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>
1.5 is lesser than 0.5. Oh, wait nevermind I meant to say -1.5 is lesser than 0.5
13: 72.25
14: 52
For 14, you need to split the figure into a triangle and rectangle.
Answer:
$77.5
Step-by-step explanation:
7.75*10 = 77.5
