Morgan is in the business of manufacturing phones. She pays a cost of $200 per phone produced for materials and labor and also must pay a daily fixed cost of $400 to rent the building and equipment

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

The pyramid shown has a square base that is 24 centimeters on each side. the slant height is 16 centimeters. what is the lateral surface area?