# 3.11 Related Rates Mon Nov 10 - PowerPoint PPT Presentation

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3.11 Related Rates Mon Nov 10. Do Now Differentiate implicitly in terms of t 1) 2). Related Rates. When we use implicit differentiation, we obtain dy/dx, or the change of y in terms of x. In many real life situations, each quantity in an equation changes with time (or another variable)

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3.11 Related Rates Mon Nov 10

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### 3.11 Related RatesMon Nov 10

• Do Now

• Differentiate implicitly in terms of t

• 1)

• 2)

### Related Rates

• When we use implicit differentiation, we obtain dy/dx, or the change of y in terms of x.

• In many real life situations, each quantity in an equation changes with time (or another variable)

• In this case, any derivative we find is called a related rate, since each rate in the derivative is related to each other

### Related Rates Steps

• 1) Make a simple sketch, if possible

• 2) Identify what rate you are looking for

• 3) Set up an equation relating ALL of the relevant quantities

• 4) Differentiate both sides of the equation in terms of the variable you want

• if you want dv/dt, you differentiate in terms of t

• 5) Substitute in values we know

• 6) Solve for the remaining rate

### Ex 1

• A 5-meter ladder leans against a wall. The bottom of the ladder is 1.5 m from the wall at time t=0 and slides away from the wall at a rate of 0.8m/s. Find the velocity of the top of the ladder at time t=1

### Ex 2

• Water pours into a fish tank at a rate of 0.3 m^3 / min. How fast is the water level rising if the base of the tank is a rectangle of dimensions 2 x 3 meters?

### Ex 3

• Water pours into a conical tank of height 10 m and radius 4 m at a rate of 6 m^3/min

• A) At what rate is the water level rising when the level is 5 m high?

• B) As time passes what happens to the rate at which the water level rises?

### Ex 4

• A spy uses a telescope to track a rocket launched vertically from a launching pad 6km away. At a certain moment, the angle between the telescope and ground is equal to pi/3 and is changing at a rate of 0.9 radians/min. What is the rocket’s velocity at that moment?

• See book

### Closure

• At what rate is the diagonal of a square increasing if its sides are increasing at a rate of 2 cm/s?

• HW: p.199 #1-37 every other odd

• Ch 3 Test next week? Mon?

### 3.11 Related Rates Cont’dTues Nov 11

• Do Now

• Air is being pumped into a spherical balloon at a rate of 5 cm3/min.  Determine the rate at which the radius of the balloon is increasing when the radius of the balloon is 10 cm.

• (hint: Volume = 4/3 pi x r^3)

### HW Review p.199 #1-35

• Probably all of them

• worksheet

### Closure

• Hand in: A 15 foot ladder is resting against the wall.  The bottom is initially x feet away from the wall and is being pushed towards the wall at a rate of 0.5 ft/sec.  How fast is the top of the ladder moving up the wall when the bottom of the ladder is 4 feet from the wall?? (Hint: Use Pythagorean Theorem)

• HW: p.199 #1-35 all other odd

• p.AP3-1 #1-20, 1-4 due Thurs

• P.203 #5-11, 17-25, 29-75 85-115 119-123 due Fri