Alan

Right formula, but wrong G Melody!

G = 6.6742*10^-11 m³/(kg.s²)

so:

Force = 6.6742*10^-11*7*7/2² N

$${\mathtt{Force}} = {\frac{{\mathtt{6.674\: \!2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{7}}}{{{\mathtt{2}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{Force}} = {\mathtt{0.000\: \!000\: \!000\: \!817\: \!589\: \!5}}$$

Force ≈ 8.2*10^-10 N

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This reduces to

 4 = 6x - 20  Add 20 to both sides

24 = 6x   Divide both sides by 6

x = 24/6 or  x = 4

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√(c*d) = (√c)*(√d) if c and d are non-negative real numbers

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Here's my (somewhat long-winded) reasoning:

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Any reason why x should be restricted to integers?

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Here's a way of tackling the problem (approximately):

You could always improve on this by using the exact expression for small values of n, and switching to Stirlings approximation when you can no longer evaluate the exact expression.

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Use the fact that, in this situation P/T =constant, where P = pressure and T = absolute temperature. 

500000/(273+16) = 550000/T

T = (55/50)*289 = 317.9K

or T = 317.9 - 273 = 44.9°C

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To plot a 3-d function, say z = f(x,y), you need a 3-d plotting tool.  In general there will be more than one slope at any point, depending on which direction you are interested in.  If you want the slope in the x-direction, for example, you would find the partial derivative of z with respect to x. 

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Hi Melody,

Because the message started with the words "Hi Alan,..." I took it as a friendly pointer to a possible error (let's face it, I make enough mistakes!).

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