A 7750 kg space probe, moving nose-first toward Jupiter at 179 m/s relative to the Sun, fires its rocket engine, ejecting 72.0 kg of exhaust at a speed of 230 m/s relative to the space probe. What is the final velocity of the probe?

179.47m/s

Explanation:

Using the law of conservation of momentum

m1u1 + m2u2 = (m1+m2)v

m1 and m2 are the masses

u1 and u2 are the initial velocities

v is the final velocity

Substitute

7750(179)+72(230) = (7750+72)v

1,387,250+16560 = 7822v

1,403,810 = 7822v

v = 1,403,810/7822

v= 179.47m/s

Hence the final velocity of the probe is 179.47m/s

To solve which ordered pair lie on the graph of the given function f(x) = 128(0.5^2)

You mus substitute each ordered pair then check if it satisfy the given function

(0,1)

1 = 128(0.5^0)

1 = 128 so wrong

(1, 64)

64 = 128(0.5^1)

64 = 64 correct

(3, 16)

16 = 128(0.5^3)

16 = 16 correct

0.5 = 128(0.5^8)

0.5 = 0.5 correct