# X S2.0.2A rocket is fired upward with an initial velocity v of 80 meters per second. The quadratic function S(t) = -52 + 80t can be used

###### Question:

the heights of the rocket, in meters, at any time t in seconds. Find the height of the rocket 8 seconds after it takes off. During the

course of its flight, after how many seconds will the rocket be at a height of 290 meters?

## Answers

9514 1404 393

320 m after 8 seconds5.6 seconds, 10.4 seconds to height of 290 mStep-by-step explanation:

To find the height at 8 seconds, evaluate the formula for t=8.

S(t) = -5t^2 +80t

S(8) = -5(8^2) +80(8) = -320 +640 = 320

The height of the rocket is 320 meters 8 seconds after takeoff.

__

To find the time to 290 meters height, solve ...

S(t) = 290

290 = -5t^2 +80t

-58 = t^2 -16t . . . . . . . divide by -5

6 = t^2 -16t +64 . . . . . complete the square by adding 64

±√6 = t -8 . . . . . . . . . take the square root

t = 8 ±√6 ≈ {5.551, 10.449}

The rocket is at 290 meters height after 5.6 seconds and again after 10.4 seconds.

[tex]X S2.0.2 A rocket is fired upward with an initial velocity v of 80 meters per second. The quadratic[/tex]

First one is 1 second one is 3

answer: the answer is one of

[tex]f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.[/tex]

step-by-step explanation: we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

[tex]f=\dfrac{1}{2},~\dfrac{1}{4},~\dfrac{3}{4},~\dfrac{1}{6},~\dfrac{5}{6},~\dfrac{1}{8},~\dfrac{3}{8},~\dfrac{5}{8},~\dfrac{7}{8}.[/tex]