Andrea is designing the seating arrangement for a concert in her local park.

the 1st row can only have 10 seats, and each row must have 4 more seats than the row in front of it.

how many seats will be in the 10th row of seats?

There are 46 seats in row 10

Step-by-step explanation:

In order to find that we need to write this as an equation. We know that 6 is the constant and 4 is the coefficient for the variable. This would give us the equation:

y = 4x + 6

And this satisfies the equation for row 1, since when we put in the row number for x, it gives us the correct number of seats.

y = 4x + 6

y = 4(1) + 6

y = 4 + 6

y = 10

Now we can use that equation for any row. Let's use it for row 10

y = 4x + 6

y = 4(10) + 6

y = 40 + 6

y = 46

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.