Ms. Pace walks miles in each hour. How far will Ms. Pace walk in one hour?

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.

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

which is true.

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

Which is also true.

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

Which is true.

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

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>

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

3 0

3 years ago

Ramona is counting the posts between mile markers on the highway. In 1 mile, she counts 33 posts. If the posts are evenly spaced

Naddika [18.5K]

Answer:

160 feet

Step-by-step explanation:

In order to solve this, we need to realize that the mile is being divided into 33 equal parts. Therefore our operation should look like this:

5,280 (the number of feet in 1 mile) / 33

5,280/33=160

The posts are 160 feet apart from each other.

HTH :)

5 0

3 years ago

who does the number, of zeros in the product of 8 and 5000 compara to the number of zeros in the factors ? explain.

mezya [45]

If one of the numbers we multiply (factors) has zeros at the end, and the other isn't a fraction: all those zeros will stay in the product.

But there might be additional zeros if the other numbers in the factors (the numbers which aren't 0) mupliply to "end" in zero and this is the case here:

8*5=40.

so the product will be 40 and the zeros of the 5000:

40 000

the number of zeros in the product will be bigger than the number of zeros in the factors if the non-zero parts of the fractions multiply to a number with 0 at the end.

4 0

3 years ago

What is the volume of the following rectangular prism????help fast pleasee

Dmitrij [34]

Answer:

28/3

Step-by-step explanation:

3 0

3 years ago

PLEASE ANSWER AS QUICK AS POSSIBLE

Lady_Fox [76]

Answer:

(a) h^-1(x) = (x+6)/6

Step-by-step explanation:

The inverse relation can be found by solving for y: x = h(y).

<h3>Solution</h3>

x = h(y) . . . . . the inverse relation

x = 6y -6 . . . . . use the function definition

x +6 = 6y . . . . add 6

(x +6)/6 = y . . . . divide by 6

The inverse function is ...

$\boxed{h^{-1}(x)=\dfrac{x+6}{6}}$

4 0

2 years ago