Shop Assignment 5

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec. How fast is the area of the outer circle changing when the diameter is 8 in?

• 80pi in/sec

• 20pi in/sec

• 60pi in/sec

• 40pi in/sec

All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing each edge is 1 centimeter.

• -12 cm^3/sec

• -9 cm^3/sec

• 12 cm^3/sec

• 9 cm^3/sec

What is this thing?

• Pikachu

• something from my nightmares

• Furby

• An alarm clock

• A small robot that may become self-aware at some point...

Answer explanation

The Furby is an electronic toy created by Tiger Electronics in 1998. The toy was produced until 2000, and in that time became one of the most popular toys of the era. The Furby is a strange creature, not unlike an owl in appearance. It has a number of different parts that can move, giving it a semblance of life and emotion. The Furby begins its life-cycle speaking exclusively in a gibberish language known as Furbish, but over time, as it is interacted with more, it begins to speak more and more English and less Furbish. A Furby is able to interact with another Furby by means of an infrared port in its head. This allowed two Furbies to interact with each other.

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

• 4/3 ft/sec

• 8/7 ft/sec

• 1 ft/sec

• 8/3 ft/sec

Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm³/sec.  How fast is the diameter changing when the diameter is 8 cm?

• -1/(16pi) cm/sec
• -1/16 cm/sec
• -1/(4pi) cm/sec
• 1/(4pi) cm/sec

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the height of the water changing when the water is 2 ft deep?

• -9/(8pi) ft/sec
• 9/(8pi) ft/sec
• -8/(9pi) ft/sec
• 8/(9pi) f/tsec

Devin set up a toy rocket. For safety, he stands 6 meters from the rocket. He sets off the rocket and it heads straight up at a constant rate of 4 m/s.  How fast is the distance between the rocket and Devin changing after 2s?

• -2.5 m/s
• 2.5 m/s
• 3.2 m/s
• -3.2 m/s