goreisthebest

Make the 3 by 3 grid as  9 squares in a row. the number of ways to do this is 9 choose 5 or 9 choose 4, or 126.

What does the question even mean Can you rephrase it?

I didnt get 3sqrt(2).

Finding the arithmetic sequence which is 2, 6, 10, 14. The product of the 4 terms are 1680.

I did not get 3/8 as my answer.

Let the first integer be x so we don't have to answer the question after we have finished the problem. So the 100th term will be x+99. So the sum of these 100 integers are 100x + 4950. Since the sum are 100^100. So 100x is 100^100 - 4950 so x will be 10^99 - 99/2. 

~~GF

Doing some bashing we get the answer a/b as 19/21 which leaves the answer of b as 21.

There are a total of 10*9*8 or 720. Lets see what 3 numbers sum up to 15. 

We have the following:

1 6 8 gives us 6 ways.

1 5 9 gives us 6 ways.

1 4 10 gives us 6 ways.

2 6 7 gives us 6 ways.

2 5 8 gives us 6 ways.

2 4 9 gives us 6 ways.

2 3 10 gives us 6 ways.

3 4 8 gives us 6 ways.

3 5 7 gives us 6 ways.

4 5 6 gives us 6 ways.

Adding up the possible ways we get 60 ways.

60/720 is 1/12.

Formula for circumradius is ("Multiply the three sides)"/4R = "The area of the triangle"

So using this formula we get 3* 5 * 7/ (4R) = 15sqrt3/4

So 105/(4R) = 15sqrt3/4

Dividing by 15 yields

7/(4R) = sqrt3/4

Multiplying by 4 yields

7/R = sqrt3

So R = 7sqrt3/3.

~~GF

HINT

I think you can solve this problem by using coordinates. Let BC be the x axis and let B have coordinates of (0,0). So C has coordinates of (7,0). You can find M by doing slopes. M has coordinates of (7/2, 0) because it is the midpoint. So AM can be found by using distance formula.