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To solve differential equations we use a method called separation of variables. This is where we take all the ‘y’ values to one side of the equation and all the ‘x’ values to the other side of the equation m...

Expand 5( x - 4) To expand the brackets, you must mutilpy the number outside the bracket by everything inside. Step 1) 5 x x = 5 x Step 2) 5 x (-4) = -20 Remember to include the minus sign Adding the answers...

Let f(x) = x^3 - 6x^2 + 11x - 6. Try x = 1： f(1) = 1 - 6 + 11 - 6 = 0 So x - 1 is a factot of f(x). Try x = 2： f(2) = 8 - 24 + 22 - 6 = 0 So x - 2 is a factot of f(x). Try x = 3： f(3) = 27 - 54 + 33 - 6 = 0 ...

First, we need to recall 2 basic definitions of vector operations: The dot product is defined on vectors u =[u 1 , u 2 ,...u n ] and v =[v 1 , v 2 ,..., v n ] as u . v = u 1 v 1 +u 2 v 2 +...+u n v n The len...

Suppose you have a quadratic equation: x 2 + 5x + 6 You are told it has TWO REAL ROOTS and you are to find them. The factorised quadratic with two roots will look like this: (x+ a )(x+ b ) Where a and b are ...