Math Is Fun Forum

EDIT: The first paragraph adds no real value in hindsight; removed.

As Daniel points out, it has to do with the deformation of the cotton. Watermelons contain a large amount of water and water cannot be compressed, so there's very little give when it impacts. Also, their thick, spherical rind makes watermelons very resistant to any change in shape.

Cotton, on the other hand, contains an awful lot of void space. Even if you compress down into something similar to felt, then there's still room for the fibers to move. Especially since there won't be a hard rind to keep it in a spherical shape! If the fibers give when you are struck by the ball, then the ball will absorb most of the impact. A watermelon, being stubbornly resistant to change, is not so kind.

The simplest answer is x, y, z = 1.

If you want x, y, z to have different values and you want those values to work for all three equations, then here's the messy way...

We know:

So:

If you subtract the left side from the right, then you have:

Because the square roots on the left side can be either positive or negative, you don't know whether you will increase or decrease the number on the right side.
Using the third equation, we can deduce:

So:

And using the subtraction again:

So if you pick a value for X and Y, you might be able to work out what the corresponding Z value is.
For example, I've picked x=1, y=2. If we substitute these values and simplify then, we end up with:

We know √z = 3 - √y - √x from the first equation, so we can substitute in that:

So, dividing and then rearranging:

Because of the plus-minuses and the square roots, I think the right side might have 256 possible combinations (some combos will have the same value, though). Since z²+z is quadratic, I think that each of those combinations could have two answers.

So... rather than bother with any of the above, x=1, y=1, z=1.

I suppose what I'm saying is that "logic" isn't a universal concept:
Logic in Math <> Logic in Science <> Logic in Religion.

If logic in Math fails, we have the liberty of redefining things such that our logic reinstates itself. Think about what went through the mind of the first person who ever got  x² = -1 as their answer to an equation. We had to deal with that and invent imaginary numbers.
To some extent, Science and Religion do the same thing. Wave/particle duality and Satan are a couple good examples.

Thanks very much guys.

I do code, but I use Visual Basic (esp. within Excel) since Excel is pretty heavily used where I work and it's a pretty widely available program given the
proliferation of Microsoft. I'm glad that method worked, Ricky, as I had thought of trying that, but wasn't sure if it would be the ideal. I can follow the
logic involved with 10,003 being optimal, but you know how it is; sometimes you think of something that sounds so simple you can't help but self-doubt!

Actually, with a bit of afterthought, I'm perfectly happy with f(1) - 1 = f(1) + 1.

How about this? f(1) = √1

#4 doesn't hold up to that, unfortunately, unless you say:
f(x) = √1
For f(-x) < 0, x = √0.5
For f(-x) > 0, x = √z (such that 1/z = 0)

But that means making up crazy new Maths where we define the inputs for functions based on the output and 0z = 1.

And what kind of oddball would want to do that...?

10,003. Amusing considering there's 10,000 combinations.

I was hoping for something more formulaic, but I did say I wanted varied approaches, too.
I must admit ignorance, Ricky; I don't know C++. Any way you could comment that for me? Just to make sure I understand what it's doing.
I'd like to hear your thoughts on how you approached this problem, too.

I like how if it took you half a second to type in each digit then this particular string would have you poking buttons for about 84 minutes

Depends on your interpretation of God.

I see no reason not to believe that some force created life, the universe, and everything.  I'd just like someone to prove that it is (or ever was) sentient.

No reason I can't love inanimate things though. Especially when they result in me.

Hmm. If thats the case, then the form is actually probably something like D = f1(Ep,Lp) ? f2(Er,Lr)
(I renamed your variables to Entering or Leaving with a subscript of Process or Regeneration)
I would suggest there's probably a relation to the air that goes in and out of the P and R sides, but I couldn't make a guess at what operation(s) "?" should represent or what f1 and f2 are. As John says, you probably just have to stare at it and try different things that fit the context.

As far as my experience has been (which is by no means exhaustive), writing an program for this type of thing is hard because you pretty much need to tell the program what sort of things to look for in the first place.

Sorry I can't be of more help.

This might be far too simplistic, but have you tried seeing if the dew point can be the outcome of 4-variable simultaneous equations?

So for instance, with your example:
Test nr.     dew point    T1     T2     T3     T4
1                 -25          10     20     30     40
2                 -35          44     88     99     66   
4000            -34          12     54     49     5

Could you rewrite these as:
-25 = 10w + 20x + 30y + 40z
-35 = 44w + 88x + 99y + 66z
-34 = 12w + 54x + 49y + 5z

for instance? by solving what your variables (w, x, y, z) are you might find a relationship such that:
D = T1w + T2x + T3y + T4z
Where D is your dew point and T1, T2, T3, T4 are your observed/predicted temperatures?

As I say, it's probably grossly over-simplified, but it's probably worth a try if you haven't? At worst you'd be wasting very little of your time.

A man and his wife have been married for 40 years. The man, believing that his wife has lost her hearing as she's got older decides to test her.

He waits until she's sitting on the sofa, watching TV. He stands behind her in the doorway and says quietly, "Margaret? Can you hear me?" There's no answer.

He moves halfway to the sofa and says again, "Margaret? Can you hear me?" Still, there's no answer.

He moves the rest of the way to the sofa and whispers near her ear, "Margaret? Can you hear me?"
This time, she turns around and says angrily, "For the third time, John, yes I can!"