freman1075 said:hi everyone,
i am having trouble with this rate of change question.
I need to find the rate of change of a sphere with a volume of V= 4/3*pi*r^3 in respect to it's surface area of A= 4*pi*r^2
can anyone give me a hand?
Thanks
HallsofIvy said:So you want to find dV/dA? Use the chain rule dV/dr= (dV/dA)(dA/dr) so dV/dA= (dV/dr)/(dA/dr). Find dV/dr and dA/dr and divide.
freman1075 said:hi everyone,
i am having trouble with this rate of change question.
I need to find the rate of change of a sphere with a volume of V= 4/3*pi*r^3 in respect to it's surface area of A= 4*pi*r^2
can anyone give me a hand?
Thanks
HallsofIvy said:So you want to find dV/dA? Use the chain rule dV/dr= (dV/dA)(dA/dr) so dV/dA= (dV/dr)/(dA/dr). Find dV/dr and dA/dr and divide.
Well, that is what I said in the post you quoted!freman1075 said:so if dV/dr = 4*pi*r^2
and if dA/dr = 8*pi*r
i just divide the two?
The rate of change in a problem refers to how much a particular quantity changes over a given period of time. It is often represented by the symbol "m" and is typically measured in units such as meters per second or dollars per hour.
To calculate the rate of change, you need to determine the change in the dependent variable (y) divided by the change in the independent variable (x) over a specific time interval. This can be represented as (y2-y1)/(x2-x1), where y2 and y1 are the final and initial values of y, and x2 and x1 are the final and initial values of x.
The average rate of change is the overall rate of change over a specific time interval, while the instantaneous rate of change is the rate of change at a specific point in time. The average rate of change can be calculated using the formula mentioned in question 2, while the instantaneous rate of change can be found by taking the derivative of the function at that point.
The concept of rate of change is used in many real-life situations, such as calculating the speed of a moving object, determining the growth rate of a population, or analyzing the change in stock prices over time. It is a useful tool in understanding and predicting patterns and trends in various fields.
One common misconception about rate of change is that it always has to be a constant value. In reality, the rate of change can vary over time and can even be negative. Another misconception is that the rate of change always has to be positive, but it can also be negative if the quantity is decreasing over time. It is important to understand the context and interpretation of the rate of change in a problem to avoid these misconceptions.