Alan

Combined average wage = $(32.5*8 + 28.5*8)/16 = $30.5

There are far more females with less than 5 years experience than there are males, so it's not surprising that their average wage is lower.

Here's my solution:

It should be checked (it's different from your suggested result).

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The 8 is in the "ten-thousands" place.  The 6 is in the "thousands" place; the 9 in the "hundreds" place; the 7 in the "tens" place and the 4 in the "units" place.

Is that what you are after?

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Wien's displacement law says the maximum wavelength is given by 

λ_max = b/T  where b = 2.897721*10^-3 m.K and T is the absolute temperature (in K).

So λ_max = 2.897721*10^-3/6900 m = 4.2*10^-7 m

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A little experimentation shows that the successive powers of 490497 end in 1, 7, 9, 3, 1, 7, 9, 3, 1, 7, 9, 3, .... etc.

So if the remainder of the power, when divided by 4 is zero the result ends in 1, if the remainder is 1 the result ends in 7, etc.

Now, mod(252,4) = 0, so the units digit of 490497²⁵² is 1

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Here's a 3d plot of the function (in blue) on the left-hand side of the equation, showing where it intersects with the zero plane (in grey).  There is also a 2D plot showing the lines of theta vs beta on the zero plane.  The axes are in radians (0 to pi/2 for both theta and beta).

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Using log(m*n) = log(m) + log(n)  and log(m^n) = n*log(m) we get:

3log(A) + x*log(a) = 12log(a)

x*log(a) = 12log(a) - 3log(A)

x = 12 - 3log(A)/log(a) 

(If A and a are meant to be the same then this reduces to x = 9)

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√108 = 6√3

√18 = 3√2

√12 = 2√3

So Manuel owes Rico  6√3 - 3√2 +2√3 = 8√3 - 3√2 pesos

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