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The height of a soft ball that is thrown 4 feet from the ground can be approximated by the function [tex]y = - 7x {}^{2} { + 20x + 4} [/tex]where y is the height of the soft ball in feet x seconds after it is thrown. graph this function. find the time it takes the soft ball to reach its maximum height, the soft balls maximum height, and the time it takes the soft ball to return to the ground

The Height Of A Soft Ball That Is Thrown 4 Feet From The Ground Can Be Approximated By The Function Texy 7x 2 20x 4 Texwhere Y Is The Height Of The Soft Ball In class=

Sagot :

Answer:

Time taken to reach the maximum height = 1.43 seconds

Maximum height of the ball = 18.29 feet

Time taken to return to the ground = 2.86 seconds

Explanations:

The function representing the height of the softball at time x seconds is given as:

[tex]y=-7x^2\text{ + 20x + 4}[/tex]

The graph of the quadratic function is plotted below:

At maximum height, dy/dx = 0

For y = -7x² + 20x + 4

dy/dx = -14x + 20

Since dy/dx = 0 at maximum height

-14x + 20 = 0

14x = 20

x = 20 / 14

x = 1.43 seconds

Time taken by the soft ball to reach its maximum height = 1.43 seconds

To find the maximum height of the soft ball, substitute x = 1.43 into

y = -7x² + 20x + 4

y = -7 (1.43)² + 20(1.43) + 4

y = -14.31 + 28.6 + 4

y = 18.29 feet

The time it takes the soft ball to return to the ground

This will be double of what it takes to reach the maximum height = 2 x 1.43 = 2.86

The time it takes the ball to return to the ground = 2.86 seconds

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