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Pi is the ratio between a the circumference and the diameter of a circle. It's just a number which happens to describe this ratio for any circle you can think of. Let me explain, using the whiteboard...

If we let y = lnx, we then know that x = e^y. By differentiating both sides of this equation with respect to y we get:dx/dy = e^y, as the exponential function differentiates to itself ...

We start with sec^2 x + 2tanx = 0 for 0 ≤ x ≤ 2π
Note that sec^2 x = tan^2 x +1
tan ^2 x + 2tan x +1 = 0
(tan x +1)^2=0
tan x = -1
x=3π/4 or x=7π/4

In a proportional equation, you represent the factor of proportionality as k. In this case it means that y=kx^2. In the question you're given a number for both y and x. Sub these in in order to solve for ...

No atoms are lost or made during a chemical reaction, so the total mass of the products is equal to the total mass of the reactants.