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Will you please tell me what I did wrong here, and show me it should have been done correctly?

Will you please tell me what I did wrong here, and show me it should have been done-example-1
User Espinchi
by
6.8k points

1 Answer

7 votes

Answers:

1. 25

2. 1.25

3. 2.5

Step-by-step explanation:

The equation that models the height of the ball is h(t) = -16t² + 40t

This is an equation of a parabola, so the maximum height occurs at the vertex of the parabola. The first coordinate for the vertex is t = -b/2a

Where b is the number besides t and a is the number besides t².

Therefore, a = -16 and b = 40, and the ball reaches its maximum height at

t = -40/2(-16)

t = -40/(-32)

t = 1.25

Now, we can calculate the maximum height replacing t = 1.25 on the equation for h(t)

h(t) = -16t² + 40t

h(1.25) = -16(1.25)² + 40(1.25)

h(1.25) = -25 + 50

h(1.25) = 25

Finally, the ball falls back to the ground when the height is 0, so we need to solve the equation

h(t) = -16t² + 40t = 0

Solving for t, we get:

-16t² + 40t = 0

t(-16t + 40) = 0

Then,

t = 0

or

-16t + 40 = 0

-16t + 40 - 40 = 0 - 40

-16t = -40

-16t/(-16) = -40/(-16)

t = 2.5

Therefore, the ball falls back to the ground at 2.5

User Tsal Troser
by
6.7k points
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