4.5 MCQ

If the basebof a triangle is increasing at a rate of 3 inches per minute while its heighthis decreasing at a rate of 3 inches per minute, which of the following must be true about the areaAof the triangle?

• A is decreasing only when b<h

• A is decreasing only when b>h

• A is always increasing

• A is always decreasing

Functions,, andare differentiable with respect to time and are related by the equation. Ifxis decreasing at a constant rate of 1 unit per minute andyis increasing at a constant rate of 4 units per minute, at what rate iswchanging with respect to time when and? x=6 and y=20

• -384

• -240

• -96

• 276

The sides and diagonal of the rectangle above are strictly increasing with time. At the instant whenx=4 andy=3 , and and. What is the value ofkat that instant?

• (A) 1/4

• (B) 1/3

• (C) 3

• (D) 4

• (E) It cannot be determined from the information given.

The positive variables p and c change with respect to time t. The relationship between p and c is given by the equation . At the instant whenandwhat is the value of

• -82/75

• -2sqaure root of 5/3

• -3sqaure root of 5/2

• -82 sqaure root of 5/15

A cup has the shape of a right circular cone. The height of the cup is 12 cm, and the radius of the opening is 3 cm. Water is poured into the cup at a constant rate of 2cm^3/sec. What is the rate at which the water level is rising when the depth of the water in the cup is 5 cm? (The volume of a cone of height h and radius r is given by)

• 32/25pi cm/sec

• 96/125pi cm/sec

• 2/3pi cm/sec

• 2/9pi cm/sec

A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant?

• The surface area is increasing by 28pi square millimeters per second.

• The surface area is decreasing by 28pi square millimeters per second.

• The surface area is increasing by 32pi square millimeters per second.

• The surface area is decreasing by 32pi square millimeters per second.

The volume of a sphere is decreasing at a constant rate of 3 cubic centimeters per second. At the instant when the radius of the sphere is decreasing at a rate of 0.25 centimeter per second, what is the radius of the sphere? (The volume V of a sphere with radius r is.)

• 0.141 cm

• 0.244 cm

• 0.250 cm

• 0.489 cm

• 0.977 cm

A container has the shape of an open right circular cone, as shown in the figure above. The container has a radius of 4 feet at the top, and its height is 12 feet. If water flows into the container at a constant rate of 6 cubic feet per minute, how fast is the water level rising when the height of the water is 5 feet? (The volumeVof a cone with radiusrand height h is .)

• (A) 0.358 ft/min

• (B) 0.688 ft/min

• (C) 2.063 ft/min

• (D) 8.727 ft/min

• (E) 52.360 ft/min

A spherical snowball is melting in such a way that it maintains its shape. The snowball is decreasing in volume at a constant rate of 8 cubic centimeters per hour. At what rate, in centimeters per hour, is the radius of the snowball decreasing at the instant when the radius is 10 centimeters? (The volume of a sphere of radius r is .)

• sqaure root of 5/4pi

• 125/12pi

• 5 sqaure root of 12pi

• 125/36pi

The fuel consumption of a car, in miles per gallon (mpg), is modeled by, wheresis the speed of the car, in miles per hour. If the car is traveling at 50 miles per hour and its speed is changing at the rate of 20 miles/hour2 what is the rate at which its fuel consumption is changing?

• (A) 0.215 mpg per hour

• (B) 4.299 mpg per hour

• (C) 19.793 mpg per hour

• (D) 25.793 mpg per hour

• (E) 515.855 mpg per hour