Alan

nCr(242797824,4) = 144799782100787625509125247069376

Can also write this as 242797824!/(4!*242797820!) = 242797824*242797823*242797822*242797821/4!

$${\frac{{\mathtt{242\,797\,824}}{\mathtt{\,\times\,}}{\mathtt{242\,797\,823}}{\mathtt{\,\times\,}}{\mathtt{242\,797\,822}}{\mathtt{\,\times\,}}{\mathtt{242\,797\,821}}}{{\mathtt{4}}{!}}} = {\mathtt{144\,799\,782\,100\,787\,625\,509\,125\,247\,069\,376}}$$

That's how many combinations there are.  I don't intend to list them all!

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Is it the average acceleration that you are after?

If so, use v² = u² + 2as where v = final velocity, u = initial velocity a = acceleration and s = distance

Rearrange as:  a = (v² - u²)/(2s)

$${\mathtt{a}} = {\frac{\left({\left({\mathtt{2.5}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{6}}}\right)}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{5}}}\right)}^{{\mathtt{2}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{0.019}}\right)}} \Rightarrow {\mathtt{a}} = {\mathtt{164\,210\,526\,315\,789.473\: \!684\: \!210\: \!526\: \!315\: \!8}}$$

This is in m/sec²

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LCM means Lowest Common Multiple

To find the LCM first find the prime factors of each number, then take the prime factors with the largest powers that occur and multiply them all together.  So:

Prime factors of 4:  2² 

Prime factors of 12:  2²*3

The highest power term with 2 is 2² and the highest power term with 3 is just 3, so we multiply 2²*3 to get 12.

This means the LCM of 4 and 12 is 12 itself.

Let me do a different example: suppose we want the LCM of 9 and 12:

Prime factors of 9:  3²

Prime factors of 12:  2²*3

Now we take 2² and multiply by 3² to get 2²*3² = 36

So 36 is the LCM of 9 and 12

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Here's yet another way of looking at the problem:

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I count 9.

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If you are doing it by hand choose several values of x (greater than 4) and calculate the corresponding values of y, then plot the pairs of values on graph paper.

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This is just a quadratic on its side.  See if the following helps:

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You haven't made a mistake asinus, you just haven't completed the calculation of what was asked for (namely the squares of the ratios)!

I'll give you points anyway!

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Since the only solutions to this equation are 0 and -2, any other value will provide a counter example.

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