Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
- 8. Definite Integrals3h 25m
4. Applications of Derivatives
Related Rates
Problem 3.11.5c
Textbook Question
A rectangular swimming pool 10 ft wide by 20 ft long and of uniform depth is being filled with water.
c. At what rate is the water level rising if the pool is filled at a rate of 10ft³/min?
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1
Identify the volume of the rectangular swimming pool using the formula V = length × width × depth, where the length is 20 ft and the width is 10 ft.
Express the volume V in terms of the depth h, so V = 20 ft × 10 ft × h = 200h ft³.
Differentiate the volume equation with respect to time t to find the relationship between the rate of change of volume and the rate of change of depth: dV/dt = 200 * (dh/dt).
Substitute the given rate of volume change, dV/dt = 10 ft³/min, into the differentiated equation to solve for dh/dt.
Rearrange the equation to isolate dh/dt, which represents the rate at which the water level is rising.
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