Question 19
1 pts
a boat sails 60 km east, then 10 km south, and then 20 km
west. the distance, in kilometers, of the boat from its
starting point is:

10√17

Step-by-step explanation:

The movement of the boat takes the shape of a trapezium as shown in the attached photo.

The distance of the boat from its starting point is represented by x kilometers.

To determine the distance, x, we would apply Pythagoras theorem on the right angle triangle ABC formed. It is expressed as

Hypotenuse² = opposite side² + adjacent side². It becomes

x² = 40² + 10² = 1600 + 100

x² = 1700

x = √1700 = √100 × √17

x = 10√17

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.