Algebra ii question explain how i do this?

It usually works well to follow the instructions in the problem.

a. Start by making a graph.

b. The curve has decreasing slope, so could be a log or square root function. The square root function best describes the data. A graphing calcluator can help you decide here. (It is also helpful to have a little background in physics, where you learn that a pendulum period is approximately proportional to the square root of its length.)

c. For this, you draw a horizontal line on your graph at time = 4.5 s, and read the string length value. It may be about 5 or 5.1 m.

d. For this, you draw a vertical line on your graph at length = 14 m, and read the period. It may be about 7.5 s.

_____

Note: you are not being asked to find the function, just characterize its shape. The answers to parts c and d come from reading your graph.

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.