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I dont think therell be a fight here tonight

no matter what, queen guinevere I will always be the ruler, so theres no point in fighting over control of Camelot

So this needs explaination but to cheer you, this is very easy!

now they are saying y is directly propotional to x.

when y is 20 then x is 4......so in other words y is 4 *5 that is 20.

now let is take the other situation.

when y is 80 then we gotta find x so in other words y is 16 *5 thats 80.

Now that was only for your understanding......direct proportion means that there are two amounts and they are increasing in proportion....that is if suppose amount a has increased...then even amount b will increase...keeping in pace with amount a as before.....

So to write the answer in your notebook we will solve this "direct proportion" problem like this:

$$\frac{x}{y}=\frac{4}{20},\frac{x}{80}$$

(actually there was supposed to be a line instead of a comma......you will put this info in a table)

$$\frac{4}{20}=\frac{x}{80}$$

(this is how we will place both the quantities...now do cross multiplication)

$$20x=80 * 4$$

(to make our work easier we will not multiply now but take 20 to the other side and devide)

$$x=\frac{80*4}{20}$$

(now cut the two zeroes , devide 2 by 8 and multiply the remaining)

$$x = 16$$

so that is our answer 16

to check , devide 16 by 80 and see what you get.........youll get 1/5.........if not....then we'll have an argument....whoever wins will be the ruler.....HAHA!

Hope youve got it..........

As  i always say....to find the percent of anything we will follow the following steps....

24%/100% x 36

=

reducing or cutting that will give you your answer......can u do it or shall i do it?

In 5 hours he earns £30 therefore

in 1 hour he earns £30/5 so

in 6 hours he earns 6*£30/5 = £36

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1st b)  Assuming k stays the same (i.e. at 2 hours), then D = 2*9 or D = 18 km

2nd b)  Again assuming the proportionality constant stays the same, then D = 1.5*12 or D = $18

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Thanks Alan. Thats excactly how mine is. Thanks 

Do you mean it's like this:

If so, your first solution is correct.

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(a) One.  The number 2^19 has twenty divisors, all of the form 2^n where n is an integer going from 0 to 19.  The only prime involved is the number 2.

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Nope

no graph. 

That's weird, I can see the graph just fine. Let me see if I can do something about it. 

We can't tell; we can't see the graph!

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The locus (loci is plural) is the set of all points, lines or surfaces that satisfy a given condition.

For example, the locus of all points at the same distance from another point is a circle.

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Use the fact that tan(angle) = opposite/adjacent, so angle = tan^-1(opposite/adjacent) .

On many calculators (including the one on the home page here) tan^-1 is called atan (press 2nd then atan), which is short for arctan.

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There are two possibilities:  n = 0 or n = -1

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Just divide 32 by 8.

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$$(x+\frac{1}{x})^N=x^N+Nx^{N-1}x^{-1}+\frac{N(N-1)}{2!}x^{N-2}x^{-2}+...$$

The fifth term will therefore contain x^N-4x^-4 or x^N-8.  For this to be independent of x we must have N - 8 = 0 or N = 8

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Im going to try to solve this using a new technique I'm practicing ......Diophantine Equations...

First....use the Euclidian Algorithm to generate a sequence of quotients starting with the coefficients of the given equation......so we have

164 = 4(37) + 16

37 = 2(16) + 5

16 = 3(5) + 1

5 = 4(1) + 1

1 = 1(1) + 0

Write a three row table, thusly......

          4     2     3     4     1

1 0     1     2     7    30    37

0 1     4     9    31  133  164

The top line is just the quotients (in bold) that we found in the Euclidian Algorithm

The        1 0

              0 1     

matrix is a starting point for generating the rest of the table......each entry in the the table is found - working left to right - by multiiplying the number at the top of the columm by the entry to the immediate left of where our entry is to be placed, and then adding the number found two cells to the left of where our entry is to be placed... .......for instance......the "9"  entry in the table is generated by multiplying the number at the top of the column (2) times the number immediately to the left of the cell where the "9" will go....in this case, that number is 4....to this product we add the number two cells to the left of where the "9" will go....in this case that number is "1"......so we have 2(4) + 1 = 9  

The entries in the last column should be the coefficients in our equation...if not....we've made a mistake  !!!

The general solution comes from the determnant of the 2 x 2 matrix in the last two columns, i. e.,  the matrix....

30        37

133    164

Taking the determinant, we have   164*30  - 37*133  = -1

However, we  need a "1".....so multiplying by -1 all the way through, we have 

164(-30) + 37(133) = 1    (It should be noted that this determinant will always be either a "1" or a "-1" )

So.....we have one solution  x = -30  and y = 133

However......because this is linear....it will have infinite solutions....and all of them can be described by the general form ....[(x + bk), (y - ak) ]  =   [ (-30 + 37k ), (133 - 164k) ]  where k is any integer.......

[This form is generated by the fact that ..... ax + by = a(x+bk) + b(y-ak) ]

Note one other fact about this type of equation..... ax + by = c  ......if a, b have a common factor not shared by c, there are no integer solutions  !!!!!   In our case....164 and 37 are co-prime......

I'll answer the second one, first....I believe that "n"  = 6    thus 6n  = 6(6) = 36

The positive divisors are   1, 2, 3, 4, 6, 9, 12, 18 and 36

So...the number of prime divisors of "6n"  is just  ... two .....  [ 2 and 3  ]