- #1
zimsam
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skeeter said:(a) $\dfrac{d}{dt}\bigg[(x-1)^2+ 2y^2=2 \bigg]$
you are given $\dfrac{dx}{dt}$ and the position of the planet.
use the derivative to calculate $\dfrac{dy}{dt}$
(b) hint …
$\theta = \arctan\left(\dfrac{y}{x}\right)$
skeeter said:
zimsam said:I already know that dy/dt must be changing as well...
How did I make a mistake in my implicit differentiation?
In order to identify the related rates in a problem, you need to look for variables that are changing with respect to time. These variables are typically represented by letters such as "x" or "y" and are usually given in units of distance, volume, or area.
The first step in solving a related rates problem is to clearly define the variables and their relationship to each other. This can be done by drawing a diagram and labeling the given and unknown variables.
To set up an equation for a related rates problem, you need to use the chain rule to relate the rates of change of the different variables. This involves taking the derivative of each variable with respect to time and then multiplying them together.
Units are crucial in solving a related rates problem because they help to ensure that the rates of change are consistent and can be properly multiplied and divided. It is important to keep track of units throughout the problem and to convert them as needed.
You can check the correctness of your solution by plugging in the given values and comparing the resulting rate of change with the given rate of change. If they match, then your solution is likely correct. It is also a good idea to double check your calculations and units to ensure accuracy.