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(ii) Prove by induction that, for all positive integers n, f(n) = 3^(3n–2) + 2^(3n+1) is divisible by 19

Let P(n) represent the statement that 'f(n) is divisible by 19'. For the basis step, I prove that P(1) is true: f(1) = 3^3(1)-2+ 2³⁽¹⁾⁺¹ = 19. 19 is divisible by 19 so P(1) is true. I...

Answered by Daniel L. • Maths tutor

8663 Views

Make x the subject of, 4(x+1)/(x+2) = y

The fundamental rule to keep in the back of your head is 'whatever happens to one side must happen to the other'. This way we can be sure that whatever is on the left hand side of the equals sign will be ...

Answered by Jack W. • Maths tutor

4180 Views

How do you find stationary points of an equation, eg. y=x^2+3x+2

Stationary points of an equation are found where the gradient of the tangent at this point equals zero. A diagram can illustrate this. To find them differentiate the given equation (which gives the gradie...

Answered by Ellie C. • Maths tutor

2845 Views

Solve the equation 3x + 1 = 4x - 2

In order to tackle this equation, we have to keep in mind that whatever we do to one side of the equation we have to do to the other. Our aim is going to be to get all of the x's together on one side of t...

Answered by Codie W. • Maths tutor

6917 Views

ABC and BCD are two attached triangles, attached along line BC. AB = 5.8cm, AC=5.2cm, BD=4.3cm. Angle BDC = 30 degrees, and angle DCB is a right angle. Calculate angle CBA.

This question teaches the importance of drawing diagrams to figure out what a question is asking, as well as deeply testing how well the student understands trigonometry and equation rearrangement, combin...

Answered by Charles S. • Maths tutor

5082 Views