Alan

There isn't an explicit degrees, minutes, seconds function on the calculator here.  

To enter the value as degrees, use value = degrees + minutes/60 + seconds/3600

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$$125^{\frac{2}{3}}\rightarrow(125^{\frac{1}{3}})^2\rightarrow5^2\rightarrow25$$

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More explanation is needed!

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The exclamation mark is the factorial sign.  So 21!, spoken as twenty-one factorial, means 21*20*19*...*3*2*1,

$$\frac{21!}{5!6!10!}=\frac{21*20*19*...*11*10*9*...*2*1}{5!*6!*10*9*...*2*1}=\frac{21*20*...*11}{5*4*...*2*1*6*5*...*2*1}\\\\=\frac{14079294028800}{120*720}=\frac{14079294028800}{86400}=162954792$$

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Does this help:

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$$\\\text{Do you mean }M^2\times M^5\text{ ?}\\\\\text{If so, this is }M^{2+5}\rightarrow M^7$$

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I did it as follows:

$$\\\frac{1}{ax}-\frac{a}{x+a-1}=0\\\\1-\frac{a^2x}{x+a-1}=0\\\\x+a-1-a^2x=0\\\\\text{ or }\\\\xa^2-a+1-x=0\\\\\text{Now I just used the quadratic formula to get }\\\\a=\frac{1\pm \sqrt{1-4x(1-x)}}{2x}\\\\a=\frac{1\pm(2x-1)}{2x}\\\\a=1 \text{ and }a=\frac{1}{x}-1$$

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It plots separate solutions from a single equation in a single colour. e.g. 

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That is an unusual graph :)

That's because it is actually two graphs:   y = -1 + 1/x  and y = 1

The question that I am now asking myself is how do I determine the ends of the hole around a=1 the graphs indicate that it is more than just one point ????

It's just a plotting oddity (possibly arising because of plotting two functions as though they are 1?).  Plot y=-1+1/x on the same graph and you will see it overwrites the curve without a large hole around x = 1.

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His health score will reduce by a factor of 4, so it will be 25% of what it was before. i.e. it will reduce by 75% of its original value.

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