Answer:

Step-by-step explanation:
Let f(x) be the 3rd degree polynomial function.
The roots of this function are:
x=-2, x=-1 and x=3.
The factored form is:

This equation passes through (2,12)
This implies that;

The polynomial function is

9514 1404 393
Answer:
- 320 m after 8 seconds
- 5.6 seconds, 10.4 seconds to height of 290 m
Step-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.
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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.
Answer:
See below.
Step-by-step explanation:
2( x+3) = 5(x-4)
2x + 6 = 5x - 20
2x - 5x = -20 - 6
-3x = -26
x = 8
Answer:
236
Step-by-step explanation:
We assume the cost is a linear function of the number of lessons. That means the slope is the same everywhere.
Let (lessons, cost) = (x, y). We have (4, 84), (8, 160), (12, y3).
(y2 -y1)/(x2 -x1) = (y3 -y2)/(x3 -x2)
(160 -84)/(8 -4) = (y3 -160)/(12 -8)
76 = y3 -160
y3 = 160 +76 = 236
The cost will be $236 for 12 lessons.
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The cost function is ...
y = 19x +8 . . . . for x lessons