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Related Rates Notes Steps: 1. Draw picture.

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Page 1: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Steps:1. Draw picture.

Page 2: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Steps:1. Draw picture.2. Write equation(s).

Page 3: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Steps:1. Draw picture.2. Write equation(s).3. Write all variables (include rates of change).

Page 4: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Steps:1. Draw picture.2. Write equation(s).3. Write all variables (include rates of change).4. Get equation in terms of one variable (may need another equation).

Page 5: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Steps:1. Draw picture.2. Write equation(s).3. Write all variables (include rates of change).4. Get equation in terms of one variable (may need another equation).5. Take derivative with respect to t.

Page 6: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Steps:1. Draw picture.2. Write equation(s).3. Write all variables (include rates of change).4. Get equation in terms of one variable (may need another equation).5. Take derivative with respect to t.6. Substitute and solve.

Page 7: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Steps:1. Draw picture.2. Write equation(s).3. Write all variables (include rates of change).4. Get equation in terms of one variable (may need another equation).5. Take derivative with respect to t.6. Substitute and solve.7. Answer the question.

Page 8: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesRight Δ's: a2 + b2 = c2 (Ladder problems)

Page 9: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesRight Δ's: a2 + b2 = c2 (Ladder problems)

Circles: A = πr2 C = 2 πr

Page 10: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesRight Δ's: a2 + b2 = c2 (Ladder problems)

Circles: A = πr2 C = 2 πr

Cones: V = (1/3)πr2h

Page 11: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesRight Δ's: a2 + b2 = c2 (Ladder problems)

Circles: A = πr2 C = 2 πr

Cones: V = (1/3)πr2h

Cylinders: V = πr2h

Page 12: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesRight Δ's: a2 + b2 = c2 (Ladder problems)

Circles: A = πr2 C = 2 πr

Cones: V = (1/3)πr2h

Cylinders: V = πr2h

Spheres: V = (4/3)πr3 S = 4πr2

Page 13: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Example: The famous ladder problem -- A.P.' s absolute favorite!

Page 14: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Example: The famous ladder problem -- A.P.' s absolute favorite!

Question: A ladder, 10 feet long is leaning against a building.

Page 15: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Example: The famous ladder problem -- A.P.' s absolute favorite!

Question: A ladder, 10 feet long is leaning against a building. The bottom of the ladder is moved away from the building at the constant rate of 0.5 ft/sec.

Page 16: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Example: The famous ladder problem -- A.P.' s absolute favorite!

Question: A ladder, 10 feet long is leaning against a building. The bottom of the ladder is moved away from the building at the constant rate of 0.5 ft/sec. Find the rate at which the ladder is falling down the building when the ladder is 6 feet from the building.

Page 17: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

Page 18: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

x

y

Page 19: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 Write equation(s).

10

x

y

Page 20: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 Write equation(s). x2 + y2 = 102

10

x

y

Page 21: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 Write equation(s). x2 + y2 = 102

10

x

y

Note: You may substitute a value only AFTER taking the derivative if that value is changing!

Page 22: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #3 Write all variables (include rates of change).

x2 = 6

Page 23: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #3 Write all variables (include rates of change).

x2 = 6 dx/dt = 0.5

Page 24: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #3 Write all variables (include rates of change).

x2 = 6 dx/dt = 0.5

y2 = 8

Page 25: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #3 Write all variables (include rates of change).

x2 = 6 dx/dt = 0.5

y2 = 8 (62 + y2 = 102)

Page 26: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #3 Write all variables (include rates of change).

x2 = 6 dx/dt = 0.5

y2 = 8 (62 + y2 = 102) dy/dt = ?

Page 27: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #3 Write all variables (include rates of change).

x2 = 6 dx/dt = 0.5

y2 = 8 (62 + y2 = 102) dy/dt = ?

Step #4

Get equation in terms of one variable (may need another equation).

Page 28: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #3 Write all variables (include rates of change).

x2 = 6 dx/dt = 0.5

y2 = 8 (62 + y2 = 102) dy/dt = ?

Step #4

Get equation in terms of one variable (may need another equation).

No second equation to substitute for this problem

Page 29: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #5 Take derivative with respect to t.

x2 + y2 = 102

Page 30: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #5 Take derivative with respect to t.

x2 + y2 = 102

(dx/dt)(2x) + (dy/dt)(2y) = 0

Page 31: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #5 Take derivative with respect to t.

x2 + y2 = 102

(dx/dt)(2x) + (dy/dt)(2y) = 0

Recall: x = 6 and y = 8 when dx/dt = 0.5

Page 32: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #5 Take derivative with respect to t.

x2 + y2 = 102

(dx/dt)(2x) + (dy/dt)(2y) = 0

Step #6 (0.5)(2*6) + (dy/dt)(2*8) = 0

Recall: x = 6 and y = 8 when dx/dt = 0.5

Page 33: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #5 Take derivative with respect to t.

x2 + y2 = 102

(dx/dt)(2x) + (dy/dt)(2y) = 0

Step #6 (0.5)(2*6) + (dy/dt)(2*8) = 0

6 + 16(dy/dt) = 0

Page 34: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #5 Take derivative with respect to t.

x2 + y2 = 102

(dx/dt)(2x) + (dy/dt)(2y) = 0

Step #6 (0.5)(2*6) + (dy/dt)(2*8) = 0

6 + 16(dy/dt) = 0

dy/dt = -6/16 = -3/8

Page 35: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #7

The ladder is falling at a rate of 3/8 feet per second.

