Math People: Help me simplify this equation!

[bicentennial_baby]

This isn't for a class, I'm trying to help another student, and my brain is fried...

Ok, here's the original eq:

(?Q/.5) x ((2.5/2)/(5,000+ (?Q/2))

When simplified, it's supposed to look like this:

(?Q x 2.50)/(10,000+?Q)

I'm trying to work out the steps to get from one to the other, and I"m just not seeing it. Not enough sleep, I guess. Help?

:)

PS- The ? symbols are supposed to be deltas, but it's not coming through for some reason. :shrug:

[Zuiderelle]

1. Those do not equate. If you replace the Q with 7, for example,

you get 0.003497552 as a result from the first equation (although you are missing a right parentheses, it should be "(?Q/.5) x ((2.5/2)/(5,000+ (?Q/2)))" ). With the second equation, also using 7, the result is 0.001748776, which is half of the first. So, it would have to be (((Q x 2.50)/(10000 + Q)) x 2). Or maybe I'm missing something.

[bicentennial_baby]

2. That's what I'm thinking...unless I'm losing it.

I keep trying to work it over in different ways, but...

Here's the original eq in it's entirety, with the eventual answer (I'll just say delta Q though.)

-1=(DeltaQ/.50) (((2+.50)/2) / (5000 + DeltaQ/2))

After it's simplified and solved, Delta Q is supposed to equal -1,000.

:shrug:

[La Lioness Priyanka]

11. i agree, i tried it with 10 which is easily divisible

and it doesnt work.

[bicentennial_baby]

12. Textbook typo?

:shrug:

[La Lioness Priyanka]

13. maybe. unless delta Q, by itself means something that i have long since forgotten

[bicentennial_baby]

14. It's just "the change in quantity", which

is what I'm solving for, if you see my response above. Beats the hell outta me.

[flvegan]

3. Uh

my cat's breath smells like cat food.

[bicentennial_baby]

4. d00d....

Not helpful! x(

:rofl:

[buddhamama]

5. skip it

that's simple. :D

[bicentennial_baby]

6. Can't, it's for one of the students that I tutor...

Sigh.... x(

[DS1]

7. ...

[bicentennial_baby]

8. OMG....You're like an LOLCat Deity...

:rofl: :rofl: :rofl:

[DS1]

9. I'm trying to make ones so bad

that they make everyone realize the lolcat fad is over ;-)

[bicentennial_baby]

10. Nooooooo!

Not yet! I still haven't done one of PB! :x(

[Zuiderelle]

16. I think you've made it even more faddish with that.

:rofl:

[idgiehkt]

20. agreed.

:rofl:

[graywarrior]

15. Fuck off. I can't fit myself anywhere into that equation.

Bastids.

[bicentennial_baby]

17. You can be the question mark!

:bounce:

[graywarrior]

18. and the mysterians.

[smedwed]

19. ummm

kks

?Q/0.5 = 2?Q
2.5/2 = 1.25
1/(5000 + (?Q/2)) = 2/(10000 + ?Q)

The easiest way to write it out (keeping the ?) is:

2?Q * 1.25 * 2/(10000+?Q) = 5?Q/(10000+?Q)

Twice your answer, I suspect the book has a mistake. What in particular is the question
trying to teach? Maybe you can work out what its meant to be from there.

[bicentennial_baby]

22. It's Economics...

Arc Elasticity problem :)

[smedwed]

24. :P

Have you checked you're finding the change in the right things then. :)
It's a mistake I always make x(

Why do you want it to equal 2.5?Q/(10000+ ?Q)?

I don't think this solves to equal -1 when ?Q is -1000?

[Orrex]

21. Multiply both sides by zero

Everything cancels out, and you're all set!

:hi:

[chemenger]

23. rewrite the equation as follows

(deltaQ/0.5) x ((2.5/2)/(5,000+ (deltaQ/2)) = (deltaQ x 2) x (2.5/2) x (1 / (5000 + deltaQ/2))

since 1/0.5 = 2 and you can separate the numerator of the fractional part of the expression from the denominator (i.e. a/b = a * 1/b)

Now cancel the 2's in the numerator of the first and denominator of the second and you get

2.5 deltaQ x (1 / (5000 + deltaQ/2))

Now multiply (5000 + deltaQ/2) by 2 to eliminate the 2 in the denominator and you get 10,000 + deltaQ so you finally wing up with:

2.5 x deltaQ / (10000 + deltaQ)

Nes pas???

Edit:

As this is written now, you cannot solve this for deltaQ. This expression in its simplest form is just a number. The only way to solve for deltaQ is if this were written as:

2.5 x deltaQ / (10000 + deltaQ) = something (a constant or another expression involving deltaQ)

[bicentennial_baby]

25. That appears to make sense...

:D

[smedwed]

26. I not sure

I'm kinda sleepy :beer: but i don't think that quite works. :)

1/(5000 + deltaQ/2) doesn't equal 1/(10000 + deltaQ) it equals 2/(10000 + deltaQ)

Or so I think lol

[chemenger]

27. You're right !

I screwn that up didn't I.

Lets' try this again:

DelQ/0.5 * (2.5/2)/(5,000+(DelQ/2)) = 2DelQ * (2.5/(10,000+DelQ) * (1/2)/(1/2)
factoring out a 1/2 from the numerator and denominator of the second part of the expression.

Now, since (1/2)/(1/2) = 1 you're left with

2DelQ * (2.5/(10,000+DelQ) or (5DelQ)/(10,000+DelQ)

I checked this with a couple of numbers replacing DelQ and it works out so the book (and me initially) are wrong. And this ties in with PelosiFan's observation that the first expression is twice the second.

Give me a D-.

[smedwed]

29. :)

I'd been sitting doing maths Step papers all day :)
Could hardly read numbers anymore they all just look like little wriggles lol:)
I think I agree with you now though :P

[LSK]

28. I took 3 calculus courses and differential equations in college

And I dont remember a thing!

Sorry!

:hi:

[Rabrrrrrr]

30. As others have said, textbook has a typo

Should be 5?Q, not 2.5?Q

[bicentennial_baby]

31. Thank you!

I knew I wasn't that crazy... :P

[Jamastiene]

32. I plugged this into Derive 5 and this is what I got:

smoke coming out the back of my computer...















nah, not really, but it said this:

DeltaQ = -5005000/503

which equals something like:
-9950.2982107355864811133200795229

That's about as close as you are going to get to -1000 for your answer with this problem.

I'd say it's about 8950.2982107355864811133200795229 off.

Does not compute.