Answer:

Explanation:
The problem tell us that the temperature as function of time in downtown mathville is given by:

The average temperature over a given interval can be calculated as:

Where:

So, the initial temperature in this case, would be the temperature at noon, and the final temperature would be the temperature at midnight:
Therefore:


Hence, the average temperature between noon and midnight is:

Answer:
54.67 N
Explanation:
The total energy produced is the product of power and time duration:
E = Pt = 82 * 1 = 82 J
Which is converted from work, product of forced extended over a displacement
W = E = Fs = F*1.5 = 82
F = 82 / 1.5 = 54.67 N
So the magnitude of the force exerting on the handle is 54.67 N
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50N is your force and the acceleration is -9.8m/s^2 due to gravity.
So, you just plug that in.

BUT you know that mass cannot be negative, so you just disregard the negative sign and the mass of the rock is 5.102 grams.