A rocket is stopped 12 feet from a satellite when it begings accelerating away from the satellite at a constant rate of 12 feet per second. The distance between the rocket and the satellite is given by the polynormial P(t)= 6t^2+12. Find the distance between the rocet and the satellite 5 seconds after the rocket started moving.
To find the distance between the rocket and the satellite 5 seconds after the rocket started moving, we need to evaluate the polynomial P(t) = 6t^2 + 12 at t = 5.
First, substitute t = 5 into the polynomial:
P(5) = 6(5)^2 + 12
= 6(25) + 12
= 150 + 12
= 162
Therefore, the distance between the rocket and the satellite 5 seconds after the rocket started moving is 162 feet.
Here is the step-by-step breakdown of the solution:
1. Start with the polynomial P(t) = 6t^2 + 12.
2. Substitute t = 5 into the polynomial.
3. Evaluate 6(5)^2 as 6 times 25, which is 150.
4. Add 150 and 12 to get the final answer, 162.
5. Hence, the distance between the rocket and the satellite 5 seconds after the rocket started moving is 162 feet.