Sam is flying a kite. the length of the kite string is 80 meters, and it makes an angle of 75° with the ground. the height of the kite from the ground

We are given with the length of the kite string of 80 meters and an angle of 75 degrees of the string with the ground. In this situation, the kite string is the hypotheneuse of the triangle and 75 degrees is the angle of elevation. The height of the kite from the ground is 80 sin 75  or 77.27 meters. 

Iplay an instrument and i'm in band

Answer

1 number

explanation

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.