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>Center: (3,3)</em>
<em>Radius: </em><em />
Step-by-step explanation:
<u>Midpoint and Distance Between two Points</u>
Given two points A(x1,y1) and B(x2,y2), the midpoint M(xm,ym) between A and B has the following coordinates:
The distance between both points is given by:
Point (5,7) is the center of circle A, and point (1,-1) is the center of the circle B. Given both points belong to circle C, the center of C must be the midpoint from A to B:
Center of circle C: (3,3)
The radius of C is half the distance between A and B:
The radius of C is d/2:
Center: (3,3)
Radius:
Answer: b. histogram
Step-by-step explanation:
A histogram is a graphical summary of data previously summarized in a frequency distribution. It is an accurate representation of the distribution of numerical data, the height of each bar shows how many fall into each range(the frequency of each range). Data from a frequency distribution table can be easily summarised graphically on a histogram.
An example of histogram is shown in the attachment