Melody

Hi Tiggsy and George.

Assuming that 3u + v neq 0, simplify (54u^2 v + 18uv^2)(9u + 3v).

In a standard Australian High School I taught that simplify means "Get rid of the brackets and then collect like terms."

I think that is all that is required. 

You need to show the diagram.

I think answer 1 is the correct one.  :)

Yes it is a sloppy question but you are basically expected to assume that it is the height of the bird that you are finding and that the ground is all level.

The answer I got was 39 feet.   Do you want me to explain further or did you just want to check your answer.?

I also commented on the original :)

Nicely answered guest. :)     

My only suggestion is that you could have simplied the first equation to make it a lettle simpler

(10A + B)  =  (10B + A) + 45

9A-9B=45

A-B=5

But that is certainly no big deal :)

There are 6 variables

One could be 8 and the rest zero        6 ways

One could be 7,1,0,0,0,0                  6*5=30 ways

6,1,1,0,0,0                                  6*5C2 = 60 ways

6,2,0,0,0,0                                  6*5 = 30 ways

5,1,1,1,0,0                                 6*5C3 = 60 ways

5,2,1,0,0,0                                 6*5*4 = 120 ways

5,3,0,0,0,0                                6*5 = 30 ways

4,1,1,1,1,0                                6*5 = 30 ways

4,2,1,1,0,0                                 6*5*4C2 = 180 ways

4,2,2,0,0,0                                6*5C2 = 60 ways

4,3,1,0,0,0                                6*5*4 = 120 ways

4,4,0,0,0,0,                                6*5 = 30 ways

3,1,1,1,1,1                                 6 ways

3,2,1,1,1,0                                 6*5*4 =  120 ways

3,2,2,1,0,0                                 6*5*4C2 = 180 ways

3,3,1,1,0,0                                 6C2*4C2 = 90 ways

3,3,2,0,0,0                                 6C2*4 = 60 ways

2,2,2,2,1,1                                 6C2=15 ways

2,2,2,2,2,0                                 6 ways

Add all those up and I think you will have your answer. :)                  

Hint:

Any integer is divisable by three if the its digits add up to a multiple of 3.     [sum of digits is a multiple of 2]

So what do you think the answer is?

You will have to work out 4 digit numbers, 3 digit numbers, 2 and 1 digit numbers all seperately.

sqrt2 is less than pi

so

\(h(\sqrt2)=\lfloor4\sqrt2 \rfloor \\ h(\sqrt2)=\lfloor 5.65 \rfloor \\ h(\sqrt2)=5 \\ now\\ h(5)=\)

and you can finish it

Thanks Juriemagic but getting stuck on the wrong method happens to me quite often too.

Sometimes I can see the answer or at least an approach fairly quickly but that is just from years of exposure and practice.

Also teaching  helps you cement a deeper understanding. Sort of knowing it and muffling your way through may be good enough on a personal level but if you are teaching it effectively you really have to understand it at a deeper, more organised level.  Teaching a topic always made me think about it more.