What are the coordinates of the point on the directed line segment from ( − 7 , − 9 ) (−7,−9) to ( 5 , 6 ) (5,6) that partitions the segment into a ratio of 2 to 1?

In a circle, a 45° sector has an area of 32π cm2. what is the radius of this circle? 32 cm 12 cm 16 cm 8 cm

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

Find the exact value of each of the following. in each case, show your work and explain the steps you take to find the value. (a) sin 17π/6 (b) tan 13π/4 (c) sec 11π/3