Aball is thrown across a playing field from a height of h = 6 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. it can be deduced from physical principles that the path of the ball is modeled by the functiony = −32/((20)^2)x^2 + x + 6 where x is the distance in feet that the ball has traveled horizontally find the maximum height attained by the ball. (round your answer to three decimal places.)

(b) find the horizontal distance the ball has traveled when it hits the ground. (round your answer to one decimal place.

maximum height attained by the ball: 9.125 ft

horizontal distance the ball has traveled when it hits the ground: 16.93 ft

Step-by-step explanation:

The function

y = −32/((20)^2)x^2 + x + 6

y = -0.08x^2 + x + 6

is a parabola. Its maximum is at its vertex. x-coordinate of the vertex:

x = -b/(2a) = -1/(2*-0.08) = 6.25

y-coordinate of the vertex:

y = -0.08*6.25^2 + 6.25 + 6 = 9.125 ft

When the ball hits the ground, y = 0, so we have to find the roots of the function with help of the quadratic formula:

The negative solution is not correct because it doesn't have a physical meaning

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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