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I'll take a stab at this one......

Notice that 1000!  has   1000 / 7  =  142  numbers that are divisible by at least one  7

And 1000!   has    1000/49  = 20 numbers that are divisible by  7^2  [ 20 additional 7s]

And it has    1000/343   =  2   numbers that are divisible by 7^3  [ 2 additional 7s ]

So.......the largest n such that 7^n will divide 1000!   =    (142 + 20 + 2)  = 164

Aww you spent all that time typing and didn't post it?

Also I wasn't really really sure that they were the heights but it just kind of looked like they were. 

Is there a way to tell for sure?

Very nice, hectictar...!!!

Since 3² + 4² = 5², ABC is a right triangle with 3 as the height and 4 as the base.

So the area of ABC is (1/2)(4)(3) = 6 un.²

The lines AG, BG, and GC split the big triangle, ABC, into 3 equal pieces since they go from the vertices to the centroid.

The areas of ABG, BCG, and CAG, are all equal. They are all 6/3 = 2 un².

GR, GQ, and GP are all the heights of the 3 triangles. We know the bases and the areas, so just solve for the heights.

Triangle ABG:

2 = (1/2)(3)(GR)

4/3 = GR

Triangle BCG:

2 = (1/2)(4)(GP)

1 = GP

Triangle CAG:

2 = (1/2)(5)(GQ)

4/5 = GQ

4/3 + 1 + 4/5 = 47/15 = 31 and 2/15

That is probably what your teacher wants :)

Well you can do what liveevillevi did, but....

Another (and better) way to do it is to find two numbers that when divided equal the original number.

So if i want to put 6 into a fraction, I can say 18/3. 

Sum =F x [1 - R^N] / [1 - R]

315 = 5 x [1 - 2^N] / [1 - 2]

Solve for N over the real numbers:
315 = 5 (2^N - 1)

315 = 5 (2^N - 1) is equivalent to 5 (2^N - 1) = 315:
5 (2^N - 1) = 315

Divide both sides by 5:
2^N - 1 = 63

Add 1 to both sides:
2^N = 64

64 = 2^6:
2^N = 2^6

Equate exponents of 2 on both sides:
Answer: |N = 6

thanks you sooo much

If the 15 minutes starts after the 45 second report, then the answer is a 33.33% chance of turning on the radio and waiting over minutes forthe report. 

you take the number and put it over 1. SO I have the number 45, and I want  it in fraction form. It will be 45 over 1

To input inverse tan(or inverse cos and sin), you can do multiple things:

1. Press the "2^nd" button and click "atan"
2. Press the shift key to trigger the "2^nd" button and click "atan"
3. Simply type "atan"
4. Simply type "tan^-1"

You can do the same for cos and sin, also! Hope this helps.

Distributing and combining like terms is very useful.

Lets say you have 5 + 3 = 0.

When you combine like terms, you add all the like terms to their counterparts, so in this case, 5 and 3.

So it is now 8 = 0.

A more complicated example:

Lets say you have 5y + 3x + 8y + 5x = 2.

You have to combine all like terms, so you combine 5y and 8y to get one value of y, and 3x and 5x to get one value of x.

So 13y + 8x = 2.

Now, distributing.

Distributing is also known as factoring. It's when you put a group of numerical properties (numbers or variables) into a more simplified group multiplied by a common factor (preferrably the greatest common factor).

Take 3x + 3 = 0.

Now just take the left handed side.

The greatest common factor for 3x + 3 is 3.

So, you can do this: 3 * (x + 1).

As you can see, this expression turns out to be 3x + 3.

You can also do it the other way around to further simplify an expression.

If you have 4(x - 1) = 0

You can evaluate that to be 4x - 4 = 0.

I'm sorry I don't have an explanation, but I have an answer.

The four numbers are 21, 98, 219, and 461, so the largest is 461.

I found this by making a table and scrolling through to find all four of them.

DO 1200 / 30

to find how many boys can go on the bridge

i ate half a pie :)

It did a lot.

Thanks for another way of doing it! The more ways there are, the more ways there are to verify an answer.

Thank you both so much! I see where I made some mistakes now. Thank you!

That's what I plan to do. I just don't want to make others get it wrong just because they happen to see mine. Oh well, I am human after all.

Hey CPhill, I was trying to follow the Guest's work and it looks like the first step was square every term. I was just wondering is that really allowed??

20% = .20   ....so......

.20 * 18   =   3.6

Simple!

Just type in this: (Numerator/Denominator)

If you have a fraction inside a fraction, then: (Numerator/(Numerator/Denominator))

Using the principle of principle you should get....

4

0.6(7)^2 = (0.6)(7)(7) = 29.4