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A trough is $ 10 ft $ long and its ends have the shape of isosceles triangles that are $ 3 ft $ across at the top and have a height of $ 1 ft. $ If the trough is being filled with water at a rate of $ 12 ft^3/ min, $ how fast is the water level rising when the water is $ 6 inches $ deep?

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02:22

Wen Zheng

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Campbell University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

04:15

A trough is 12 feet long a…

06:25

11:57

Filling a Trough A trough …

02:37

(Filling a trough) The cro…

We're trying to figure out how fast the water level is rising, so we know that B is three H because three over one is B over H. Therefore we know V is be times Age, so three h times age. Remember, be a screech. Times 10 divide by two Go for V is 15 h squared 30 over 2 15 Therefore, Devi over DT is 30 h times d h over DT, which means that 12 is 30 times 0.5 times d h over DT, which means that the age over D she is for over 50.8 feet per minute.

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