Question

In: Math

Consider the following scenario: A drum used for percussion has sides modeled by a hyperbola. Suppose...

Consider the following scenario:

A drum used for percussion has sides modeled by a hyperbola. Suppose the total height of the drum is known. The diameter at the top of the drum is 16 inches, and the minimum diameter is 7 inches, occurring at a height of 9 inches. Assume that the center of the hyperbola occurs at the height where the diameter is the least.

Choose your own value for the height of the drum based on the scenario above and address the following:

Draw a graph or figure to represent this situation.
Describe how the concepts from this module can be applied in this case.
Determine the equation of a hyperbola that models the sides of the drum.
Provide another example of a scenario that involves the same concept.

Expert Solution

Given data in the question is as follows:

The diameter at the top of the drum is 16 inches

Minimum diameter is 7 inches

And occurring height is 9 inches.

Using the standard form of a hyperbola equation

Figure to represent the question situation

2a is the length of the transverse axis (distance where the side are closest)

2b is the length of the conjugate axis

X is half of the diameter at the top of the drum.

Suppose the total height of the drum is H.

Y=total height – original height from the bottom

Calculate the value of b, substituting all the value in equation (1)

Taking total height of drum is 30 inches,

Hence the equation of the hyperbola is

Another Practical example of Hyperbola:

Cooling tower

milcah answered 2 years ago

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