A doorway into a store is in the shape of an arch whose equation is h=-4x² + 6x, where x represents the horizontal distance, in feet, from the left side of the bottom of the doorway, and h is the height, in feet, of the doorway. The bottom left side of the doorway is located at (0,0). Show or explain how you arrived at your solution a. How wide is the doorway at its base?

b. What is the maximum height of the doorway? c. Can a box that has the dimensions 6 feet by 6 feet by 5 feet, be moved through the

doorway without damaging the box? Explain your answer.

Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.

Ascientist places 24 cells in a petri dish. she knows the cells grow at an exponential rate, doubling in number every hour. how long will it take (in hours) for there to be 1100 cells in the dish? time to 1100 cells: 5.51832530 hours how long will it take to reach 110 cells? time to 110 cells : 2.1963972 hours what is the average rate of change in the number of cells between 9 hours and 11 hours? average rate of change: cells per hour what is the instantaneous rate of change after 7 hours? instantaneous rate of change: cells per hour note: you can earn partial credit on this problem.

90.0% complete a b c d e confirm last week, your delivery runs took 7 hours 12 minutes on monday, 6 hours 46 minutes on wednesday, and 6 hours 53 minutes on friday. what was your average time for a delivery run?