3 years ago

The line that divides a parabola in half is..?

Mathematics

1 answer:

mojhsa [17]3 years ago

4 0

The line of symmetry.

It divides the parabola into to halves that are exactly the same.

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Let n be a natural number. Show that 3 | n3 −n

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Let $n=1$ . Then $n^3-n=1^3-1=0$ . By convention, every non-zero integer $n$ divides 0, so $3\vert n^3-n$ .

Suppose this relation holds for $n=k$ , i.e. $3\vert k^3-k$ . We then hope to show it must also hold for $n=k+1$ .

You have

$(k+1)^3-(k+1)=(k^3+3k^2+3k+1)-(k+1)=(k^3-k)+3(k^2+k)$

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