Lee Floyd
08/14/2023 · Middle School
LFad belagth of the paractric corve
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Step-by-step Solution
It seems like there might be a typo in your question. If you're asking about the "length of the parametric curve," I can help with that!
To find the length of a parametric curve defined by the equations \( x(t) \) and \( y(t) \) over an interval \( [a, b] \), you can use the following formula:
\[
L = \int_a^b \sqrt{\left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2} \, dt
\]
Here, \( \frac{dx}{dt} \) and \( \frac{dy}{dt} \) are the derivatives of \( x(t) \) and \( y(t) \) with respect to \( t \).
If you have specific functions for \( x(t) \) and \( y(t) \) and a specific interval, please provide them, and I can help you calculate the length of the curve!
Quick Answer
To find the length of a parametric curve, use the formula: \( L = \int_a^b \sqrt{\left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2} \, dt \).
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