Show that tan4x=sec2xtan2x+1-sec2x

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Typically a point in a three dimensional cartesian coordinate system is represented by which of the following answers in the picture !

Aconstruction worker needs to put a rectangular window in the side of a building he knows from measuring that the top and bottom of the window have a width of 8bfeet and the sides have a length of 15 feet he also measured one diagonal to be 17 feet what is the length of the other diagonal