ cm3 cm3 2 cm 3 cm 4 cm 5 cm 6 cm 7 cm cm3 cm3 cm³ cm³ Use the table to estimate a range of dimensions within which the maximum volume is produced. The x-value is between 1 cm and 3 cm. The x-value is between 3 cm and 5 cm. The x-value is between 5 cm and 7 cm.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
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Transcribed Image Text:An open box is to be made from a square piece of material, 36 centimeters on a side by cutting equal squares with sides of length
x from the corners and turning up the sides (see figure).
36 - 2x
(a) Determine which of the following functions V(x) represents the volume of the box.
Ov(x) = x(36 - 2x)²
Ov(x) = x²(36 - 2x)²
Ov(x) = x²(36 - 2x)
Ov(x) = (36 - 2x)²
O v(x) = x(36 - 2x)
(b) Determine the domain of the function V.
O 0 cm < x < 6 cm
O x > 36 cm
0 cm < x < 18 cm.
O x < 18 cm
O 0 cm < x < 36 cm
(c) Use the table feature of a graphing utility to create a table that shows various box heights x and the corresponding
volumes V. (Fill in the table below.)
Box Height, x Box Volume, V
1 cm
cm³
cm3
cm3
2 cm
3 cm
4 cm
5 cm
6 cm
7 cm
cm3
cm3
cm³
cm³
Use the table to estimate a range of dimensions within which the maximum volume is produced.
The x-value is between 1 cm and 3 cm.
The x-value is between 3 cm and 5 cm.
O The x-value is between 5 cm and 7 cm.
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