Answered

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The function h(t)=-16t^+144 represents the height, h(t), in feet of an object from the ground at t seconds after it is dropped. A realistic domain for this function is?

Sagot :

MrRoyal

Answer:

[tex]0 \le t \le 3[/tex]

Step-by-step explanation:

Given

[tex]h(t) = -16t^2 + 144[/tex]

Required

Determine a reasonable domain

The domain is the possible values of t for which h(t) is true

Before the object is released, the value of t is:

[tex]t = 0[/tex]

Next, is to calculate the value of t after the ball reaches the ground.

At this point, h = 0.

So, we have:

[tex]h(t) = -16t^2 + 144[/tex]

[tex]0 = -16t^2 + 144[/tex]

[tex]16t^2 = 144[/tex]

Divide both sides by 16

[tex]t^2 = 9[/tex]

Take the positive square root of both sides

[tex]t = 3[/tex]

This means that the ball reaches the ground in 3 seconds.

So, the domain is:

[tex]0 \le t \le 3[/tex]

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