You have 13 gallons of lemonade to sell. You use cone-shaped cups that are 7 centimeters in diameter and 11 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)

87

Step-by-step explanation:

the formula for the volume of a cone is  h

then one cone is

11

= 564.43948

3785*13/ 564.43948 = 87.1749 cups

so 87 full cones ,but when would you ever really fill the cones to the very top?  soo maybe a few more,  but by math, you'd only need 87

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.