Math Help... O.o

[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?

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?

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?

I have no idea what I need to do to show my work and get the correct answer, so could someone please help me?

[GDwarf]

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?

10 - (-10) = 20.

When you subtract a negative it becomes a positive and you add it.

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?

x = length
y = width
xy = 600
Amount of fence = x(2y)

That should help.

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?

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.

[Spartan-117]

Thanks for the help, GDwarf. The last 2 are kinda confusing, but I think I got the hang of it. The one that bothers me the most is the first. I should've known something as simple as that.

Anyway, thanks for your help. It'll do me much good for the upcoming test.

[GDwarf]

Negatives are tricky at first.

However, I found it helps to look at it this way: A negative number and a number with a minus sign in front of it are the same thing. There's no difference.

Also, two negatives cancel out. (x - (-x) = x+x. -x*-x = x*x. etc.)

That tends to help quite a bit.

As for the last one, it's been a while since I had to solve one of these, so I've forgotten exactly what you have to do, and I know that I didn't give you quite enough info to solve it. I'm reasonably certain, however, that you know enough to solve the 2nd one.

[Rock lee]

have you solved the problems now?
do you still need help with them?
...
or if you need help with other problems, post them...

[Layke]

Originally Posted by GDwarf

x = length
y = width
xy = 600
Amount of fence = x(2y)

That should help.

The bolded statement above is incorrect.

I'm sorry I can't help you with the math, but maybe if you know the answer it might help you work out the rest of the problem.

Since you have an unknown length of stream on one side of the lot with 600m worth of fence enclosing the rest of the lot forming a rectangle with the maximum amount of area, each side of the lot should be equal, forming a square. Yes, squares are rectangles.

Since the lot's area is maximized, and we know the each side of the lot is now equal to the other, then the 600m of fence for three sides must be divided by three to produce sides of 200m each, with the stream acconting for the fourth side and being 200m long as well.

The maximum amount of area enclosed is 200m x 200m which equals 40,000m squared.

Sorry that I can not provide the work, but I hope this helps anyways.

[GDwarf]

It is correct, my apologies.

I misread the question, and thought that the fence enclosed an area of 600.

So, x(2y) = 600.

Probably a bit late to help, but with luck anyone else having trouble with similar problems will get some help from this.