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What is the Pythagorean Theorem?
$a^2 + b^2 = c^2$
Area of a rectangle?
$A = l cdot w$
Steps to solve related rates problems?
1. Read carefully & identify key values. 2. Draw a diagram. 3. Set up an equation. 4. Implicit differentiation. 5. Substitute known values. 6. Solve for the desired rate.
First step when solving related rates?
Read the problem carefully and identify significant values. Circle, underline, or rewrite these values.
What to do after setting up the equation?
Differentiate the equation implicitly with respect to time (t), applying the chain rule.
What's the last step in related rates?
Solve for the desired rate, ensuring units match the expected units.
Define 'related rates'.
Problems involving finding the rate at which a variable changes with respect to time, given the rate of change of another related variable.
What is implicit differentiation?
Differentiating an equation with respect to a variable (often time), treating other variables as functions of that variable and applying the chain rule.