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How do you 'complete the square' of a quadratic equation?

To complete the square, we need to rearrange the quadratic equation in the form of ax 2 + bx + c into the form r(x + p) 2 + q, where our task is to find the values of the unkowns of r, p and q. Let's take th...
RB
Answered by Ryan B. • Maths tutor
3485 Views

Using the trigonometric identity (sinx)^2 + (cosx)^2 = 1, show that (secx)^2 = (tanx)^2 + 1 is also a trigonometric identity.

We can divide by (cosx)^2 across the identity (sinx)^2 + (cosx)^2 = 1 (which can be derived from properties of the unit circle and a bit of Pythagoras’ theorem) to achieve [(sinx)^2 / (cosx)^2] + [(cosx)^2 /...
AB
Answered by Annie B. • Maths tutor
4202 Views

These are the selling prices of 5 houses in 2007: £145 000, £170 000, £215 000, £90 000, £180 000 (a) Work out the mean selling price.

The mean is also known as the average. To work out the mean you need to add all the house prices together and then divide by the number of houses. So in this example the total price of the houses is 145000+1...
JP
Answered by James P. • Maths tutor
3359 Views

The random variable J has a Poisson distribution with mean 4. Find P(J>2)

P(J>2) = P(J=0)+P(J=1) [split it up] P(X=t)= (V^t)/t!*e^V where V=4 in this case [use the formula] P(J>2) = 4^0/0!*e^4 + 4^1/1!*e^4 =1/e^4 + 4/e^4 = 5e^-4 which is roughly 0.0916
NC
Answered by Nathan C. • Maths tutor
4620 Views

Given 2x^2-3y^2=2, find the two values of dy/dx when x=5.

First solve for the exact point on the line by substituting 5 into the original equation. You should get y=+-4. Now implicitly differentiate the equation: 4x-6y(dy/dx)=0. Rearranging this will yield the foll...
KU
Answered by Kalid U. • Maths tutor
7695 Views