Melody

What is the greatest positive integer n such that 3 to the power of n is a factor of 200!. (that exclamation mark is a factorial by the way)

Here is a neat little way to do it. See if you can work out why it works.  

3,9,27,81  are all powers of 3

How many multiples af 81 are there      2

How many multiples af 27 are there     7

How many multiples af 9 are there     22

How many multiples af 3 are there     66

2+7+22+66 = 97

What you have to do is factor the top and then cancel.

Not quite,

Let the point where the plane is be P      

F is the point on the ground directly below.

Obviously you must assume that the ground is flat so  A,B,C, and F all are in the same plane

This also means that  angles  PFA,   PFB,  PFC  are all 90 degrees.  

This is becasue PF is vertical and AF, BF, and CF are all lines on the horizontal ground.

also,

r, s and t are  ground distances to F   (which is directly below the plane.)

Reason for edit.

I have to edit becasue of display errors, I think this happens when I use the less  than sign to donote angles ...

No that is not an answer. 

Words and numbers without explanation are not answers.

At least they are not answers for anyone who is trying to learn anything.

\(\frac{19\;rad}{1sec}\qquad \frac{2\pi \;rad}{1revolution}\qquad \frac{9\;inchess}{rad} \qquad \frac{?inches}{sec}\\ \\~\\ \frac{9\;inches}{rad}\times \frac{19\;rad}{1sec}=\frac{9*19\;inches}{second}=171inches/sec\)

Nice work Heureka! 

Thanks Alan,  

Yes that helps me understand the question.

It probably doesn't help me answer it but it gives me a starting point.  

What do you think?  

I have not worked this question out but I would most likely look at the different probabilities and then add them together

P(BB)

+ P(WW throw back and get BB) on second try)

+ P(BW throw back the white one and get a black next time)

+ P(WB throw back the white one and get a black next time)

Hi OldTimer :)

An aeroplane is observed at the same instant from three stations A,B, C in a horizontal straight line but not in a vertical plane through the aeroplane.

If AB=BC =c and the angles of elevation from A,B C are respectively  alpha, beta and gamma prove that the height of the plane is

\(\frac{c\sqrt2 }{\sqrt{(cot^2\alpha +cot^2\gamma -2cot^2\beta )} }\)

I have not got my head around what this question is asking.  Can you (or someone else) help with a pic?

this is the bit I am not understanding 

"a horizontal straight line but not in a vertical plane"