Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
Answer:
<em>q</em> = 12<em>x</em>
Step-by-step explanation:
<em>q</em> = 3<em>x</em> + 9<em>x</em>
Combine like terms
<em>q</em> = 12<em>x</em>
10 x 3 x 2 = the volume
10 x 3 = 30
30 x 2 = 60 cm^3
it is cm^3 because all of the numbers you have are in cm
Midpoint
We know AC is a segment and B is its midpoint. This means the length of the segment AB is half the length of the segment AC. This also means the length of the segment BC is half the length of AC, and equal to AB.
This can be visualized as follows:
Since AB=7, then BC = 7 and AC=AB+BC = 14
Answer: BC = 7, and AC=!4
The next value would be 48. The values keep increasing by odd numbers. Like the first one is 3 then it goes to 5.
3, 5, 7, 9, 11, 13.....
