What are the steps to a related rate problem? What are the key words you look for and what do they mean? Give an example of a related rate problem and solve it.
There are a certain set of guidelines to follow when solving related rate problems: 1. Identify all given quantities and quantities to be determined. Make a sketch and label the quantities. 2. Write an equation involving the variables whose rates of change either are given or are to be determined. 3. Using the Chain Rule, implicity differentiate both sides of the equation with respect to time t. 4. After completing Step 3, substitute into the resulting equation all known values for the variables and their rates of change. Then solve for the required rate of change.
Key words to look for are identify, sketch and label, write an equation whose variables have been determined, differenciate with implicity, substitue and solve for rate of change.
The steps to solving a related rate problem are: 1. Identify all given quantities and quantities to be determined. Make a sketch and label the quantities. (all this means is to identify all the parts of the problem that you are given.) 2. Write an equation involving the variables whose rates of change either are given or are to be determined. (all this means is to write an equation with all the things that the problem has given you.) 3. Using the Chain Rule, implicity differentiate both sides of the equation with respect to time t. (all this is telling you to take the derivative of both sides of the equation and plug d_/dt after every thing you took a derivative of.) 4. After completing Step 3, substitute into the resulting equation all known values for the variables and their rates of change. Then solve for the required rate of change.(this is telling you to plug in the numbers that the problem gave you for the variables they go with.) Example: x²y =8 1. dy/dt =? x = 4 dx/dt = 6 2. x²y = 8 3. x² dy/dt + 2xy dx/dt = 0 4. (4)² dy/dt = -2(4)y(6) 16dy/dt = -48y dy/dt = -3y
These are the steps, as in my notes to solve a related rate problem. Actually listing and using the steps make this a lot easier when working a related rate problem.
1. Identify all given quantities and quantities to be determined. Make a sketch of the problem and label the quantities correctly.
2. Write an equation involving the variables whos rates of change either are given or are to be determined. In other words, list what you KNOW, and list what you are TRYING TO FIND. 3. Using the Chain Rule, implicity differentiate both sides of the equation with respect to time t. (this means that all rates will be d something/dt 4. After completing Step 3, substitute into the resulting equation all known values for the variables and their rates of change. Then solve for the required rate of change.
Key words to look for are: Cubic = looking for volume; the rate of = d something/ dt
-Identify all given quantities and quantities to be determined. Make a sketch and label the quantities, or Identify what you are given in the problem.
-Write an equation with the variables whose rates of change are either given or are to be determined.
-Using the Chain Rule, implicity differentiate both sides of the equation with respect to time t. Meaning rates will be (d__/dt)
-Last, substitute into the equation all the known values for the variables and their rates of change. Then solve for the rate of change you are asked for.
Steps to Related Rates Problems. -Identify all given quantities and quantities to be determined. Make a sketch and label the quantities, or Identify what you are given in the problem. -Write an equation with the variables whose rates of change are either given or are to be determined. -Using the Chain Rule, implicity differentiate both sides of the equation with respect to time t. Meaning rates will be (d__/dt) -Last, substitute into the equation all the known values for the variables and their rates of change. Then solve for the rate of change you are asked for.
-Identify all given quantities and quantities to be determined. Make a sketch and label the quantities, or Identify what you are given in the problem.
-Write an equation with the variables whose rates of change are either given or are to be determined.
-Using the Chain Rule, implicity differentiate both sides of the equation with respect to time t. Meaning rates will be (d__/dt)
-Last, substitute into the equation all the known values for the variables and their rates of change. Then solve for the rate of change you are asked for.
There are a certain set of guidelines to follow when solving related rate problems:
ReplyDelete1. Identify all given quantities and quantities
to be determined. Make a sketch and label the
quantities.
2. Write an equation involving the variables
whose rates of change either are given or are
to be determined.
3. Using the Chain Rule, implicity differentiate
both sides of the equation with respect to
time t.
4. After completing Step 3, substitute into the
resulting equation all known values for the
variables and their rates of change. Then
solve for the required rate of change.
Key words to look for are identify, sketch and label, write an equation whose variables have been determined, differenciate with implicity, substitue and solve for rate of change.
Example:
xy = 4
Step 1: dy/dt = ? x = 8 dx/dt = 10
Step 2: xy = 4
Step 3: xdy/dt + ydx/dt = 0
Step 4: xdy/dt = -10y
= -10y/x
The steps to solving a related rate problem are:
ReplyDelete1. Identify all given quantities and quantities to be determined. Make a sketch and label the quantities. (all this means is to identify all the parts of the problem that you are given.)
