Explain why rolle's theorem does not apply to the function even though there exist a and b such that f(a) = f(b). f(x) = cot x/2 [π, 7π]

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.

Which sentence uses an objective tone? we will plant the best garden of any school in the area. the new campus garden will surely be envied by other schools. a garden would provide numerous benefits to the students. you will probably agree that gardens have many benefits.

Consider that lines b and c are parallel. what is the value of x? what is the measure of the smaller angle?