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Rationalise the denominator of the following fraction: 1/(√2 + 1)

We start with 1/(√2 + 1) Normally with rationalising surd denominators we multiply the top and bottom of the fraction by the denominator. But this time we have a surd ADDED by a rational number. In this case...
RM
Answered by Richard M. • Maths tutor
33847 Views

The Curve C has the equation 2x^2-11+13. The point Q lies on C such that the gradient of the normal to C at Q is -1/9. Find the x-co-ordinate of Q

The first ste here is the find the general equation for the gradient tangential to the curve. This is done by differentiation of the equation to give 4x-11=dy/dx. dy/dx is the gradient. Now we are given the ...
MH
Answered by Matthew H. • Maths tutor
5372 Views

Factorise 15r+10

Step 1) look at the numbers Both 15 and 10 are factors of 5 step 2 ) look at the letters there is only one letter 'r' after the 15 step 3) there is only one possible thing that can be factorised out therefor...
JL
Answered by Judy L. • Maths tutor
10634 Views

How do I solve a simple simultaneous equation?

Simultaneous equations pop up all the time in maths, science, and engineering, so being able to solve them is really useful. Although they can look a bit daunting at first, the same general rules apply to so...
JM
Answered by Joe M. • Maths tutor
5354 Views

A sequence increases by 5 each time and the first term is x. The sum of the first four terms is 54. Set up and solve an equation to work out the value of x.

The first term is x, and if it increases by 5 each time then the second term is x+5, third is x+10, and the fourth is x+15. Adding these values together we get 4x+5+10+15, and this equals 54. Therefore; 4x+3...
TP
Answered by Tom P. • Maths tutor
11092 Views