When a company produces and sells x thousand units per week its total weekly profit is P thousand dollars. where P = 100x/100 + x^2. The production level at t weeks from the present is x = 4 + 2t Find the marginal profit, dP/dx and the time rate of change of profit, dp/dt. How fast (with respect of time) are profits changing when t =8? dP/dx = (Type an expression using x as the variable.) dP/dt = (Type an expression using t as the variable.) The profits are at the rate of $ per week, when t equals 8. (Simplify your answer.)

Complete the solution of the equation. find the value of y when x equals to 1 9x-5y=29

Hilary decided to purchase 3 points in order to lower her interest rate on her $140,000 mortgage. how much additional money does she need to bring to closing? a. $4200 b. $4000 c. $6 d. $400

Runners run around the school's football field. the cross country coach determines that the width of the field is seventy yards shorter than the length. part a write an expression that represents the perimeter of the football field. let x represent the length of the football field. include parentheses in your expression. next, write an equivalent expression that does not include parentheses. what property or properties did you use to simplify? explain. part b the cross country coach later determines that the length of the football field is 120 yards. all students must run five laps. using your answer from part a, determine the actual number of yards that each athlete must run in the tryouts. in order to make the team, students must complete the laps in 6 minutes. how quickly must they run each lap?