Question

Prove that Δz=mΔx+nΔy
Deceptively simple...

Answer 1

What type of math is that?

Answer 2

Calculus three. Equation of a plane

Answer 3

wow.

Answer 4

This is nothing, wait til differential equations

Answer 5

*bookmark*

Answer 6

yeah, i, im 10th grade geometry, so uhh, good luck.

Answer 7

hahaha... its just algebra... don't get intimidated... you won't learn anything that way

Answer 8

pff Algebra, its easy. i just dont feel like doing it since its 1:12

Answer 9

I think I got it but, like you said it's late so I'll post it later

Answer 10

Alright everybody, here we go.

We start off with\[\Delta z = m \Delta x +n \Delta y\]
and we want to get to \[\Delta z=\Delta z\]
So, from knowing that \[m= \Delta z/\Delta x \] and \[n= \Delta z/\Delta y\] you would think that you could just plug that in and get some nice cancellation going on but unfortunately you end up with\[ \Delta z=2 \Delta z\] which is just blatantly wrong.
The error comes from substituting in both m and n at the same time. If you were to move in the x and y direction at the same time on a plane, the slope would not be as simple, but would be \[\Delta z/\sqrt((\Delta x)^2+(\Delta y)^2)\]

So by choosing to move in only one direction at a time, the inconsistencies are ironed out and you can do this \[\Delta z = (\Delta z / \Delta x) \Delta x + n(0)\] + \[\Delta z = m(0) + (\Delta z/\Delta y) \Delta y\]___________________________ \[2 \Delta z = (\Delta z /\Delta x)\Delta x +(\Delta z/\Delta y) \Delta y\] =>\[2 \Delta z = \Delta z +\Delta z\]
And so \[ \Delta z = \Delta z \]
And the universe is happy again :)