Alan

Have a look at http://www.mathpages.com/home/kmath616/kmath616.htm, or do a more general search for "fractional calculus".

Here's another way to approach this problem:

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Or simply:  

probability that first letter is an A:  p₁ = 3/8

given that the first letter is an A the probability that the second letter is also an A: p₂ = 2/7

Overall probability = p₁*p₂ = (3/8)*(2/7) → 0.107143  

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Numerical approach needed:

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This can be written as:  4log_a2 = log_ax

which becomes;  log_a2⁴ = log_ax  so x = 2⁴ or x = 16

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Looking to match the general expression   ax^2 + bx + c

1). 2s(s-4) → 2s^2 - 8s :   a = 2,  b = -8,  c = 0.  In this case we have s standing in for x.

2).  (w + 7)(w + 3) → w^2 + 10w + 21:   a = 1,  b = 10,  c = 21.  In this case we have w standing in for x.

Try the rest yourself.  I assume 3) should be (2t -1)(t + 5) or it won't be a quadratic!

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Looks like x/2 is subtracted at each stage:

2x,  3x/2,  x,  x/2,  0,  -x/2,  -x,  -3x/2,  -2x,  -5x/2, ...

128 lbs is about 58 kg.  Assuming the 5mm refers to the diameter of the stilleto heel, then:

force = 58*9.8 N → 568.4 N

area = pi*0.0025^2 m^2 ≈ 2*10^-5 m^2

pressure = force/area → 568.4/(2*10^-5) N/m^2 ≈ 284^10^5 N/m^2 or 284 bar.

This assumes the wearer is standing on one heel!  If standing on two heels the pressure will be halved. if standing on more of her feet than just heels the pressure will be reduced further.

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For the web2.0calc calculator

1.  Choose programmer option (right side of input bar)

2. Click the 0b button

3. Enter your binary number:

4. Click the =hex button

etc.

To enter a hex number click the 0x button in step 2 above.

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Positive difference = 49m - 35n. where m and n are integers.

The greatest common factor of 49 and 35 is 7, so this is the smallest positive debt possible.

For example, if Devon owed Laura 7 dollars, he could give her 3 Harry Potters = 147 dollars, and she could give him 4 Twilights = 140 dollars in return.