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3. Scooby Inc. plans on producing the packaging of Scooby Snacks in the shape of a triangular prism with a rectangular base. The height is given to be 12x while the triangular base is 10x. Furthermore, the packaging has a volume of 11, 520 cm³. An illustration of the figure can be seen below. 12 10 (FIGURE VOT DRAKA TO SCALE: (a) Suppose that the the length of the box is given as l cm. Find e in terms of x. (b) Formulate an expression for the surface area A of the box in terms of x. (c) Suppose that Selena, an employee of Scooby Inc., wants to know whether the area of the packaging can be optimized. Use calculus to determine whether A is a maximum or a minimum, and find the value of x when this occurs.

3. Scooby Inc. plans on producing the packaging of Scooby Snacks in the shape of a triangular prism with a rectangular base. The height is given to be 12x while the triangular base is 10x. Furthermore, the packaging has a volume of 11, 520 cm³. An illustration of the figure can be seen below. 12 10 (FIGURE VOT DRAKA TO SCALE: (a) Suppose that the the length of the box is given as l cm. Find e in terms of x. (b) Formulate an expression for the surface area A of the box in terms of x. (c) Suppose that Selena, an employee of Scooby Inc., wants to know whether the area of the packaging can be optimized. Use calculus to determine whether A is a maximum or a minimum, and find the value of x when this occurs.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 25A
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3. Scooby Inc. plans on producing the packaging of Scooby Snacks in the shape of a triangular prism with a rectangular base. The height is given to be 12x while the triangular base is 10x. Furthermore, the packaging has a volume of 11, 520 cm³. An illustration of the figure can be seen below. 12 10 (FIGURE VOT DRAKA TO SCALE: (a) Suppose that the the length of the box is given as l cm. Find e in terms of x. (b) Formulate an expression for the surface area A of the box in terms of x. (c) Suppose that Selena, an employee of Scooby Inc., wants to know whether the area of the packaging can be optimized. Use calculus to determine whether A is a maximum or a minimum, and find the value of x when this occurs.
Transcribed Image Text:3. Scooby Inc. plans on producing the packaging of Scooby Snacks in the shape of a triangular prism with a rectangular base. The height is given to be 12x while the triangular base is 10x. Furthermore, the packaging has a volume of 11, 520 cm³. An illustration of the figure can be seen below. 12 10 (FIGURE VOT DRAKA TO SCALE: (a) Suppose that the the length of the box is given as l cm. Find e in terms of x. (b) Formulate an expression for the surface area A of the box in terms of x. (c) Suppose that Selena, an employee of Scooby Inc., wants to know whether the area of the packaging can be optimized. Use calculus to determine whether A is a maximum or a minimum, and find the value of x when this occurs.
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