Related Rate Problem: Finding the Rate of Concentration Decrease at Time t

  • Thread starter Thread starter BuBbLeS01
  • Start date Start date
  • Tags Tags
    Rate
BuBbLeS01
Messages
602
Reaction score
0
Related Rate Problem...HeLp!

Homework Statement


The ph of a solution is 3, ph changes at a rate of 0.01 at time t and the concentration of H3O is 10^-ph. At what rate is concentration decreasing at time t.


Homework Equations





The Attempt at a Solution


I need someone to walk me through this if possible..I've never done a related rate question (or if I did I don't remember).
 
Physics news on Phys.org


BuBbLeS01 said:

Homework Statement


The ph of a solution is 3, ph changes at a rate of 0.01 at time t and the concentration of H3O is 10^-ph. At what rate is concentration decreasing at time t.


Homework Equations





The Attempt at a Solution


I need someone to walk me through this if possible..I've never done a related rate question (or if I did I don't remember).

First things first.

Let's say you have a function y(x) and x itself is a function of time x(t). So we have y(x(t)).

If you are given dx/dt, can you write down the expression for dy/dt in terms of dx/dt? (it's basically the chain rule). If you know this, the rest will be straightforward.
 
Last edited:
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top