related rates

related rates

Assessment

Flashcard

Mathematics

12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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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

Define the term 'instantaneous rate of change'.

Back

The instantaneous rate of change of a function at a point is the limit of the average rate of change as the interval approaches zero, often represented as the derivative.

3.

FLASHCARD QUESTION

Front

What is the formula for the volume of a sphere?

Back

V = (4/3)πr³, where V is the volume and r is the radius.

4.

FLASHCARD QUESTION

Front

How do you find the derivative of a function with respect to time?

Back

Use implicit differentiation, treating all variables as functions of time.

5.

FLASHCARD QUESTION

Front

What is the relationship between the radius and the volume of a sphere?

Back

As the radius increases, the volume increases at a rate proportional to the cube of the radius.

6.

FLASHCARD QUESTION

Front

If air is leaving a balloon at a constant rate, how does that affect the radius?

Back

The radius decreases as the volume decreases, and the rate of change of the radius can be found using related rates.

7.

FLASHCARD QUESTION

Front

What is the formula for the area of a circle?

Back

A = πr², where A is the area and r is the radius.

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