Alan

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Expected value = probability of heads*$3  +  probability of tails*(-$2)  

so expected value = (1/3)*3 - (2/3)*2 = 1 - 4/3 = -1/3

You would expect to lose one third of a dollar

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(a+b+c)² = a²+2*a*b+2*a*c+b²+2*b*c+c²

so we have 

a²+2*a*b+2*a*c+b²+2*b*c+c² = a²+b²+c²

Subtract a²+b²+c² from both sides

2*a*b+2*a*c+2*b*c = 0

Divide all terms by 2*a*b*c and we are left with

1/c + 1/b + 1/a = 0

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Area of circle = pi*radius²

$${\mathtt{Area}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{5.5}}}^{{\mathtt{2}}} \Rightarrow {\mathtt{Area}} = {\mathtt{95.033\: \!177\: \!771\: \!091\: \!245\: \!5}}$$

Area of plate ≈ 95 in²

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If by that you mean the result is not a proper number then I'll agree with you!

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Try 1/0.1 then 1/0.01 then 1/0.001 then 1/0.0001 etc. where the denominator is getting closer and closer to 0.  

Does it look like the fractions are getting closer to zero?

Informally, the limit is tending to infinity, rather than zero.  However, strictly, division by zero is still undefined.  If you allow it you can prove silly things like 2 = 1.

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Division by zero is undefined mathematically, because, if you try to allow it, you get all sorts of inconsistencies appearing in your calculations.

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Possibly in your senior year, but I'm not familiar enough with what you learn when to say for certain.  Perhaps there is someone else in the forum who has learned about matrices recently who could give you a more definitive answer.

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If you have a 3x3 matrix, A, say, its inverse is another 3x3 matrix which, when multiplied by A results in a 3x3 matrix that has zeros everywhere except on the main diagonal (top-left to bottom right) where the numbers are 1.

For example:

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Have a look at Melody's picture above.  Each row starts and ends with the number 1 and the other terms are constructed by adding together the two terms nearest to it in the row above.   The triangle goes on down forever, in principle.

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