1.) The plane left LaGuardia airport at 3:25pm and about 2 minutes later struck a flock of birds (3:27.11pm).
The plane was 4 miles from LaGuardia airport and was ascending at an angle of 7.7° degrees. Calculate the
plane's height above ground level at the time of the bird strike (a). (4 points)

Explnation

The height of the plane, the point on the ground directly below of the plane, and the inclined path traveled by the plane make a right triangle, with:

The trigonometric ration sine relates the hypotenuse and the opposite leg of a right triangle:

Substitute, solve for x and compute:

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.

step-by-step explanation: 2