What are the coordinates of the point on the directed line segment from (-10, -5)(−10,−5) to (5, 1)(5,1) that partitions the segment into a ratio of 1 to 2?

An astronaut drops a rock into a crater on the moon. the distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t)0.82. what is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.

Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters of emdangl be arranged? identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.