Melody

I guess I am meant to assume Bill spends every cent of hims money so that his ONLY soruce of income his his Mickey D job.

If he works 40 hours a week, for 52 weeks a year then he earns $20million/(40*52) = $9615 per hour or $160 per minute.

I would take less than half a minute to pick up the note so yes it is probably worth his while - so long as he does not have  back problem that is. 

Does he get to keep the money?

acceleration is    change in speed/time      = 80m/s divided by 20sec 

    \( = \frac{80m}{sec}\times \frac{1}{20sec}\\ =\frac{80m}{sec*20sec}\\ =\frac{4m}{sec^2}\\ =4m/s^2\)

It is a joke noobie :)

When 11^4 is written out in base 10, the sum of its digits is 16=2^4. What is the largest base b such that the base-b digits of 11^4 do not add up to 2^4? (Note: here, 11^4 in base b means that the base-b number 11 is raised to the fourth power.)

Mmm I have to work out what is being asked first.

\((11_b)^4\\=((b+1)_{10})^4\\=(b^4+4b^3+6b^2+4b+1)_{10}\\ \qquad If \;\;b>6 \;\;then\\ =14641_b \)

1+4+6+4+1 = 16

If b =6 or less than 6  this would equal a different number and the digits would not add to 16

SO the largest b  where the digits DO NOT add to 16 is b=6

how many times does the moon rotate around the world

You need to add in how much time.

Like how many tiems does the moon go arouind the Earth in an Earth year for example.

The second does not come from the first, it comes from the BUT....

\(sin\frac{\theta}{2}<\frac{\theta}{2}\\ \qquad \text{remember that theta is describes as acute so therefore it is positive}\\ sin^2\frac{\theta}{2}<\left(\frac{\theta}{2}\right)^2\\ -sin^2\frac{\theta}{2}>-\left(\frac{\theta}{2}\right)^2\\ 1-sin^2\frac{\theta}{2}>1-\left(\frac{\theta}{2}\right)^2\\\)

180km/2 hours = 90km/hour

Many people may already have looked at it.

Many people may have already been working on it.