Question 305313: I hope this was the appropriate topic...goes to show how lost I am!! Here is the problem: "An athlete whose even is the shot put releases the shot with the same initial velocity, but at different angles. When the shot is released at an angle of 35 degrees, its path can be modeled by the function f(x)= -0.01x^2+0.7x+6.1 in which x is the shot's horizontal distance, in feet, and f(x) is its height, in feet. Use the function to determine the shot's maximum distance. Use a calculator and round to the nearest tenth of a foot."
I have attempted to work this problem numerous times and I keep coming up with 18.35. The answer in the back of my textbook says 77.8 feet, and I would like to know where I am going wrong. Rather than to waste your time with my attempts to work it out I will just see the correct way and hope I can decipher my mistake on my own. Thank you for your help! Amber
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f(x)= -0.01x^2+0.7x+6.1 in which x is the shot's horizontal distance, in feet, and f(x) is its height, in feet. Use the function to determine the shot's maximum distance. Use a calculator and round to the nearest tenth of a foot."
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I graphed the function and found its maximum at x = 35, y = 18.35
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Another way to find the max is:
x = -b/(2a) = -0.7/(2(-.01) = 35
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Then height = f(35) = 18.35
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Cheers,
Stan H.
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