Aswimmer is drowning at b, a distance a/2=10 away from the beach. a lifeguard patrolling along the very edge of the beach spots the swimmer at point a which is a distance a=20m away from the point on the beach that is closest to the drowning swimmer. the average speed of a lifeguard running along the beach is v = 8 metres per second and her average swimming speed is v=v/3

the lifeguard runs along the beach at point c before she starts swimming find the quickest time t in which the life guard can reach the drowning swimmer.

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.

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.