3 years ago

A shoekeeper uses this formula to work out the

Mathematics

1 answer:

ElenaW [278]3 years ago

3 0

Answer:

12.6

Step-by-step explanation:

1.8X7

7x1=7

0.8x7=5.6

7+5.6=12.6

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

Vladimir [108]

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

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

We assumed that $3\vert k^3-k$ , and it's clear that $3\vert 3(k^2+k)$ because $3(k^2+k)$ is a multiple of 3. This means the remainder upon divides $(k+1)^3-(k+1)$ must be 0, and therefore the relation holds for $n=k+1$ . This proves the statement.

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3 years ago

Simplify 3^8 ÷ 3^2 <br> A. 3^4<br> B. 3^10<br> C. 3^6<br> D. 3^6

olga_2 [115]

Answer: 3^6 so D or C

Step-by-step explanation:

When dividing two squares, you minus the number

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3 years ago

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2. A man drove 240 miles south at the rate of 60 miles per hour. On the return trip, he drove the rate of 40 miles per hour. The

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