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Screenshot of a worked example

I understand this until the final two lines. How does he get from 27.8766 to 1149.8hz and 7224.7rad/s?

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The answer to your first question comes from a little algebra. Subtract 7 from both sides, divide by 1.579e-5, and take the square root:

$$\sqrt{\frac{27.8766 - 7}{1.579\times10^{-5}}} = 1149.8$$

The conversion to radians per second is done by multiplying by \$2\pi\$ as they show.

To answer your follow up question about where \$1.579\times10^{-5}\$ comes from, it is equal to the expression from earlier in the same line, after factoring \$(2\pi f_{6dB})^2\$ into \$(2\pi)^2(f_{6dB})^2\$:

$$(4\times10^{-7})\cdot(2\pi)^2$$

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  • \$\begingroup\$ Thanks for the reply, I'm also a little confused as to where the 1.579x10^5 comes from? \$\endgroup\$ – James Apr 30 at 18:01
  • \$\begingroup\$ @James -- See edit \$\endgroup\$ – Justin Apr 30 at 18:05
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    \$\begingroup\$ @James I think your visual cortex might have missed the arrow in the middle of the third last line where it jumps to a whole new equation that does not equate to F(f_6db). It's a whole new inequality. I missed it too the first few times I looked at it. \$\endgroup\$ – DKNguyen Apr 30 at 18:28

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