Review for Quiz 11 (2024 only): Related Rates Word Problems

If x and y are differentiable functions of t, and they are related by y=5x³ + 12

Find dy/dt   when x=2 and  dx/dt = -3 

dy/dt = (a)  

(Type in only the number, no space)

If x and y are differentiable functions of t, and they are related by y= 12x² - 10x

Find dy/dt   when x= -5 and  dx/dt = -4 

dy/dt = (a)  

(Type in only the number, no space)

If x and y are differentiable functions of t, and they are related by y=5x³ + 12

Find dx/dt   when x=3 and  dy/dt = -270 

dx/dt = (a)  

(Type in only the number, no space)

Each edge of a square, s, is decreasing at the rate of 9cm/sec.

At what rate is the area changing when the edge of the box is 6cm.

(Area of a square A=S²)

• 108 cm²/sec

• 54 cm²/sec

• 18 cm²/sec

• -108 cm²/sec

• -54 cm²/sec

Each edge of a square, s, is increasing at the rate of 10cm/sec.

At what rate is the perimeter changing when the edge of the box is 4cm.

(Perimeter of a square P=4S)

• 40 cm/sec

• 160 cm/sec

• -160 cm/sec

• 80 cm/sec

Each edge of a cube box, s, is increasing at the rate of 2cm/sec.

At what rate is the volume changing when the edge of the box is 5cm.

(Volume of a cube V=S³)

• 75 cm³/sec

• 40 cm³/sec

• 150 cm³/sec

• 125 cm³/sec

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Each edge of a cube box, s, is decreasing at the rate of 12cm/sec. At what rate is the the total surface area of the cube box changing when the edge of the box is 2cm.

(Cube total surface area A=6S²)

• -144 cm²/sec

• 144 cm²/sec

• 288 cm²/sec

• -216 cm²/sec

• -288 cm²/sec

Tags

CCSS.6.G.A.4

 The radius r of a circle is decreasing at a rate of 12 inches per minute.

Find the rate the area is changing when the radius is 4 inches.

Use A=πr² and leave your answer in terms of π

• 48π in²/min

• 96π in²/mi

• -96π in²/mi

• -192π in²/mi

• 192π in²/mi