Theorem: In any circles the same ratio of arc length to radius determines a unique central angle that the arcs subtend; and conversely, equal central angles determine the same ratio of arc length to radius. Prove the theorem above using the definition of the radian measure of an angle.

Will give brainliest! aubrey was offered a job that paid a salary of $45,000 in its first year. the salary was set to increase by 2% per year every year. if aubrey worked at the job for 20 years, what was the total amount of money earned over the 20 years, to the nearest whole number?

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate is the height of the pile changing when the pile is 12 feet high? (hint: the formula for the volume of a cone is v = 1 3 πr2h.)

Miranda is braiding her hair.then she will attach beads to the braid.she wants 1_3 of the beads to be red.if the greatest number of beads that will fit on the braid is 12,what other fractions could represent the part of the beads that are red?