Answered: The height of a hill is given by h(x,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
The cost of driving a car includes both fixed costs and mileage costs. Assume that it costs $178.40 per month for insurance and car payments and $0.26 per mile for gasoline, oil, and routine maintenance. (a) Find values for m and b so that y = mx + b models the monthly cost of driving the car x miles. (b) What does the value of b represent?
The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: y(x) = -0.002x2+0.7x+7 where y = vertical position of football relative to the ground (ft) x = horizontal position of football relative to launch position (ft) How high above the ground is the football as it leaves the quarterback’s hand?

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The height of a hill is given by h(x, y) = 2xy- 3x2- 4y2- 18x+ 28y+12. Here, x is the distance east and y is the distance north of the origin, both measured in meters. A function like this is often used to produce topographic maps. Where is the top of the hill and how high is it?