# Related Rates Homework Problem

• muna580
In summary, the Related Rates Homework Problem involves using calculus to find the rate of change of one variable with respect to another in a given scenario. This type of problem typically involves multiple variables and rates that are related to each other through a given equation or formula. The goal is to determine the rate of change of one variable while keeping the others constant. This technique is commonly used in real-world applications, such as physics, economics, and engineering, to analyze and predict changes in complex systems.
muna580
I am trying to do the problem below but I don't understand how to do it. Can you please show me how to do it? DON'T give me the answer, explain to me how to get the answer.

http://img134.imageshack.us/img134/9168/untitled1au7.jpg

Point C moves at a constant rate along semicircle centered at ) from A to B. The radius of the semicircle is 10 cm, and it takes 30 sec for C to move from A to C. Angle COB has measure y radians, angle OCA has measure z radians, and AC = x cm as indicated in the figure.

a) What is the rate of change, in radians per sec, of x with respect to time?

b) What is the rate of change, in radians per sec, of y with respect to time?

c) x and y are related by the Law of Cosines; that is, y^2 = 10^2 + 10^2 - 2(10)(10)cos y. What is the rate of change of x with respect to time when y = π/2 radians?

d) Let D be the area of ΔOAC. Show that D is largest when x = π/2 radians.

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The first thing you should do is go back and take the time to copy the problem correctly! You have consistently confused x and y!

muna580 said:
I am trying to do the problem below but I don't understand how to do it. Can you please show me how to do it? DON'T give me the answer, explain to me how to get the answer.

http://img134.imageshack.us/img134/9168/untitled1au7.jpg

Point C moves at a constant rate along semicircle centered at ) from A to B. The radius of the semicircle is 10 cm, and it takes 30 sec for C to move from A to C. Angle COB has measure y radians, angle OCA has measure z radians, and AC = x cm as indicated in the figure.

a) What is the rate of change, in radians per sec, of x with respect to time?
You just told us that x is measured in cm, not radians! Do you mean "in cm per sec" or do you mean rate of change of y?

What is the rate of change, in radians per sec, of y with respect to time?

c) x and y are related by the Law of Cosines; that is, y^2 = 10^2 + 10^2 - 2(10)(10)cos y. What is the rate of change of x with respect to time when y = π/2 radians?
Well, they've pretty much given you the answer right there! Except that, of course you mean x^2= 10^2+ 10^2- 2(10)(10)cos y. Differentiate both sides of that with respect to t. You were also told that "it takes 30 sec for C to move from A to C" which doesn't really make sense. I think you meant that it take 30 sec for the moving point to move from A to C. Unless you are given some information about exactly where C is, I don't see how that helps you! Since they specify y= $\pi$/2 radians, do they mean it take 30 seconds to go from A to $\pi$/2 radians?

d) Let D be the area of ΔOAC. Show that D is largest when x = π/2 radians.
The altitude of that triangle is 10 sin(y). (And again, x cannot be "$\pi/2$ radians", it is a length. Presumably, you meant y.)

Last edited by a moderator:
Can you help me with the problem below except:

angle AOC = x
angle ACO = y
and AC = s
Thanks!

alyssajune said:
Can you help me with the problem below except:

angle AOC = x
angle ACO = y
and AC = s
Thanks!

Aside from the fact that you're hijacking a four-year-old thread, you need to show some work before we help you with a problem. It's forum policy.

## What is a "Related Rates Homework Problem"?

A "Related Rates Homework Problem" is a type of problem commonly found in math or physics courses where two or more variables are related to each other and changing over time. The goal of these problems is to find the rate of change of one variable with respect to another.

## How do I solve a "Related Rates Homework Problem"?

To solve a "Related Rates Homework Problem", you will need to use the chain rule from calculus to find the derivative of the related variables. Then, you can set up an equation using the given information and solve for the desired rate of change.

## What are some common mistakes to avoid when solving a "Related Rates Homework Problem"?

Some common mistakes to avoid when solving a "Related Rates Homework Problem" include forgetting to use the chain rule, confusing the variables and their rates of change, and not properly setting up the equation with the given information.

## What are some real-world applications of "Related Rates Homework Problems"?

"Related Rates Homework Problems" have many real-world applications, such as predicting the rate of change of chemical reactions, determining the speed of an object in motion, and calculating the growth rate of populations.

## Are there any tips for approaching "Related Rates Homework Problems"?

Some tips for approaching "Related Rates Homework Problems" include carefully reading and understanding the given information, drawing a diagram to visualize the problem, and breaking the problem into smaller, more manageable steps.

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