Area of a circle  :  A = r² * Pi 

d = 6 cm    =>   r = 3 cm     =>     A = 3 cm * 3 cm * 3,14 = 28,26 cm²

The last Queen of France lost her head.  

Mistress Rosala, thee want the Queen of Camelot to finish her days in jail, without her head ? 

Fortunately this Queen does not like chocolate beverages and she is protected by a charm of great magick.

The Queen hath the Magick of the Quadratic.  

This Great Charm was bequeathed by the Great Chiurgeon Tud himself.  

So Queen Guinevere's protection is immeasurable.  

She has naught to fear from upstarts such as yourself.  

This question is definitely not answered  

Rosala, what are you saying?

Are you calling the Queen stupid?  She will not like that!  

"In the heart( ah stupid queen , queens aren't awesome there royal we are awesome"

In the heart:Awww queen won't die she will just give Rosala her Kingdom and live in the jail for her sake HAHAHA 

To  the queen:my queen I would like to advise you to have a cup of hot chocolate every morning just like the last queen of France! This will make your beauty shine more. And along you can also have a modern food , a diet coke to keep in pace with your health! My queen you are just the best , no queen is better than you .....

How Dare you take the great queens place you tiny thing! 

In the heart( ah stupid queen , queens aren't awesome there royal we are awesome)

Your the only awesome existing beauty my queen!

b) How many positive divisors of 8400 have at least 4 positive divisors?

$${factor}{\left({\mathtt{8\,400}}\right)} = {{\mathtt{2}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{7}}$$

there are 8 prime factors here. (including duplicates)

Any one of these by itself will only have 2 factors.

The product of 2 identical ones will have only 2 factors (As Zac has already explained)

The product of any other combination will have 4 or more factors.

So products of 2 different primes:  4C2 = 6

Product of 3 primes:  222,223,225,227,557,553,552,4C3 = 11

Product of 4 primes:  2222,2223,2225,2227,2255,2235,2237,2257,5523,5527,5537,2357 =12

Product of 5 primes:  22223,22225,22227,22235,22237,22255,22257,22355,22357,23557=10

Product of 6 primes:  222235,222237,222255,222257,222355,222357,222557,223557 = 8

Product of 7 primes:  2222355,2222357,2222557,2223557 = 4

Product of 8 primes:  22223557 = 1

Total =

$${\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{11}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}{\mathtt{\,\small\textbf+\,}}{\mathtt{10}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = {\mathtt{52}}$$            

That is assuming I didn't miss (or double count) any      

And YES there must be a better way of counting these but I don't know what it is.  

24% of 36

I think of it like this.

% is just a rearrangment of 100 and the / (sideways 1) tells you that it is divide.

so 24% means 24/100

'of'  always means multiply

so this problems becomes

24/100*36

$${\frac{{\mathtt{24}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{36}} = {\frac{{\mathtt{216}}}{{\mathtt{25}}}} = {\mathtt{8.64}}$$

Good explanation Zac but 2-5=-3  not -7 so it is not going to be quite right.    

Doesn't really matter - your explanation of how to go about finding the answer is very good :)    

$${\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}\left({\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right) = {\mathtt{900}}$$

$${\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{7.5}} = {\mathtt{900}}$$

$${\frac{{{\mathtt{x}}}^{{\mathtt{5}}}}{{{\mathtt{x}}}^{{\mathtt{2}}}}} = {{\mathtt{x}}}^{{\mathtt{3}}}$$

$${{\mathtt{x}}}^{{\mathtt{5}}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{-{\mathtt{2}}} = {{\mathtt{x}}}^{\left({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}\right)} = {{\mathtt{x}}}^{{\mathtt{3}}}$$

ooops I just realised the question may have been x * y = 48 and x/y=3 :P

Probably a more conventional way of looking at it.

In that case nice job Rosala!... although if x is 4 and y is 12 then does x/y = 3? I think they may need to be the other way around.

:D 

x * y = 48 x / y = 3

We can solve this using simultaneous equations:

(1)....x*y = 3

48x/y = 3

48x = 3y

(2).....y = 16x

Sub (2) into (1)

x*16x = 3

16x^2 = 3

x^2 = 3/16

x = √3/4

To find y sub x=[√3/4] into (1)

(√3/4)*y = 3

y = 3/(√3/4)

y = 3*(4/√3)

y = 12/√3

y = (12*√3)/3

y = 4*√3

To check:

$$\frac{\sqrt{3}}{4}\times({4}\times{\sqrt{3}})$$

$$\sqrt{3}\times{\sqrt{3}}=3$$

Sorry for my very crude maths. I also believe thare are probably other solutions, as I did not explore the negative root of (3/16) being equal to x.

What you have, 0.92, would be correct if we were rounding to 2 decimal places.

We need the number rounded to 4 decimal places. 

To do this lets look at the first 5 decimal places:

0.9174311926605504587155963302752293577981651376146788991

If the fith decimal place is a 0,1,2,3 or 4, the 4th digit stays the same (called rounding down). If the 5th digit is a 5,6,7,8 or 9, the 4th digit is rounded up by 1.

For example, if the number was 0.91748, the result when rounded to 4 decimal places would be 0.9175 (note there are 4 digits after the decimal point.

When looking at your number we can see that because the 3 is below 5, the number should be rounded down, resulting in 0.9174

I hope this helped and that it wasn't too longwinded :)