Melody

Sorry Juriemagic,

I hadn't actually looked at the guests answer.  I still haven't. I should have let you know that before. 

Thanks for answering Chris :)

Thanks, Chozerr,

It is really good that you had a go AND that you stated your lack of confidence.

It is not a really easy question... I'll give it a go

First, like you said, the big cube is cut into 5*5*5

Starting with the top row and working down, I am going to count how many red sides each little cube has.

Top and bottom rows

3*4+2*12+9 = 12+108+9 = 129 red sides on top row and 129 on the bottom one too

3 rows in the middle

3*(2*4+1*12) = 60 other red sides

Total number of red sides = 129+129+60 = 318 red sides altogether

There are 125 little cubes so these have a total of 125*6 = 750 sides

So if you choose a little cube at random and roll it I think the probability of rolling a red is  318/750 = 53/125

I think this is correct but there might have been an easier way to do it. I am really not sure.  :)

sin< = 3/5

\(asin(.6) = \\36.869897645844^\circ +360 n\qquad n\in Z\\ or \\180-36.86989764584 = 143.130102354164^\circ+360 n\qquad n\in Z\)

Thanks Guest, 

If you need more help Juriemagic,  just let us know :)

Thanks Hectictar,

Adam, I hope that you said 'thank you' to both of your answerers!

So far I have not seen even one though   

12)   Euclidean Geometry      13-9-17

CPhill has assumed that this is a paralellogram, I assumed that it did not have to be.

Mine failed because i did not have all the information?

Was it a parallelogram?  

Perhaps the question (not you) forgot to mention this?

If it did not have to be a parallelogram, or if you were suposed to prove that it had to be a parallelogram, then CPhill's answer is not valid, or at least not complete.  I suppose CPhill has stated his assumption in the first line. 

I also acknowledge that we do a lot of maths detective work in this forum so I shall congratulate CPhill for assuming a (possible) fact that was not given.

I guess even in my attempt I did assume that P, E and S were collinear points, I guess there is no great reason why I should have assumed this either.

I am glad that CPhill helped you Juriemagic :))

We always welcome bright, thinking students like yourself here :)

Oh, I know you are really busy and there is such a lot for you (and every other student) to learn.

But GeoGebra is a great program and a lot of fun to use. The diagram I made was interactive so I could move the points around and still meet all the given criterion. It's a lot of fun to use a program like that, and it helps a lot when trying to see what is happening with these types of problems.   

No they are definitely not all independent triangles!

Can you work out what the equation of the line is?  

Hi Juriemagic,

I tried drawing it and I found that only very specific angles will work (in order to make PES a straight angle.)

I randomly chose an x angle and then constructed it from there (using GeoGebra)

This is what I got - only in GeoGebra you can move things to try and make it better.

As you can see, even with the 72 degrees, PES is not a straight angle.

So obviously only a limited number of x angles can work (maybe only one)

I have not gotten further than this yet but  the focus of my thoughts is what angles are necessary in order to make PES a straight angle.......