Could someone explain what this question really means and how to start solving it....

Ifmis a fixed constant such that the two families of curves and are orthogonal trajectories of each others, what must be the value ofm?

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- October 21st 2007, 06:36 AMpolymeraseorthogonal trajectories
Could someone explain what this question really means and how to start solving it....

If*m*is a fixed constant such that the two families of curves and are orthogonal trajectories of each others, what must be the value of*m?* - October 21st 2007, 06:45 AMTD!
The functions y = g(x) and y = h(x) are orthogonal at x = a, if g'(a)h'(a) = -1.

- October 21st 2007, 07:01 AMpolymerase
- October 21st 2007, 09:14 AMtopsquark
- October 21st 2007, 10:10 AMpolymerase
- October 21st 2007, 10:12 AMtopsquark
- October 21st 2007, 10:16 AMpolymerase
- October 21st 2007, 12:26 PMTD!
Ok, so far so good! You know have m/(...) = 1.

A fraction is 1 if numerator and denominator are equal.

So you can easily solve this for m. We have:

Now, this m doesn't seem "constant", but dependent of x, c and k!

But, where do we have to look for ortogonality? At their intersection!

Let's try to find something useful, equalling both equations:

You recognise this? Filling in, in what we had for m earlier:

- October 21st 2007, 01:42 PMpolymerase
- October 21st 2007, 11:29 PMTD!
You're welcome :)