Related Rates Practice
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What are related rates in calculus?
Back
Related rates are a method used in calculus to find the rate at which one quantity changes in relation to another quantity that is also changing.
2.
FLASHCARD QUESTION
Front
How do you set up a related rates problem?
Back
1. Identify the quantities that are changing and what rates are given. 2. Write an equation that relates these quantities. 3. Differentiate the equation with respect to time. 4. Substitute known values and solve for the unknown rate.
3.
FLASHCARD QUESTION
Front
What is the formula for the distance between two points in a plane?
Back
The distance d between two points (x1, y1) and (x2, y2) is given by d = √((x2 - x1)² + (y2 - y1)²).
4.
FLASHCARD QUESTION
Front
In the context of related rates, what does 'dx/dt' represent?
Back
'dx/dt' represents the rate of change of x with respect to time t.
5.
FLASHCARD QUESTION
Front
What is the significance of the Pythagorean theorem in related rates problems involving distance?
Back
The Pythagorean theorem helps relate the sides of a right triangle, which is often used to find distances between moving objects in related rates problems.
6.
FLASHCARD QUESTION
Front
How do you find the rate at which the distance between two moving objects is changing?
Back
Use the distance formula to express the distance as a function of time, differentiate with respect to time, and substitute the known rates of change.
7.
FLASHCARD QUESTION
Front
What is the relationship between the volume and radius of a sphere?
Back
The volume V of a sphere is given by V = (4/3)πr³, where r is the radius.
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