MA 141 NCSU HW 2.7

Give your answer accurate to 3 decimal places. Gas is escaping from a spherical balloon at the rate of 14 ft3/hr. At what rate (in feet per hour) is the radius of the balloon decreasing when the volume is 300 ft3?

0.065

Give your answer accurate to 3 decimal places. The area of an equilateral triangle is decreasing at a rate of 3 cm2/min. Find the rate (in centimeters per minute) at which the length of a side is decreasing when the area of the triangle is 300 cm2.

0.132

Give your answer accurate to 3 decimal places. Water is flowing at the rate of 9 ft3/min into a tank that is in the shape of a right circular cylinder whose base radius is 3 ft. How fast (in feet per minute) is the water level rising?

0.318

Give your answer accurate to 3 decimal places. A streetlight is on a pole 17 ft tall. A boy 4 ft tall walks away from the pole at a rate of 5 ft/sec. At what rate is his shadow lengthening when he is 20 ft from the pole? At what rate (in feet per second) is the tip of his shadow moving?

1.538 6.538

Give your answer accurate to 3 decimal places. Claire starts at point A and runs east at a rate of 11 ft/sec. One minute later, Anna starts at A and runs north at a rate of 7 ft/sec. At what rate (in feet per second) is the distance between them changing after another minute?

12.604

A point P(x, y) moves along the graph of the equation y = x3 + x2 + 3. The x-values are changing at the rate of 4 units per second. How fast are the y-values changing (in units per second) at the point Q(1, 5)?

20

Give your answer accurate to the nearest whole number. An airplane, flying at a constant speed of 360 mi/hr and climbing at a 30 degree angle, passes over a point P on the ground at an altitude of 5,280 ft. Find the rate (in miles per hour) at which its distance from P is changing one minute later.

357

Give your answer accurate to the nearest whole number. As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at the rate of 8 in/min, find the rate (in cubic inches per minute) at which the sand is leaking out when the height is 14 in.

4926

Give your answer accurate to 3 decimal places. A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat at a point that is 1 ft above water level. The rope goes from the bow of the boat to a pulley located at the edge of the dock 8 ft above water level. If he pulls in the rope at a rate of 3 ft/sec, how fast (in feet per second) is the boat approaching the dock when the point of attachment is 18 ft from the dock?

unsure