2. Write an equation involving the variables whose rates of change either are given or are to be determined. (all this means is to write an equation with all the things that the problem has given you.)
3. Using the Chain Rule, implicity differentiate both sides of the equation with respect to time t. (all this is telling you to take the derivative of both sides of the equation and plug d_/dt after every thing you took a derivative of.)
4. After completing Step 3, substitute into the resulting equation all known values for the variables and their rates of change. Then solve for the required rate of change.(this is telling you to plug in the numbers that the problem gave you for the variables they go with.)
Example: x²y =8
1. dy/dt =? x = 4 dx/dt = 6
2. x²y = 8
3. x² dy/dt + 2xy dx/dt = 0
4. (4)² dy/dt = -2(4)y(6)
16dy/dt = -48y
dy/dt = -3y
These are the steps, as in my notes to solve a related rate problem. Actually listing and using the steps make this a lot easier when working a related rate problem.
ReplyDelete1. Identify all given quantities and quantities
to be determined. Make a sketch of the problem and label the
quantities correctly.
2. Write an equation involving the variables
whos rates of change either are given or are
to be determined. In other words, list what you KNOW, and list what you are TRYING TO FIND.
3. Using the Chain Rule, implicity differentiate
both sides of the equation with respect to
time t. (this means that all rates will be d something/dt
4. After completing Step 3, substitute into the
resulting equation all known values for the
variables and their rates of change. Then
solve for the required rate of change.
Key words to look for are: Cubic = looking for volume; the rate of = d something/ dt
Example:
xy = 6
Step 1: dy/dt = ? x = 4 dx/dt = 8
Step 2: xy = 6
Step 3: xdy/dt + ydx/dt = 0
Step 4: xdy/dt = -10y
= -2y
here are the rules for rate of change in my own words.
ReplyDelete1. you have to first lay out everything that is given to you in the problem.
2. after you've done so you write an equation.
3. you take the derivative of both sides of the equation that you have found.
4. after this you plug in and solve for dy/dx
here is an example:
dy/dt=? dx/dt=7
x=4
2. XY=8
3. XDY/Dt+ydx/dt=0
4 4 dy/dt=7y
dy/dt=-7y/4
Steps to Related Rates Problems.
ReplyDelete-Identify all given quantities and quantities
to be determined. Make a sketch and label the
quantities, or Identify what you are given in the problem.
-Write an equation with the variables
whose rates of change are either given or are
to be determined.
-Using the Chain Rule, implicity differentiate
both sides of the equation with respect to
time t. Meaning rates will be (d__/dt)
-Last, substitute into the equation all the known values for the variables and their rates of change. Then solve for the rate of change you are asked for.
Example:
xy^2 = 2
dy/dt = ? x = 5 dx/dt = 4
xy^2 = 2
2xy(dy/dt) + y^2(dx/dt) = 0
2(5)y(dy/dt)=y^2(4)
10y(dy/dt)=4y^2
dy/dt=4y^2/10y
Steps to Related Rates Problems.
ReplyDelete-Identify all given quantities and quantities
to be determined. Make a sketch and label the
quantities, or Identify what you are given in the problem.
-Write an equation with the variables
whose rates of change are either given or are
to be determined.
-Using the Chain Rule, implicity differentiate
both sides of the equation with respect to
time t. Meaning rates will be (d__/dt)
-Last, substitute into the equation all the known values for the variables and their rates of change. Then solve for the rate of change you are asked for.
Ex:xy^3=3
dy/dt=?x=5 dx/dt=4
xy^3=3
3xy(dy/dt)+y^2(dx/dt)=0
3(50y(dy/dt)=y^3(4)
15y(dy/dt)=3y^2
dy/dt=4y^2/15y
Steps of a Related Rate problem:
ReplyDelete-Identify all given quantities and quantities
to be determined. Make a sketch and label the
quantities, or Identify what you are given in the problem.
-Write an equation with the variables
whose rates of change are either given or are
to be determined.
-Using the Chain Rule, implicity differentiate
both sides of the equation with respect to
time t. Meaning rates will be (d__/dt)
-Last, substitute into the equation all the known values for the variables and their rates of change. Then solve for the rate of change you are asked for.
EXAMPLE:
xy=2
1. dy/dt=? x=4 dx/dt=2
2. xy=2
3. 1dx/dt + 1dy/dt=0
4. dy/dt=-2