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Originally Posted by Spartan-117
Ok, so I have an upcoming test on parabolas, and we were given a worksheet on problem solving with parabolas. It seemed simple enough, until I came to a few questions. Here are the ones I need help with:
1. Two numbers have a difference of 20. Find the numbers if the product of their squares is a minimum.
Now they say the answer is 10 and -10, but they equal 0 and not 20 when you subtract one from the other. Is this the correct answer, or not? If not, then how do I find the correct answer?
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10 - (-10) = 20.
When you subtract a negative it becomes a positive and you add it.
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2. A rectangular lot is bordered on one side of a stream and on the other three sides by 600m of fencing. Find the dimensions if its area is is a maximum.
How do I do this? They only give me the sum of the three sides bordered by the 600m fence, so how can I find the total perimeter of the lot, and the area?
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x = length
y = width
xy = 600
Amount of fence = x(2y)
That should help.
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3. A theatre seats 2000 people and charges $10 for a ticket. At this price, all the tickets can be sold. A survey indicates that if the ticket price is increased, the number sold will decrease by 100 for every dollar of increase. What ticket price would result in te greatest revenue?
... what?
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If you charge $10 a ticket you can make $200 000. However, if you increase the price of a ticket by $1 the number of people who show up will drop by 100.
How much should you increase the ticket price by to get the maximum amount of revenue?
(This is similar to the above problem.)
x = # of tickets sold
y = cost per ticket
xy = Revenue
You'll need to find at least one more relation, but that should help.