Alan

16^-3/2 → 1/16^3/2 → 1/(16^1/2)³ → 1/4³ → 1/64 → 0.015625

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The cable will form the hypotenuse of a right-angled triangle where sin(40°) = 9.5/L where L is the length of the hypotenuse in feet, so

L = 9.5/sin(40°) feet.  

You can crunch the numbers!

10^8/1.8 → (10/1.8)*10^7 → 5.556*10^7   (the 5's recur forever)

Rearrange in the form:  h = PE/(mg)

If this is a right-angled triangle with sides of length x and y and hypotenuse 20, then we have:

x = y - 4      (given)  and

x^2 + y^2 = 20^2   (Pythagoras)

Put the first into the second:

(y-4)^2 +y^2 = 20^2   Expand:

y^2 -8y +16 + y^2 = 20^2

2y^2 - 8y -384 = 0  Divide by 2:

y^2 - 4y - 192 = 0  This factors as:  (y+12)(y-16)=0 

Because the triangle must have positive length sides this means y = 16

So x = 16-4 = 12

The side lengths are 12cm and 16cm

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Let d = cost of a discus and k = cost of a kois.

40k = 2*8d

d = k+15

So 40k = 2*8*(k+15)   or 40k = 16k + 240  or  24k = 240 so k = 10

This means that d = 10+15 = 25

Total spend = $(8*25+40*10) = $600

Press 2nd then atan

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As follows:

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Chris's answer is correct (and probably the one that was wanted) but it isn't unique!

For example we could also have f(x) = x  and g(x) = (x^2 + 1)^(1/2)

or    f(x) = x^2  and  g(x) = (x^2 + 1)^(1/4)

or   f(x) = x^3    and  g(x) = (x^2 + 1)^(1/6)

or ... etc.

Can also be done as follows:

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