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3 years ago

Need help with geometry!! Thank you :)

Mathematics

1 answer:

DochEvi [55]3 years ago

6 0

Answer:

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>

Recursive equation for the pattern followed is given by,

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

<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.

At,

n = 1

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

which is true.

At,

n = 2

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

Which is also true.

At,

n = 3

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

Which is true.

At,

n = 4

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

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

Therefore, the recursive equation for the pattern followed is given by,

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

3 0

3 years ago

afron made a chicken dish for dinner she added a 10 ounces package of vegatables and a 14 ounce package of rice to 40 ounces of

aleksandrvk [35]

$10+14+40=x$ then divide $x$ by $16$ , which is the number of ounces in a single pound. What is the number you wind up with? :)

4 0

3 years ago

Choose the expression that correctly compares 0.720 and 0.7200

Alex

Answer:

0.720 = 0.7200

Step-by-step explanation:

These decimals are equivalent.

HTH :)

5 0

3 years ago

Read 2 more answers

HELP MATH

Serga [27]

I say it is A. thanks

4 0

3 years ago

Read 2 more answers

Factor with step by step explanation. n2+40-28

hjlf

N2+40-28=
Combine like terms
n2+40-28=n2+12
Factor out 2
n•2+12=2(n+6)
Therefore the answer is 2(n+6)

5 0

3 years ago

Need help with geometry!! Thank you :)​

Need help with geometry!! Thank you :)