Maths problem

[pokerfan]

simplify the expression: (x-a) * (x-b) * (x-c) * (x-d) * ... * (x-z)

[Iggo]

1. Okay. I'll give it a go.

Math.

[Lionel Mandrake]

2. The answer is 0

The factor (x-x)=0 makes the whole expression equal to 0.

[pokerfan]

3. yep

[Dr. Strange]

4. I got nothing.

:)

[Rabrrrrrr]

5. It would be kind of fun to actually mutiply it all out, and see just how it turns to zero.

Especially since the x-x pair comes so late in the game, you'd have 23 (x-?) terms already multiplied out, and then it all disappears in three more moves.*

Cool.


* assuming that one does this by taking two terms at a time, say turn (x-a)(x-b) into (x2 - bx - ax + ab) and then multiply that by (x-c) and then by (x-d) and so on.

[pokerfan]

6. you have a funny sense of fun

x²⁶ + ...

[femmocrat]

7. Why?

I could never see the point of algebra. (That is algebra, isn't it?)

[pokerfan]

8. Algebra is important

because without algebra you can't do calculus.

[femmocrat]

9. Need a smilie for:

:pullinghairout:

What do you ever use calculus for?

[pokerfan]

10. Calculus is important

because without calculus you can't solve differential equations.

[femmocrat]

11. Ok.... now I need a :surrender: smilie!

This will have to do instead :hide:

[pokerfan]

12. seriously, it's useful

For example, let's say you have a 3' by 4' sheet of cardboard and you want make a container by cutting squares from each corner so you can fold up the sides. What's the largest volume box you can make?

[Ptah]

15. About 5239.82 cu. in?

cut a 6.79" square.

:shrug:

[pokerfan]

17. you didn't show your work

:P

[Ptah]

18. Excell is my friend.

[pokerfan]

19. ah, I see

Now a multiple choice. Which is closest to the correct answer:

1) 6.78889744906445
2) 6.78889744907068
3) 6.78889744907202

[Ptah]

20. being a shop rat, I'll cut it to 6.79 and invite the engineer to prove me wrong.

[pokerfan]

21. reminds me the time I sprung the crossed ladder problem

on a mechanical engineer and he "solved" it on a drafting table.

[Ptah]

22. What is the calculus solution for your volume OP?

[pokerfan]

23. standard min/max approach

Take the formula for the volume:

V = (4-2x)(3-2x)(x) = 4x³ - 14² + 12x

Which looks like your spreadsheet:



Take the derivative:

dV/dx = 12x² - 28x + 12

The derivative is the rate of change, i.e. slope:



The place where the slope is zero corresponds to the maximum volume. Setting this expression equal to 0:

12x² - 28x + 12 = 0

Solving for x:

[Dr. Strange]

13. You had me then you lost me.

:rofl:

[pinniped]

14. You need algebra to calculate some chemistry junk.

.

[rug]

16. Ok.

0.