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Gravel is being dumped from a conveyor belt at a rate of $ 30 ft^3/min, $ and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is $ 10 ft $ high?

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02:01

Wen Zheng

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

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.

03:24

Gravel is being dumped fro…

02:03

02:51

At a sand and gravel plant…

04:45

Height At a sand and grave…

02:21

Sawdust is falling onto a …

03:14

02:28

we know the volume of a cone as pi r squared times h over three. We know that two are is H. Therefore we have high times h over too squared times H Divide by three which gives us V is Hi, it's cubed over 12 which gives us Devi over. DT. There's pie H squared over four times d h over d t now plugging in DV over ditches 30 30 is part of times 10. Remember h is 10 feet, so pi times 10 square divide by four times d h over DT gives us d h over DT is equivalent to sex over five pie units or feet per minute.

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