The height (in feet) of a ball thrown by a child is
y = -1/14x^2 + 6x + 5
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) What is the maximum height of the ball?
(b) How far from the child does the ball strike the ground?
y = -1/14x^2 + 6x + 5
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) What is the maximum height of the ball?
(b) How far from the child does the ball strike the ground?
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Y = -(1/14) x^2 + 6x + 5 >> to find the max height first find the derivative
dy/dx = d/dx[(-1/14) x^2] + d/dx [ 6x] + d/dx [ 5]
dy/dx = - ( 2/14) x +6 >>>> now to find x, set equation equal to zero
0 = (-1/7) x + 6 >>>> subtract 6 from both sides
(-6) = (-1/7) x >>> multiply by (-7)
42 = x >>>>> substitute in 42 for x
y = (- 1/14) ( 42^2) + (6*42) + 5
y= - 126 + 252 +5
y= -126 + 257
y=131 ft
a= 131ft and b = 42 ft
dy/dx = d/dx[(-1/14) x^2] + d/dx [ 6x] + d/dx [ 5]
dy/dx = - ( 2/14) x +6 >>>> now to find x, set equation equal to zero
0 = (-1/7) x + 6 >>>> subtract 6 from both sides
(-6) = (-1/7) x >>> multiply by (-7)
42 = x >>>>> substitute in 42 for x
y = (- 1/14) ( 42^2) + (6*42) + 5
y= - 126 + 252 +5
y= -126 + 257
y=131 ft
a= 131ft and b = 42 ft
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The maximum height of the ball is about 48ft.
The ball lands about 84ft from the child.
The ball lands about 84ft from the child.