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3 years ago

Prove that for any natural n the number 3^(n+4)−3n is divisible by 16.

Mathematics

1 answer:

Pani-rosa [81]3 years ago

3 0

Answer:

Step-by-step explanation:

Prove that for any natural number 3^(n+4)-3n is divisible by 16.

(I'm going to assume that you mean 3^(n+4)-3^n.)

1. We can break up 3^(n+4)-3n into 3^n * 3^4-3^n (by the rule a^b*a^c = a^b+c).

2. Solve to get 3^n * 81 - 3^n

3. Factor out the 3^n, and you'll get 3^n(81-1), and simplify: 3^n(80)

You may notice that 80 is divisible by 16.

4. Rewrite what we got from the last step as: 3^n*5(16).

Hope this helped you!

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Prove that the two circles shown below are similar.

Setler [38]

Answer:

The scale factor is $\frac{R_{A}}{R_{C}}=\frac{5}{2}$

We can say that both circles are similar.

Step-by-step explanation:

If we move the little circle to the center of the bigger circle, so the translate vector will be (3,5).

Now we realize that the bigger circle is just a dilation of the smaller circle, the scale factor is:

$R_{A}=5$

$R_{C}=2$

$\frac{R_{A}}{R_{C}}=\frac{5}{2}$

Therefore, we can say that both circles are similiar.

I hope it helps you!

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Step-by-step explanation:

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