Ateacher is making tutus for the school play. she wants to make at least 24 tutus and needs 1.25 yards of tulle for each tutu. determine the amount of tulle she needs to buy. then interpret the solution

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?

At which value in the domain does f(x) =0?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).