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The formula for the area of a circle is π r^{2}. To use this formula we first need to find r, the radius of the circle. The radius is the distance from the centre of the circle to the edge, and is equal to half of the diameter. The radius of this circle is half of 14, or 14/2 = 7. Now we can use the formula for area. π x 7^{2 }= π x 49 = 153.938..... or 159.3 to 1 decimal place. It is important not to forget units with your final answer if they are given in the question, so the area of our circle C = 159.3 cm^{2}.

Answered by Tamsyn H.

Studies Mathematics at Cardiff

As a university student i know all about the right address that pupils need i can really help them understand math

Answered by Jack L.

Studies computer science at Kings, London

In this example, we want to find values for both x and y which are our unknowns.

So we start by rearranging x to be on its own but still in terms of y. We then can plot it into the next equation.

Hence we get the following equations:

. x=20-4y (See, 4y has been taken over to the other side and hence the sign changes)

. 3x+2y=20

Then we substitute this new value of x in the other equation:

3(20-4y)+2y=20

60-12y+2y=20 (we have multiplied out the 3 and its bracket to simplify)

-10y=20-60 (make sure you change the sign when taking the 60 across!)

-10y=-40

-y=-4 (here we divided 40 by 10)

y=4 (the minus signs cancel each other out)

Now that you've found y we must plot it back into the original equation to find x:

x+4y=20

x+4(4)=20

x+16=20

x=20-16

x=4

Therefore, x=4 and y=4.

Answered by Phillipa S.

Studies Engineering at Exeter

With sequences we should follow the general formula of **An + B**.

The **n **refers to the position in the sequence i.e. for the 3rd number in the sequence (which is 2 in the above sequence) n=3.

The **A** refers to the *difference between* each number in the sequence. In the case of the sequence above, __A= -3__ (each number is 3 lower than the previous one in the sequence).

The **B **refers to the difference between a particular number in the sequence compared with the number in the same position if it were the 'expected sequence'. In other words if it were just **An**. So for the sequence above it would be -3n so plugging in n=1, the first value in the sequence would be -3 x 1 = -3.

However we can see that this isn't the case, the first number is actually 8. 8 is 11 higher than -3 (8 - -3 = 8+3 = 11). So __B=11__.

Therefore the general formula for this sequence is -3n + 11.

All we now have to do is plug in the values for the poisiton in the sequence into n.

So the 4th term in the sequence is when n = 4:

(-3 x 4) = -12 + 11 = **-1**

And the 50th term in the sequence is when n = 50:

(-3 x 50) = -150 + 11 = **-139**

Answered by Aneesh S.

Studies Medicine MBBS BSc at University College London

We can calculate the area of a circle using the following formula:

A = pi x r^{2}

The area we are given is 16pi. Therefore, we can divide both sides by pi. So,

16pi = pi x r^{2}

becomes

16 = r^{2}

We can squareroot both sides to calculate the value of r.

sqrt16 = sqrt r^{2}

Therefore r = 4

We can then use the formula d = 2r to calculate the diameter.

Therefore the diameter of the circle is 2x4 = 8cm.

To answer this question, we need to form an equation to work out the nth term of the series.

To do this, the first thing we do is calculate the difference between each term.

7 - 3 =4

11 - 7 = 4

15 - 11 = 4

The difference each time is 4. Therefore, the equation could be 4n. Let's try it out with the first term.

4n = 4 x 1 = 4 which is not equal to the first term, 3.

To get 3 from the equation we have at the moment, we need to subtract 1.

Let's try the second term with the equation 4n -1.

4n-1 = 4x2 -1 = 7 which is equal to the second term.

To double check that we're right, let's use the equation to calculate the 5th term.

4n -1 = 4x5 -1 = 19.

19 is 4 greater than 15, so we're right!

Now let's calculate the 100th term.

4n -1 = 4x100 -1 = 399

Therefore the 100th term of this sequence is 399

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