Math 125 Hwk for Oct. 19 & 24
Related Rates.

15b. Page 231, 1,2,3,5,9,19,&23

1. The three dimensions of a box are increasing at the rates of 5 cm/min, 7 cm/min, and 2 cm/min. At what rate is the volume increasing at the moment when the box is a cube with edge 10 cm? At what rate is the surface area increasing?

2. The base of a triangle is increasing at the rate of 3 cm/min, while the altitude is decreasing at the same rate. At what rate is the area changing when (a) the base is 10 cm and the altitude is 6 cm? (b) the base is 6 cm and the altitude is 10 cm?

3. The area of a circle is increasing at the rate of ¹ cm²/min. At what rate is the radius increasing when the area is 4¹ cm²?

5. A kite is 100 ft high. There are 260 ft of string out and it is being paid out at the rate of 5 ft/s. If this results in the kite being carried along horizontally, what is the horizontal speed of the kite?

9. A light inside a garage is 10 ft above the floor and 6 ft behind the door opening. If the overhead door is descending at the rate of 1 ft/s, with the bottom of the door remaining in the same vertical plane, at what rate is the door’s shadow approaching the garage when the bottom of the door is 2 ft above the floor?

19. A point is moving along the curve y = Ãx in such a way that its "x" coordinate is increasing at the rate of 3 units per minute. At what rate is "y" changing (a) when x = 1? (b) when x = 4?

23. A trough that is 12 m long and 2 m high is 2 m wide at the top and has triangular ends. If water is put in at the rate of 1 m³/min, how fast is the depth increasing when it is 1.5 m deep?