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Derivatives can be used to work out rates of change of non-linear systems which are encountered everyday. Moreover derivatives allow us to describe the shape of a function.

The eigenvalues are given by the characteristic equation (1-x)((1-x)^2-4)=0, which gives the values x=1, x=-1 and x=3 . These eigenvalues correspond to the eigenvectors (0, 1, 0), (1, -1, -1) and (1, -...

The probability that John picks out a red ball is: The number of red balls divided by the total number of balls = 4/10
Because the balls are replaced, each event is independent so every time John pic...

equation of a circle: (x - a)^2 + (y - b)^2 = r^2, where the circle has centre (a, b) and radius r.
Let's draw the diagram, where (x, y) is some point on the circle, which for ease we'll call P, and...

Use the method of substitution to answer this question.
Step 1: Rearrange one of the equations to find x or y.
y-x=3 y=x+3
Step 2: Substitute your y into the first equation
x^2<...