Page 36: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

The famous CONE problem -- A.P.'s 2nd favorite question!

Page 37: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

The famous CONE problem -- A.P.'s 2nd favorite question!

If a cone is expanding or contracting, then the radius and height remain proportional r1/h1 = r2/h2

Page 38: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

The famous CONE problem -- A.P.'s 2nd favorite question!

If a cone is expanding or contracting, then the radius and height remain proportional r1/h1 = r2/h2

Thus, you can substitute for r such that your V = (1/3)πr2h equation will only have h.

Page 39: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

The famous CONE problem -- A.P.'s 2nd favorite question!

If a cone is expanding or contracting, then the radius and height remain proportional r1/h1 = r2/h2

Thus, you can substitute for r such that your V = (1/3)πr2h equation will only have h.

Thus, you won't have to do the product rule!

Page 40: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Example:

Water is withdrawn from a conical reservoir 20 ft in diameter and 50 ft deep (vertex down) at the constant rate of 12 cubic feet per minute.

Page 41: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Example:

Water is withdrawn from a conical reservoir 20 ft in diameter and 50 ft deep (vertex down) at the constant rate of 12 cubic feet per minute.

How fast is the water level falling when the depth of water in the reservoir is 20 ft?

Page 42: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

Page 43: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

50

Page 44: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

50

h2

Page 45: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

50

h2

Page 46: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

50

h2

Page 47: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

50

h2

Page 48: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

50

h2

Page 49: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #1 Draw Picture

10

50

h2

r2

Page 50: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 V = (1/3)πr2h

10

50

h2

r2

Page 51: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 V = (1/3)πr2h and (10/50) = (r2/h2)

10

50

h2

r2

Page 52: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 V = (1/3)πr2h and (10/50) = (r2/ h2)

10

50

h2

r2

So, 50r2 = 10 h2

Page 53: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 V = (1/3)πr2h and (10/50) = (r2/ h2)

10

50

h2

r2

So, 50r2 = 10 h2

r2 = (10/50) h2

Page 54: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #2 V = (1/3)πr2h and (10/50) = (r2/ h2)

10

50

h2

r2

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

Page 55: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #3 V = (1/3)πr2h and (10/50) = (r2/ h2)

10

50

h2

r2

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

Page 56: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #3 V = (1/3)πr2h and (10/50) = (r2/ h2)

10

50

h2

r2

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

Page 57: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #4 V = (1/3)πr2h and (10/50) = (r2/ h2)

10

50

h2

r2

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

Page 58: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #4 V = (1/3)πr2h and (10/50) = (r2/ h2)

10

50

h2

r2

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

Page 59: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #4 V = (1/3)πr2h and (10/50) = (r2/ h2)

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/3)π(0.2h)2h

Page 60: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #4 V = (1/3)πr2h and (10/50) = (r2/ h2)

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/3)π(0.2h)2hV = (1/3)π (.04h 2 )h

Page 61: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #4 V = (1/3)πr2h and (10/50) = (r2/ h2)

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/3)π(0.2h)2hV = (1/3)π (.04h 2 )h

V = (1/75)πh 3

Page 62: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #4 V = (1/3)πr2h and (10/50) = (r2/ h2)

So, 50r2 = 10 h2

r2 = (10/50) h2

r2 = 0.2 h2

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/3)π(0.2h)2hV = (1/3)π (.04h 2 )h

V = (1/75)πh 3

Use this equation for Volume!

Page 63: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #5 Take derivative with respect to time

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3

Page 64: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #5 Take derivative with respect to time

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

Page 65: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

Page 66: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

Page 67: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

Page 68: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

Page 69: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

Page 70: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

-12=(1/25)π(20) 2(dh/dt)

Page 71: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

-12=(1/25)π(20) 2(dh/dt)

-12=(1/25)π(400)(dh/dt)

Page 72: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

-12=(1/25)π(20) 2(dh/dt)

-12=(1/25)π(400)(dh/dt)

-12= 16π(dh/dt)

Page 73: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates NotesStep #6 Solve for dh/dt

h2 = 20

dv/dt = -12

V =

r2 = 0.2*20 = 4

dh/dt = ?

V = (1/75)πh 3 (dv/dt) = (1/25)πh 2(dh/dt)

-12 = (1/25)πh 2(dh/dt)

-12=(1/25)π(20) 2(dh/dt)

-12=(1/25)π(400)(dh/dt)

-12= 16π(dh/dt)

dh/dt = -3/(4π)

Page 74: Related Rates Notes Steps: 1. Draw picture.. Related Rates Notes Steps: 1. Draw picture. 2. Write equation(s)

Related Rates Notes

Step #7

The water level is falling at a rate of -3/(4π) feet per minute!