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The height of a toy rocket [tex]\( t \)[/tex] seconds after launching is determined by the function [tex]\( f(t) = -16 t^2 + 160 t \)[/tex].

What is the rocket's height after 5 seconds?

A. 720
B. 400
C. 640
D. 1200
E. 880

Answer :

To find the rocket's height after 5 seconds, we start with the height function

[tex]$$
f(t) = -16t^2 + 160t.
$$[/tex]

1. First, substitute [tex]$t = 5$[/tex] into the function:

[tex]$$
f(5) = -16(5)^2 + 160(5).
$$[/tex]

2. Calculate [tex]$(5)^2$[/tex]:

[tex]$$
(5)^2 = 25.
$$[/tex]

3. Multiply [tex]$-16$[/tex] by [tex]$25$[/tex]:

[tex]$$
-16 \times 25 = -400.
$$[/tex]

4. Multiply [tex]$160$[/tex] by [tex]$5$[/tex]:

[tex]$$
160 \times 5 = 800.
$$[/tex]

5. Add the two results:

[tex]$$
-400 + 800 = 400.
$$[/tex]

Thus, the height of the rocket after 5 seconds is [tex]$\boxed{400}$[/tex] feet.

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