What is the Correct Approach for Calculating Connected Rates of Change?

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In summary, a connected rate of change is the relationship between two changing quantities, where the change in one quantity affects the change in the other quantity. It is calculated by finding the ratio of the change in one quantity to the change in the other quantity and is significant in fields such as calculus, physics, and economics. It is closely related to the concept of limits and can be negative, indicating that the two quantities are changing in opposite directions.
  • #1
AntSC
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Homework Statement



CRoC.jpg

Homework Equations

The Attempt at a Solution


CRoC Solution.jpg
My problem is with part ii)
To me, my logic seems sound for the rate of change of depth but apparently it's wrong.
Does anyone see what I'm missing?
Thanks
 
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  • #2
AntSC said:

Homework Statement



View attachment 93778

Homework Equations

The Attempt at a Solution


View attachment 93779My problem is with part ii)
To me, my logic seems sound for the rate of change of depth but apparently it's wrong.
Does anyone see what I'm missing?
Thanks

In part ii) check your arithmetic. What is 4 ⋅ 14?
 
  • #3
Oops! Thanks. Working too fast.
 

Related to What is the Correct Approach for Calculating Connected Rates of Change?

1. What is a connected rate of change?

A connected rate of change refers to the relationship between two changing quantities, where the change in one quantity affects the change in the other quantity. It is also known as a derivative or slope.

2. How is a connected rate of change calculated?

A connected rate of change is calculated by finding the ratio of the change in one quantity to the change in the other quantity. This can be represented as a fraction or written in the form of a function.

3. What is the significance of connected rates of change in mathematics?

Connected rates of change are essential in mathematics as they help us understand and analyze the relationship between two changing quantities. They are used in fields such as calculus, physics, and economics to model and solve real-world problems.

4. How do connected rates of change relate to the concept of limits?

Connected rates of change are closely related to the concept of limits because they can be used to find the instantaneous rate of change at a specific point. This is done by taking the limit as the change in one quantity approaches zero.

5. Can connected rates of change be negative?

Yes, connected rates of change can be negative. A negative rate of change indicates that the two quantities are changing in opposite directions. This can be seen in situations such as the decreasing temperature of a hot object, where the rate of change of temperature is negative.

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