Optimization and Related Rates

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

Tags

CCSS.8.G.B.8

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
• 4opi in/sec

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.1

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

Tags

CCSS.HSG.GMD.A.3

A baseball diamond is a square with a side of 90 ft. Tucker hits the ball and runs towards first base at 16 ft/sec.  How fast is the distance between second base and Tucker changing when he is 30 ft from first base?

• 8.875 ft/sec
• 5.060 ft/sec
• -5.060 ft/sec
• -8.875 ft/sec

Tags

CCSS.HSA.CED.A.2

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.

• A=l*w
• V=3s²
• A=s²
• V=s³

Tags

CCSS.HSG.GMD.A.3

CCSS.HSG.GMD.A.1

A conical tank is 10 feet across the top and 12 feet deep.  If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water if 8 feet deep.

• V=(1/3)πr²h
• V=(4/3)πr³
• d=√(x²+y²)
• S=2lh+2lw+2hw

Tags

CCSS.HSG.GMD.A.3

Brie is what type of food?

• vegetable
• bread
• cheese
• fruit

Tags

CCSS.RI.11-12.5

CCSS.RI.6.5

CCSS.RI.7.5

CCSS.RI.8.5

CCSS.RI.9-10.5

What planet is the closets to earth?

• Venus 
• Mars 
• Saturn 
• Earth

Which comic book character was not in 'THE AVENGERS'

• Iron Man
• Captain American
• Spiderman
• The Hulk

Tags

CCSS.RL.1.10

CCSS.RL.K.5

Who are the Teenage Mutant Ninja Turtles?

• Donatello, Michelangelo,Leonardo, Raphael
• Donatello, Michelangelo,Leonardo,Galileo
• Donatello, Michelangelo, Leonardo, Vincent
• Donatello, Michelangelo,Leonardo, Pablo

Tags

CCSS.RL.2.6

CCSS.RL.8.3