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The question is to PROVE that dy/dx = (dy/dt)/(dx/dt). This follows from the chain rule (without getting into any heavy formalism).
We know x and y are functions of t. Given an appropriate curve (we can integrate piece-wise if necessary), y can be written as a function of x where x is a function of t, i.e., y = y(x(t)).
By the chain rule, we have dy/dt = dy/dx * dx/dt. For points where the derivative of x with respect to t does not vanish, we therefore have (dy/dt)/(dx/dt) = dy/dx.
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What advantages are there to using a parametric equations or numeric values?
Some curves are easier to describe and perform calculations on if using parametric equations
What is parametric equation for pear shaped quartic?
I looked all over the internet and could not find a parametric equation for this shape. You can look at the link below to find the regular cartesian equation. If you are good at parametric equations you could probably convert this into parametric form. I am not so good at parametric equations.
What disadvantages are there to using parametric equations for numeric values?
It might be easier to calculate using numeric values directly if the equation is really simple.
What advantages are there to using parametric equations instead of numeric values?
Frequently you have to solve complex sets of equations with many variables of different units. It is impractical to use numeric values because it makes the solving process obscure and therefore prone to bugs. It is easier to solve parametric equations down to the point where you have a relatively simple equation and then put in numeric values with their respective units. Plus, you can reuse the parametric equations easily and track how did you solve them any time later.
How do you find parametric equations to represent the graph of a given rectangle equation?
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