Aspace vehicle deploys its re-entry parachute when it's traveling at a vertical velocity of -150 meters/second (negative because the parachute is going down.) it comes to rest at 0 meters/second after 30 seconds. what's the average acceleration of the shuttle during this time span?

The initial velocity is -150m/s.
Remember that:
V(t) = Vi + at, where v(t) is velocity at time t, Vi is initial velocity, and a is acceleration.
We know that the vehicle stopped after 30 seconds, so V(30) = 0.
Let's plug the useful info into our function and solve for a:
0 = -150 + a*30     Add 150 to both sides
150 = 30a             Divide both sides by 30
a = 5 m/s²
The average acceleration is 5 meters per second squared. 

8. (10/7)x^(0.7) +C

10. (x^-2)/2 -x^-1 +C

Step-by-step explanation:

The integral of x^a is x^(a+1)/(a+1).

8. a = -.3, so the integral is x^0.7/0.7

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10. This is the difference of two integrals, one with a=-2; the other with a=-3, so ...

the integral is (x^-1)/(-1) -(x^-2)/(-2)

Of course, an arbitrary constant is added to each result to complete the indefinite integral.