When the slope is 1/3 what is the slope of the perpendicular line

What is the point of inflection for the function f(x)=2cos4x on the interval (0, pi/2)

Aquality characteristic of new iphone x made at the amsterdam plant at apple computers has a manufacturing specification (in mm) of 0.200 +/- .07. historical data indicates that if the quality characteristic takes on values greater than 0.27 or smaller than 0.13 the component fails at a cost of20.19. based on these data: determine the taguchi loss function (must show work) calculate an estimated loss for a quality characteristic of .30 calculate an estimated loss for quality characteristic of .40.

The associative, commutative, and distributive properties can be used on rational equations. true or false