C) Am I Solving this Hyperbolic Functions Homework Correctly?

In summary, the conversation discusses a problem with question C) and how to approach it. The person has already solved A and B correctly and is unsure about their method for C). They are advised to consider the relationship between coefficients and to scale x accordingly in order to satisfy that relationship.
  • #1
orbsoner
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0

Homework Statement


Attached is the problem


Homework Equations



My question is am i going about it the right way for question C). I have done A and B and am sure they are correct.


The Attempt at a Solution


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  • #2
orbsoner said:
[am i going about it the right way for question C).
I don't think so.
Look at how you solved b). What relationship between the coefficients did the method depend upon? E.g. suppose the constant term had been something other than -2. Would that have radically changed the method of solution? What about the other two?
When you've determined what the relationship is, you need to scale x to make the more general equation satisfy that relationship.
 

1. What are hyperbolic functions?

Hyperbolic functions are mathematical functions that are derived from the hyperbolic sine (sinh) and cosine (cosh) functions. They are used to describe the relationship between the sides and angles of a hyperbola, similar to how trigonometric functions describe the relationship between sides and angles of a circle.

2. How are hyperbolic functions related to exponential functions?

Hyperbolic functions are closely related to exponential functions, as they can be expressed in terms of exponential functions. In fact, the hyperbolic sine and cosine functions can be defined as the sums of two exponential functions.

3. What is the difference between hyperbolic and trigonometric functions?

The main difference between hyperbolic and trigonometric functions is the shape of the curve they create. Trigonometric functions create circular curves, while hyperbolic functions create hyperbolic curves. Additionally, the domains and ranges of the two types of functions are different.

4. How are hyperbolic functions used in real-world applications?

Hyperbolic functions have a wide range of applications in physics, engineering, and mathematics. They are commonly used in electrical engineering to describe the behavior of alternating current circuits. They also have applications in the fields of geometry, astronomy, and statistics.

5. What are the inverse hyperbolic functions?

Inverse hyperbolic functions are functions that can "undo" the effects of a hyperbolic function, similar to how inverse trigonometric functions undo the effects of trigonometric functions. They are denoted with the prefix "arc" and the corresponding hyperbolic function, such as arsinh, arcosh, and artanh.

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