Suppose the temperature of a liquid decreases from 72∘ 72 ∘ F to 55∘ 55 ∘ F after being placed in a 31∘ 31 ∘ F freezer for 55 55 minutes. Use Newtons Law of Cooling, T=A+(T0−A)e−kt, T = A + ( T 0 − A ) e − k t , to find the number of minutes needed for the liquid to cool from 75∘ 75 ∘ F to 58∘ 58 ∘ F in a 28∘ 28 ∘ F freezer. Hint: Round the k k -value to the nearest ten thousandth.

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?

Two lines that do not intersect are skew. always sometimes or never

Drag the tiles to the correct boxes to complete the pairs. using the properties of integer exponents, match each expression with the correct equivalent expression.