Answer:
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You want to find the time <em>t</em> such that

Divide both sides by $200 :

Take the logarithm of both sides:

Divide both sides by 0.04 and solve for <em>t</em> :

The vibration period of the spring will be 0.2 seconds
<em><u>Explanation </u></em>
The relationship between the vibration period "T" (in seconds) and the weight "w" (in kilograms) is given by...

Given that, the weight(w) = 2.0 kilograms
So, <u>plugging w = 2.0</u> into the above equation, we will get...

So, the vibration period of the spring will be 0.2 seconds.
Answer:
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Step-by-step explanation:
<span>The distance between two cities is ninety miles, and a woman drives from one city to the other at a rate of 45 mph. At what rate must she return if the total travel time is three hours and forty minutes?
1st leg DATA:
distance = 90 mi ; rate = 45 mph ; time = d/r = 2 hrs.
</span><span>2nd leg DATA:
distance = 90 mi ; time = [3 2/3 - 2] = 1 2/3 hrs; rate = 90/(5/3) = 54 mph
Ans: 54 mph</span>