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Sagot :
Answer:
The rate of change is 12ft/s
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 20t[/tex]
Required
Rate of change from when she jumps till 1/2s
The time she jumps is represented as: t = 0
So, calculate h(0)
[tex]h(t) = -16t^2 + 20t[/tex]
[tex]h(0) = -16 * 0^2 + 20 * 0 = 0[/tex]
At t = 1/2
[tex]h(t) = -16t^2 + 20t[/tex]
[tex]h(1/2) = -16 * 1/2^2 + 20 * 1/2 = 6[/tex]
Rate of change is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
In this case:
[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]
Where
[tex](a,b) = (0,1/2)[/tex]
So, we have:
[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]
[tex]Rate = \frac{h(1/2) - h(0)}{1/2 - 0}[/tex]
[tex]Rate = \frac{6 - 0}{1/2 - 0}[/tex]
[tex]Rate = \frac{6}{1/2}[/tex]
[tex]Rate =12[/tex]
The rate of change is 12ft/s
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