Andrea is designing the seating arrangement for a concert in her local park. To give everyone a good view, each row must have 4 more seats than the row before it, and the 1st row can only have 10 seats. Explain to Andrea how to create an equation to predict the number of seats in any row. Then, using your equation, show your work to determine the number of seats in row 20.

s=4x+6; 86 seats in row 20

Step-by-step explanation:

Each row has more more seats than the row in front of it, so if we write out the number of seats in each row, we get 10,14,18... which is an arithmetic sequence.

We can express this arithmetic sequence by first finding the common difference, which is the difference between each term of the sequence. In this case, they already give us the common difference of 4 as there are 4 more seats in each consecutive row. This means that every time the number of the row increases, that row will have 4 more seats, and this can be represented b 4x, where x is the number of the row.

Now, we can begin to make an equation, where s is the amount of seats in a row. s would have to equal 4x+ a constant, as there are already some seats in the front row. So, as we know how many seats are in the first row, we can solve for the constant. We would get the equation 10=4(1)+c. Solving the equation we get 10=4+c or c+6. This means our equation is s=4x+6 where x is the number of the row and s is the number of seats in a row.

Now to find how many seats are in row 20 we can replace x with 20 and solve:

answer: yes youre right.

step-by-step explanation:

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.