word problems?

Question

Any chance could someone help figure out these two word problems for me.

1) A 45-foot long irrigation sprinkler line rotates around one end. The sprinkler moves through an arc of 0º in .6 hours. Find the speed of the moving end of the sprinkler in feet per minute.

The answer is 2.4 but i have no idea hwo to get that.
The picture shown is a radius of 45ft, and the degree of theta is 110º.

Also, how do you achieve the answer of ::
2) Use the period of the function to identify an angle in the interval [0,pi] that generates the same value for the function. Show your reasoning and give the value of the function.
Yet again, i have a select answer but no way of how to get it. One choice of answer is -1/2.

How do i figure out these two problems? It'll help me tremendously if someone could show me teh steps or a website that takes you step by step through math problems.

Thank You!!

Answer 1

The first one, 110 degrees is 11/36 of the circle, and the circumference of the circle is 2(45)(pi) or about 282.6 ft, so the sprinkler travels 11/36 of this in 0.6 hours, which is 36 minutes. 11/36 of 282.6 is 86.35 feet in 36 minutes, so divide 86.35 by 36 to get feet per minute.

I don't get the second one though. Is it related to the first, or is there another function given?

Answer 2

0.6 hours is 0.6*60 = 36 minutes, so if it moves 110 degrees in this time, the angular speed is 110 / 36 = 3.06 degrees/min

If you have an arm that is 45 feet, then the complete circumferance is 45 * 2 * pi = 282.1 feet and that is 360 degrees.

So you are basically needing 3.06/360 th of 282.1 feet.

.... which is 2.4 feet.

I can't help you with the second one because you have not said that the function is like.