A lighthouse is due east of a sailboat. The sailboat's dock is 30 km straight north of the lighthouse. The captain measures his viewing angle between the sailboat and dock and
find it to be 35 degrees. How far is the sailboat from the dock?

step-by-step explanation:

i dont know

step-by-step explanation:

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.