What is Related Rate Calculator?
Related Rate Calculator is a useful tool that assists in calculating the rate of change of one variable with respect to another variable that is changing. It is frequently employed in calculus classes to solve problems involving two or more related variables that shift over time.
The related rate formula is a mathematical expression that calculates the rate of change of one variable with respect to another variable that’s also changing.
RLR = dV1 / dV2(1)
Where,
- RLR is the Related Rate
- dV1 is the change in the first variable
- dV2(1) is the change in the second variable relative to the first variable.
How to Calculate the Related Rate?
To use the formula, you need to determine the values of dV1 and dV2(1) at a given point in time and plug them into the formula to calculate the Related Rate.
Here is an example to demonstrate how to calculate the Related Rate:
Imagine that a rectangular tank is being filled with water at an average rate of 2 cubic feet per minute. If its length is 6 feet and width increases at 0.5 feet per minute, what is the rate at which the height of the water is rising?
Solution:
Let’s assume that the height of the water is h feet, and it is increasing at a rate of dh/dt. According to the problem statement, the volume of the water is given by:
V = lwh
where l = 6 ft and w = h ft.
Differentiating both sides of the equation with respect to time, we get:
dV/dt = 6h dh/dt
Since the tank is being filled at a rate of 2 cubic feet per minute, we can say that:
dV/dt = 2 cubic feet per minute
Also, the width of the tank is increasing at a rate of 0.5 feet per minute, which means:
dw/dt = 0.5 feet per minute
Substituting the values of dV/dt, l, w, and dw/dt into the equation, we get:
2 = 6h dh/dt * 0.5
Simplifying the equation, we get:
dh/dt = 2 / (6h * 0.5) = 1 / (3h)
Therefore, the rate at which the height of the water is rising is 1/ (3h) feet per minute.
Conclusion:
In conclusion, a Related Rate Calculator is an invaluable tool for solving real-world problems that involve multiple variables changing over time.
Calculating the Related Rate is done through a formula: RLR = dV1 / dV2(1), where dV1 represents any change in the first variable and dV2(1) represents any shift in the second relative to it.
By finding the values of dV1 and dV2(1) at a specific point in time and plugging them into a formula, we can calculate the rate of change of one variable with respect to another variable that is changing.
