A plane is flying at a constant rate of 500 mph at a constant altitude of 1 mile toward a person. a. How fast is the angle of elevation changing when the.

Slides:

Advertisements

Similar presentations

4.6 Related Rates Any equation involving two or more variables that are differentiable functions of time t can be used to find an equation that relates.

Advertisements

1 Related Rates Section Related Rates (Preliminary Notes) If y depends on time t, then its derivative, dy/dt, is called a time rate of change.

2.6 Related Rates.

2019 Related Rates AB Calculus.

RELATED RATES PROBLEMS

ITK-122 Calculus II Dicky Dermawan

Section 2.6 Related Rates.

Section 2.6: Related Rates

1. Read the problem, pull out essential information and identify a formula to be used. 2. Sketch a diagram if possible. 3. Write down any known rate of.

A rocket launches vertically, 5 miles away from a tracking device at the same elevation as the launch site. The tracking device measures the angle of elevation.

Teresita S. Arlante Naga City Science High School.

A conical tank (with vertex down) 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,

Related Rates Objective: To find the rate of change of one quantity knowing the rate of change of another quantity.

Sec 2.6 Related Rates In related rates problems, one tries to find the rate at which some quantity is changing by relating it to other quantities whose.

8. Related Rates.

DERIVATIVES Related Rates In this section, we will learn: How to compute the rate of change of one quantity in terms of that of another quantity.

Section 2.8 Related Rates. RELATED RATE PROBLEMS Related rate problems deal with quantities that are changing over time and that are related to each other.

Aim: How do we solve related rate problems? steps for solving related rate problems Diagram Rate Equation Derivative Substitution.

Definition: When two or more related variables are changing with respect to time they are called related rates Section 2-6 Related Rates.

Section 2.6 Related Rates Read Guidelines For Solving Related Rates Problems on p. 150.

RELATED RATES Mrs. Erickson Related Rates You will be given an equation relating 2 or more variables. These variables will change with respect to time,

2.8 Related Rates.

1 Related Rates Finding Related Rates ● Problem Solving with Related Rates.

Related Rates Test Review

Aim: How do we find related rates when we have more than two variables? Do Now: Find the points on the curve x2 + y2 = 2x +2y where.

Section 4.1: Related Rates Practice HW from Stewart Textbook (not to hand in) p. 267 # 1-19 odd, 23, 25, 29.

R ELATED R ATES. The Hoover Dam Oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant.

Related Rates Section 4.6a.

3.9 Related Rates 1. Example Assume that oil spilled from a ruptured tanker in a circular pattern whose radius increases at a constant rate of 2 ft/s.

Calculus warm-up Find. xf(x)g(x)f’(x)g’(x) For each expression below, use the table above to find the value of the derivative.

Warmup 1) 2). 4.6: Related Rates They are related (Xmas 2013)

In this section, we will investigate the question: When two variables are related, how are their rates of change related?

Warm-Up If x 2 + y 2 = 25, what is the value of d 2 y at the point (4,3)? dx 2 a) -25/27 c) 7/27 e) 25/27 b) -7/27 d) 3/4.

Related Rates. I. Procedure A.) State what is given and what is to be found! Draw a diagram; introduce variables with quantities that can change and constants.

6.5: Related Rates Objective: To use implicit differentiation to relate the rates in which 2 things are changing, both with respect to time.

Miss Battaglia AP Calculus Related rate problems involve finding the ________ at which some variable changes. rate.

Differentiation: Related Rates – Day 1

Related Rates Section 4.6. First, a review problem: Consider a sphere of radius 10cm. If the radius changes 0.1cm (a very small amount) how much does.

4.1 - Related Rates ex: Air is being pumped into a spherical balloon so that its volume increases at a rate of 100cm 3 /s. How fast is the radius of the.

RELATED RATES DERIVATIVES WITH RESPECT TO TIME. How do you take the derivative with respect to time when “time” is not a variable in the equation? Consider.

Related Rates Objective: To find the rate of change of one quantity knowing the rate of change of another quantity.

The fuel gauge of a truck driver friend of yours has quit working. His fuel tank is cylindrical like one shown below. Obviously he is worried about running.

Sec 4.1 Related Rates Strategies in solving problems: 1.Read the problem carefully. 2.Draw a diagram or pictures. 3.Introduce notation. Assign symbols.

