Question

4. how many people can sit around 3 tables 5. how many people can sit around 8 tables6. how many people can sit around 72 tables 7. write the linear equation for the hexagonal table pattern y=mx+b form

Answer 1

In the table one

there are six sides, So 6 person can sit

In table two there are two hexagon joun together with one thier sides

So, there are 10 sides in the table 2, SO, 10 people can sit

In table three, there are three hexagon join each other

So, there are 14 sides available thus 14 people can sit

Sequence : 6, 10, 14

The sequence show the common difference of 4,

thus the given sequence is an airthmetic sequence with common difference 4

The expression for the nth term on Airthmetic sequence:

`\begin{gathered} a_n=a_1+(n-1)d \\ \text{ where a}_1=\text{ first term, d = common difference} \end{gathered}`

Here first term = 6, Common Difference = 4

1) how many people can sit around 3 tables

For 3 tables : n = 3

So,

`\begin{gathered} a_n=a_1+(n-1)d \\ a_3=6+(3-1)4 \\ a_3=6+8 \\ a_3=14 \end{gathered}`

14 people can sit around 3 tables

2) how many people can sit around 8 tables

For 8 tables : n = 8

`\begin{gathered} a_n=a_1+(n-1)d \\ a_8=6+(8-1)4 \\ a_8=6+7*4 \\ a_8=6+28 \\ a_8=34 \end{gathered}`

34 people can sit around 8 tables

3) how many people can sit around 72 table

for 72 tables: n = 72

`\begin{gathered} a_n=a_1+(n-1)d \\ a_(72)=6+(72-1)4 \\ a_(72)=6+71*4 \\ a_(72)=6+284 \\ a_(72)=290 \end{gathered}`

290 people can sit around 72 tables

4) the linear equation for the hexagonal table pattern y=mx+b form​

The equation of line is express as :

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Consider the number table as the x coordinates and the numbe of people as y coordinate

So: (x,y) = (1,6), (2,10)

Substitute them on the equation of line:

`\begin{gathered} y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1) \\ y-6=(10-6)/(2-1)(x-1) \\ y-6=4(x-1) \\ y-6=4x-4 \\ y=4x-4+6 \\ y=4x+2 \end{gathered}`

The linear equation is : y = 4x + 2

Answer :

4) 14 people can sit around 3 tables

5) 34 people can sit around 8 tables

6) 290 people can sit around 72 tables

7) The linear equation is : y = 4x + 2