Answer:
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Step-by-step explanation:
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The Lagrangian is

It has critical points where the first order derivatives vanish:



From the first two equations we get

Then

At these critical points, we have
(maximum)
(minimum)
The first thing any good mathematician does is convert the measurements to the same unit as what the question is asking. In this problem, it states that the pool fills at a rate of 20 cubic meters per hour. Just keep in mind that an hour is 60 minutes.
The next step is to see how many cubic meters will cost $300. This can be done by dividing 300 by 10. This gets you 30 cubic meters of water.
You already know that 60 minutes is 20 cubic meters of water. That leaves the remaining 10 cubic meters of water. By dividing the rate given, you get that 30 minutes is 10 cubic meters of water. Add the 60 and 30 together to get 90 minutes.
It will take 90 minutes for the pump to use $300.
Answer:
Divide the number of contestants by 4 and when there is 120 contestants there is 30 winners
Step-by-step explanation:
Looking back at past sequences we can see that when we had 8 contestants we had 2 winners 8/4=2 and we also saw 16/4=4 so that was the formula now we just had to do it on 120 contestants and now we get 30 winners....Hope this helps! :)