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Oksi-84 [34.3K]

2 years ago

9

The ratio of the sides of two similar regular octagons is 4:7. If the measure of each side of the larger octagon is 28 cm, then

the measure of each side of the smaller octagon is ________cm. Enter a number answer only.

1 answer:

Virty [35]2 years ago

8 0

Answer:

16 cm.

Step-by-step explanation:

It is 4 times the ratio.

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Step-by-step explanation:

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A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

$a_{n}=a_{n-1}+(n-1)^{2}$

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

<u>At, </u>

<u>n = 2</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

<u>At, </u>

<u>n = 3</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

<u>At, </u>

<u>n = 4</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

$a_{n}=a_{n-1}+(n-1)^{2}$

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3 years ago

What single percentage change is equivalent to a 15% increase followed by a 16% increase?

FromTheMoon [43]

Answer:

15% increased

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Step-by-step explanation:

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3 years ago