Related Rates Seesaw Problem: Finding Average Rate of Change

In summary, a child weighing 34 kg is seated on a seesaw opposite a child weighing 40 kg. The function B(x) = 34x/40 represents the distance the 40 kg child must sit from the center of the seesaw when the 34 kg child sits x meters from the center. The seesaw is 9m long. The average rate of change in distance for the lighter child as their distance changes from 1.5m to 2.5m is -1.275. The derivative of the function is 34/40 or 0.85 and the given x value is 1.5. The correct answer is provided by the professor and it would be best to seek their help
  • #1
stokes
27
0
1. Homework Statement
A child weighs 34 Kg is seated on a seesaw. While a child who weighs 40 kg is situated on the opposite end of the seesaw. The function B(x)= 34x / 40 gives the distance that the 40 kg child must sit from the center of the seesaw when the 34 kg child sits x meters from the center. The seesaw is 9m long find the average rate of change in distance as the lighter childs distance changes from 1.5m to 2.5meters.


2. Homework Equations
I used the quotient rule to find the derivative of the function. Which turns out to be 68 / 80.


3. The Attempt at a Solution
The thing is the derivative is 34/40. Which equals to 0.85.

The prof gave us the answer which is -1.275. I haven't come close to that.

I used...

f(x) = f(b) - f(a) / b-a


I don't know how to tackle the average rate of change.
 
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  • #2
you have forgotten to use the given x value.

i.e.

34*x/40 = (34 * 1.5) / 40 = 1.275
 
  • #3
Hi stokes,

Was the problem formulated as you have given? Are you sure something's not missing?
 
  • #5
stokes, it would be best to take help from your professor.

And please let us know how he solved it.
 

Related to Related Rates Seesaw Problem: Finding Average Rate of Change

1. What is the concept of related rates in a seesaw?

Related rates in a seesaw refer to the relationship between the changing positions of two moving objects, such as the two ends of the seesaw, and how their rates of change are connected.

2. How do you set up a related rates problem involving a seesaw?

To set up a related rates problem involving a seesaw, you must identify the variables that are changing and their rates of change. Then, you can use the geometric properties of the seesaw to create an equation that relates the rates of change.

3. What is the role of calculus in solving related rates problems in a seesaw?

Calculus plays a critical role in solving related rates problems in a seesaw. The rates of change are represented by derivatives, and by using the chain rule and implicit differentiation, you can find the relationship between the rates of change.

4. Can you give an example of a related rates problem involving a seesaw?

Sure, an example of a related rates problem involving a seesaw could be: "Two children are playing on a seesaw. One child is moving up at a rate of 2 feet per second, while the other child is moving down at a rate of 3 feet per second. If the seesaw is 10 feet long, how fast is the seesaw rotating at that moment?"

5. What are some real-life applications of related rates in a seesaw?

Related rates in a seesaw can be applied to real-life scenarios, such as calculating the speed of a rollercoaster, the flow of water in a fountain, or the rate of change of air pressure in a hot air balloon. It is also used in physics and engineering to analyze the motion of objects and systems.

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