Alan

Or you could simply say

8y - 11 = 13   and   8y - 11 = -13   are the two possibilities

From one you get y = (13 + 11)/8 → 3

From the other you get y = (-13 + 11)/8 → -1/4

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There are an infinite number of solutions as you can see from the following:

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The tangent line is horizontal at x = a.

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"The best argument that I could see against a "last" digit of an irrational number is that the concept of a "last digit" in an irrational number doesn't make sense, but that doesn't necessarily mean that it doesn't exist."

That sentence makes grammatical sense, but is semantic nonsense!  By definition, an irrational number doesn't have a last digit and hence there is no last digit!

The proof that pi is irrational was first demonstrated by Lambert in the 18th century.  There are several proofs which are more or less complicated (I wouldn't call any of them simple!) - see http://www.mathpages.com/home/kmath313.htm for example.  

I assume delta y = tan(pi/4 - 0.2) - tan(pi/4) ≈ -1.685

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"I realize that the reason why there doesn't seem to be a last digit is because irrational numbers ... go on for an infinite number of decimal places"

Hence there is no last digit!

"If one root of the quadratic equation x^2-6x+k=0 is the square of the other root , find the value of k"

As follows:

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Use ncr(150,90) in the calculator on the home page here.

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