Question

ECON 2305 Tangent lines and the slope along a curve

The blue curve on the following graph shows the height of an airplane over 10 minutes of flight. The two black lines are tangent to the curve at the points indicated by A and B.

The slope of the blue curve measures the plane’s ( heading, altitude, rate of descent, time in the air). The unit of measurement for the slope of the curve is (miles per hour, degrees, thousands of feet per minute, thousands of feet) .

At point A, the slope of the curve is (7, 7000, -10000, -2.5, -10, -2500) which means that the plane is (ascending, descending) at a rate of (-10, 2500, -2500, -2.5, 7000, 7, -10000) feet per minute.

At point B, the slope of the blue curve is (-6.67, -10000, 2000, 2, -10, -6666.67) which means that the plane is (ascending, descending) at a rate of (6666.67, 2, -10, 2000, -6.67, -6666.67, -10000) feet per minute.

Answer 1

From the graph, the slope of the blue curve measures the plane's rate of descent, which is used to measure the speed of the aircraft miles per hour The unit of measurement for the slope of the curve is thousands of feet per minutes At point A, the tangent line is (0, 9) and (5, 10), thus slope is measured as follows Slope 10-0 5-9 10 -4 -2.5 Hence, the slope of the curve is -2,500 (-2.5x 1,000) At point A, the slope of the curve is -2.500, which means that the plane is descending at a rate of 2500 feet per minute At point B, the tangent line is (2.8, 20) and (1.2, 30), the slope is measured as follows Slope 20-30 -6.66 Hence, the slope of the curve is-6.66667(-666×1,000) At point B, the slope of the blue curve is -6.666.67 which meant that the plane is descending at a rate of 6,666.67 feet per minute