State the domain and range for the given relations. {(1,2), (2,2), (1,2)}

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

Find the equation of the line that passes through the point (3,14) and is parallel to y=2/3x -6

Ugo [173]

Y=mx+b
m=slope

paralell ines have same slope
y=2/3x-6
slope is 2/3

the equation of aline that passes through (x1,y1) and has a slope of m is
y-y1=m(x-x1)
given
(3,14) and slope is 2/3
y-14=2/3(x-3)
y-14=2/3x-2
y=2/3x+12

4 0

3 years ago

Read 2 more answers

How many cubic centimeters is 5 cubic meters.

tresset_1 [31]

The key to solving this question is first knowing how many cubic cm are in one cubic m:

The ratio is always 1000000 cubic cm in 1 cubic meter.

Knowing this, we calculate how many cubic cm are in 5 cubic meters!

1000000 cubic cm = 1 cubic m
x cubic cm 5 cubic m

x = 1000000 cubic cm x 5 cubic m ÷ 1 cubic m
x = 5000000 cubic cm

Hope this helps!
Feel free to message me if you have any questions :)

4 0

3 years ago

Read 2 more answers

If

Nikolay [14]

Answer:

46

Step-by-step explanation:

4 x 2= 8

3 x 5= 15

2(8 +15)= 2(23)=

23 x 2= 46