https://file.aiquickdraw.com/mathbot/file/1729775498100d20dobul.jpg

The equation shown in the image is:

\[
y = 60 \cosh \left( \frac{x}{60} \right)
\]

This is a hyperbolic cosine function, scaled by 60. The hyperbolic cosine function, \(\cosh(x)\), is defined as:

\[
\cosh(x) = \frac{e^x + e^{-x}}{2}
\]

Thus, the equation represents a curve that is symmetric about the y-axis and grows exponentially as \(x\) moves away from zero. It's commonly used in the study of hanging cables (catenaries) and physics.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. What is the derivative of \( y = 60 \cosh\left(\frac{x}{60}\right) \)?
2. How does the hyperbolic cosine function differ from the regular cosine function?
3. What are the applications of the hyperbolic cosine function in physics or engineering?
4. How would you find the minimum value of this function?
5. Can you graph the function and describe its behavior?

**Tip**: The hyperbolic cosine function grows much faster than the regular cosine function for large values of \(x\).

Explore the properties of the hyperbolic cosine function y = 60 cosh(x / 60), its mathematical definition, and applications. Learn how the cosh function is defined and used in calculus and physics. Suitable for Grades 11-12.

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