Please answer this necessarily with an explanation and I will mark the brilliant An astronaut working on the Moon tries to determine the gravitational constant G by throwing

a Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that the

Moon has a density ρ of 3340 kg/m3 and a radius R of 1740 km.

(a) Show with (1) that the potential energy of the rock at height h above the surface is given by:

E = −4πG

3

mρ ·

R3

R + h (2)

(b) Next, show that the gravitational constant can be determined by:

G = 3

8π

v2

ρR2 1 − RR+ h−1 (3)

(c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?

Use the frequency histogram to complete the following parts. ​(a) identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) estimate the greatest and least relative frequencies. ​(c) describe any patterns with the data. female fibula lengths 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 0 0.05 0.1 0.15 0.2 0.25 length (in centimeters) relative frequency a histogram titled "female fibula lengths" has a horizontal axis labeled "length in centimeters" from 30.5 to 39.5 in increments of 1 and a vertical axis labeled "relative frequency" from 0 to 0.25 in increments of 0.05. the histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. the approximate heights of the vertical bars are listed as follows, where the label is listed first and the approximate height is listed second: 30.5, 0.02; 31.5, 0.04; 32.5, 0.05; 33.5, 0.13; 34.5, 0.22; 35.5, 0.25; 36.5, 0.13; 37.5, 0.06; 38.5, 0.09; 39.5, 0.01. ​(a) the class with the greatest relative frequency is nothing to nothing centimeters. ​(type integers or decimals. do not round. use ascending​ order.)

Astone is thrown into a pond. what happens to the amplitude of the resulting waves as they get farther from the point where the stone hit the water? explain.

Asher cycles 12 miles in 16 hours. what is his speed?