Out of the 30 days in June, you run 13 days and swim 6 days. You lift weights 7 days and ride a bike 4 days. If you make a pie chart to show this data, how many degrees
of the circle should represent swimming?

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  72°

Step-by-step explanation:

In a properly constructed pie chart, the proportion of the circle devoted to each section is the same as the proportion of that section to the the whole.

  (6 swim days)/(30 days) = (swim pie angle)/(360°)

Multiply by 360° to find ...

  swim pie angle = (360°)(6/30) = 72°

72° of the circle should represent swimming.

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.

300pi

step-by-step explanation: