An object is moving in the plane according to these parametric equations:

x(t) = πt + cos(4πt + π/2)
y(t) = sin(4πt + π/2)

the slope of the tangent line to the path at time t is

4πcos(4πt + π/2) divided by (π-4πsin(4πt+π/2))

the first time the tangent line is vertical will be t = ?

the second time the tangent line is vertical will be t = ?

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.

Angela took a general public aptitude test and scored in the 88th percentile for aptitude in accounting. what percentage of the scores were at or below her score?

Given: pqrs is a parallelogram prove: pr and qs bisect each other at t