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Bellwork:

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PRE CALCULUS Section 4.7 Forming Functions from Verbal Descriptions

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**Manufacturing and Volume/Rate Problems**

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Objective To form a function of one variable from a verbal description and, when appropriate, to determine the minimum or maximum value of the function.

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**A box with a square base and top has a**

volume of 10 meters cubed. The material for the base costs $12 per square meter and the material for the sides costs $8 per square meter. Express the cost C of the material as a function of the width.

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**Water flows into a conical tank 100 cm**

wide and 250 cm deep at a rate of 40 cubic centimeters per second. Find the volume in terms of the height of the tank and the height in terms of the time.

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**Water is flowing into a cylindrical tank**

at 6 cubic meters per second. The radius is 20 meters and the height of the tank is 100 meters. Find the volume in terms of the height of the tank and the height in terms of the time.

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**P(x,y) is an arbitrary point on the parabola y = x2**

P(x,y) is an arbitrary point on the parabola y = x2. Express the distance, d, from P to the point A (2,1) as a function of the x-coordinate of P.

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Ticket to leave: A cylinder with no top has a volume of 20 m3. Express the total surface area of the box as a function of the radius, r, of the base.

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Bellwork Lesson 4.7 P Written Ex (1, 5, 7-12all)

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