Search over 10,000 free study notes

Let the parabola be y=x² and let the family of lines be y=2x+c, in order to study the intersection points we need to consider the second order linear system given by having the two equations ab...

By multipying across and using some trigonometric identities we can turn this in to a much simpler quatratic which can be solved using the quadratic formula. This step can be simplified by using the subst...

Mode is the value that occurs most - which is 7. Median - put numbers in numerical order and find the middle number, which is 11. Mean is the average value so add up all the numbers and divide by the tota...

To differentiate composite functions, (a function within a function) like in this case we need to use the chain rule. We can see that F(x)=f(g(x)) where we let f(x)= (x^2+1)^2 and g(x)= x^2+1. To use the ...

1/10 * 60=6 red marbles 3/5 * 60=36 blue marbles Therefore the amount of green marbles must be 60-(6+36)=18