Preparation for the homecoming football game, members of the student body are painting the spirit rock in front of the school. If Angela works alone, it will take her five and a half hours. If Brandon works alone, it will take him 7 hours. If they work together, it will take them approximately hours ?

3.08 hours

Step-by-step explanation:

Preparation for the homecoming football game, members of the student body are painting the spirit rock in front of the school.

If Angela works alone, it will take her five and a half hours.

If Brandon works alone, it will take him 7 hours. If they work together, it will take them approximately hours ?

This is calculated as:

The Number of hours they worked together = T

1/5.5 + 1/7 = 1/T

= 7 + 5.5/(5.5)(7)

= 12.5/38.5

1/T = 12.5/38.5

Cross Multiply

12.5T = 38.5

T = 38.5/12.5

T = 3.08 hours

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.