7. A football is kicked from a height of 0.5 m. The height of the footballis modelled by the function h(t) = -5t² + 18t+ 0.5, where t istime in seconds and h(t) is height in metres.a) Graph the function for reasonable values of t.b)Explain why the values you chose for t in part (a) are reasonable.c) What is the maximum height of the football?d)At what time does the football reach the maximum height?For how many seconds is the football in the air?f) Express the domain and range in set notation.e)

Answered: Image /qna-images/answer/2988b6e0-04a9-4f41-8960-a9c5f5c7dc1f.jpg

Answered: 7. A football is kicked from a height…

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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Similar questions

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)
Can you help with 2 and 3, please?
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?
What is the maximum height of the ball and when does it hit the ground if a ball is thrown with a velocity of 40ft/s, its height (in feet) after t seconds is given by h(t)=-16t2+40t.
The digital music industry has been growing steadily since the 2000s. The function h represents the percentage of music sales that are digital as a function of the number of years since 2002, t. 15.8182+49.91t h(t) = 17.0418+0.52t a) Determine (and state) the Vertical Intercept. Be sure to express as a point and round values to 2 decimal places. b) Explain the Vertical Intercept's meaning in the problem context. c) Determine (and state) the Horizontal Asymptote. Be sure to express your answer as a line and round values to 2 decimal places.
A company has been producing cassettes. The following is the function that the manufacturer's monthly profits represent as a function of price: U (x) = -20x^2+ 560x-1500 a) Is this parabola concave up or concave down? b) Is the vertex a maximum or minimum point? c) Find the intercepts with the X axis and with the Y axis. d) For what price is the maximum profit reached? e) What is the maximum profit? f) For what price is no profit received? g) Graph U (x).

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