A pyramid with known bottom edge length a and height h is to be inscribed with a cuboid with square base area (side length x and height y), which has maximum volume.
(a) Formulate the nonlinear optimization problem with constraints.
(b) Give the optimal solution.

The number of hours per week that the television is turned on is determined for each family in a sample. the mean of the data is 37 hours and the median is 33.2 hours. twenty-four of the families in the sample turned on the television for 22 hours or less for the week. the 13th percentile of the data is 22 hours. approximately how many families are in the sample? round your answer to the nearest integer.

Asales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. the representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. she uses the given expression to model the number of club members, in hundreds, after advertising for t months.

Nicole purchased a container of cashews that weighs 5 kilograms. zion purchased a container of cashews that weighs 4,900 grams. how many more grams of cashews did nicole purchase?