Two ships leave port at the same time. One sails south at 21 mi/h, and the other sails east at 28 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.

Or you could write D = 35t, though the use of D(t) emphasizes we have a function.

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Explanation:

See the diagram below. This shows a right triangle with legs a = 21t and b = 28t to represent the distances each boat travels after t hours. The distance between them is the length of the hypotenuse c. Use the pythagorean theorem to solve.

The function is D(t) = 35t

For each increase of an hour, the boats will separate by another 35 miles. Put another way, the distance between each boat is increasing by 35 mph.

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.

answer: the answer for that is 22/3