Search over 10,000 free study notes

The gradient of a striaght line measures how much it changes when you move in one direction. For example when we move to the right in the x direction, the line goes down. The equation for finding the grad...

The first equation can be multiplied by 3 to give 3x + 3y = 9. Then these two equations can be added by summing both left hand sides and both right hand sides to obtain the new equation 3x + 3y - 3x + 5y ...

you need to think about how the integral will be simpliefied, basically you are trying to get to a state where only one function of x resides in the integral. so if you have an x² sin3x dx insi...

y′=3x2 −6x

use of y′ = 0

0= 3x^2 - 6x

0= 3x(x-2)

therefore either x=0 or x=2

when x=0 y=1, when x=2 y=-3

(0, 1) or (2, −3) 

y''=6x-6

when x=0 y''=6(...

This question can be solved using a tree diagram. First we need to map out the two possible outcomes from the question:

H=heads T= tails. The first scenario is HHH, as the probability of H each tim...