Can someone explain or show me how to figure out this question?
Nancy conjectures that the last digit of the fourth power of an even number is 6.
a) find 2 examples to support the conjecture
b) find a counter -example.
...??
2007-12-16 12:26:01 · 4 answers · asked by NIMsTastic 3 in Science & Mathematics ➔ Mathematics
I'd just guess and check, with some instinct you should be able to figure out a number that will never end in anything when multiplied by itself than a 0.
(2^4)=16
2007-12-16 12:29:05 · answer #1 · answered by Bushman 2 · 1⤊ 0⤋
the question being asked is this: Nancy supposes that if you multiply some even number times itself four time, then that result ends with a six.
You are supposed to find 2 examples of this where it is true, and 1 example where it is not true.
Just punch it into your calculator and find examples of it, like...
2x2x2x2 = 16
4x4x4x4 = 256
OK, so...
the numbers you will multiply together end with either 2, 4, 6 ,8 or 0. Those are the even numbers. Do any of these when mutliplied times themselves 4 times not end with 6? That will be your counter example.
2007-12-16 20:40:05 · answer #2 · answered by archaeadoc 5 · 1⤊ 0⤋
a) One answer is "2" (2^4 = 16)
Another answer is "4" (4^4 = 256)
b) A counter example is "10" (10^4) = 10,000
2007-12-16 20:29:11 · answer #3 · answered by Matt Soave 2 · 1⤊ 0⤋
2 and 4 are examples. 10 is a counterexample.
2007-12-16 20:31:06 · answer #4 · answered by jgoulden 7 · 1⤊ 0⤋