Question

two particles are simultaneously traveling along the paths y=x² and cosh ( y -4 ) = 2x. if the first path is interpreted as y1= x², what can the second path be interpreted as in terms of y2?

Answer 1

The second path can be interpreted as
`\( y_2 = 4 + \cosh^(-1)(2x) \)`.

Step-by-step explanation:

Given that the first path is represented by
`\( y_1 = x^2 \)`, we need to find the interpretation for the second path,
`\( \cosh(y-4) = 2x \)`, in terms of
`\( y_2 \)`. To do this, isolate y in the second equation, resulting in
`\( y_2 = 4 + \cosh^(-1)(2x) \)`. This interpretation for
`\( y_2 \)` allows us to understand the second particle's trajectory along the given path.

The equation
`\( \cosh(y-4) = 2x \)` involves the hyperbolic cosine function and represents a different mathematical relationship compared to the parabolic curve
`\( y = x^2 \)`. The interpretation
`\( y_2 = 4 + \cosh^(-1)(2x) \)`captures the unique nature of the second particle's path in terms of
`\( y_2 \)`.