28(pi^3)/12x^2 is less than 0.00001

I keep trying different things but getting stuck an suggestions?

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- Apr 15th 2009, 04:34 PMfattydqSolving this inequality
28(pi^3)/12x^2 is less than 0.00001

I keep trying different things but getting stuck an suggestions? - Apr 15th 2009, 04:38 PMe^(i*pi)
- Apr 15th 2009, 04:42 PMfattydq
But wouldn't it be 1 to the -5 and not 10 to the -5? or 10^-6. and what happened to that exponent in your final step, how did it just disappear?

- Apr 15th 2009, 04:54 PMe^(i*pi)
No, 1^x = 1 for all real x. The 10^-5 is from the decimal point being moved 5 squares to the left from 1.0. Since we use base 10 this corresponds to 10^-5

The exponent on went when I took the square root of the right hand side, using the rule

and

.

Since I skipped a few steps I'll explain in more detail :]

Using the first rule above:

Note that:

Using the second rule I can cancel out the and

Recombining the square roots I have left using the first rule I get

The last step I did was rationalising the denominator - sometimes it's optional, sometimes not - depends what you covered in class. Since

This can be multiplied by to give

Using the rule at the top I can combine the numerators to give - Apr 15th 2009, 05:04 PMfattydq
- Apr 15th 2009, 06:13 PMReckoner
Scientific notation

If you like, consider