Applications of Derivatives Objective: to find derivatives with respect to time.

5.8: Intermediate Related Rates. Sand is poured on a beach creating a cone whose radius is always equal to twice its height. If the sand is poured at.

Drill: find the derivative of the following 2xy + y 2 = x + y 2xy’ +2y + 2yy’ = 1 + y’ 2xy’ + 2yy’ – y’ = 1 – 2y y’(2x + 2y – 1) = 1 – 2y y’ = (1-2y)/(2x.

3.9 Related Rates In this section, we will learn: How to compute the rate of change of one quantity in terms of that of another quantity. DIFFERENTIATION.

Examples of Questions thus far…. Related Rates Objective: To find the rate of change of one quantity knowing the rate of change of another quantity.

Section 2.8 Related Rates. RELATED RATE PROBLEMS Related rate problems deal with quantities that are changing over time and that are related to each other.

Related Rates. We have already seen how the Chain Rule can be used to differentiate a function implicitly. Another important use of the Chain Rule is.

Review Implicit Differentiation Take the following derivative.

Warm-up A spherical balloon is being blown up at a rate of 10 cubic in per minute. What rate is radius changing when the surface area is 20 in squared.

3.10 – Related Rates 4) An oil tanker strikes an iceberg and a hole is ripped open on its side. Oil is leaking out in a near circular shape. The radius.

Warm up 1. Calculate the area of a circle with diameter 24 ft. 2. If a right triangle has sides 6 and 9, how long is the hypotenuse? 3. Take the derivative.

Related Rates with Area and Volume

Section 2-6 Related Rates

DERIVATIVES WITH RESPECT TO TIME

Sect. 2.6 Related Rates.

Chapter 2 In-Class Test Review

Related Rates (2.6) October 5th, 2017

Related Rates (2.6) October 7th, 2016

Section 2.6 Calculus AP/Dual, Revised ©2017

Warm-up A spherical balloon is being blown up at a rate of 10 cubic in per minute. What rate is radius changing when the surface area is 20 in squared.

Related Rates Chapter 5.5.

Chapter 7 Review.

Law of Sines and Cosines

Related Rates and Applications

Related Rates ex: Air is being pumped into a spherical balloon so that its volume increases at a rate of 100cm3/s. How fast is the radius of the balloon.

Presentation transcript:

A plane is flying at a constant rate of 500 mph at a constant altitude of 1 mile toward a person. a. How fast is the angle of elevation changing when the angle is  /4? b. How fast is the angle of elevation changing when the angle is  /3 Steps for solving related rate problems. 1. Determine the variables that are changing. 2. Determine the rate you want to find. 3. Find a relationship between the variables. This is most often done by using things like the Pythagorean Theorem, Similar Triangles, Trigonometric Relations, and formulas for area, volume, concentration etc. 4. Take the derivative with respect to time before you plug in the values of the variables. 5. Substitute the known values and solve for the unknown you want to find from step 2.  1 mile x  

A light house located 1 mile from a straight shoreline. The light beacon rotates a 3 rpm. How fast is the beam of light traveling when it is moving toward the center and making an angle of  /6 with the shoreline? Water is being added to 50 liters of pure acid at a constant rate of ½ liter per minute. How fast is the concentration changing when 50 liters of water have been added to solution? A 6 foot man is walking away from a 24 foot light post at a constant rate of 3 feet/sec. How fast is the length of the man’s shadow increasing when he is 18 feet from the light post? shoreline  /6 A boy is flying a kite and the wind blows it so that the kite flies parallel to the ground at a constant height of 40 feet. If the string is leaving the spool in his hand at a rate of 4 feet/sec when there is 50 feet of sting out how fast is the wind blowing? 

A conical tank that is 18 cm high and 3 cm in radius is being filled with water at a constant 2 cm 3 /min. How fast is the height of the water increasing when the water is 6cm high in the tank? 18cm An oil tanker runs into a rock and begins to spill oil in the form of an increasing circular oil slick a uniform ½ inch thick. The hole in the tanker is causing the oil to leak out at a constant rate of 5 ft 3 /min. a) How fast is the radius of the oil slick increasing when the radius is 100 feet? b) How fast is the area the oil slick covers increasing when the radius is 100 feet?