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The altitude of a triangle is increasing at a rate of $ 1 cm/min $ while the area of the triangle is increasing at a rate of $ 2 cm^2/min. $ At what rate is the base of the triangle changing when the altitude is $ 10 cm $ and the area is $ 100 cm^2? $

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02:07

Wen Zheng

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Missouri State University

Campbell University

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.

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in order to figure out the rate. The first thing we know is that h is altitude and abuse base. Looking at the formula 1/2 base times height, we can plug in, let me know 100 centimeters squared his area. I only know H is 10 centimetres. Giving us B is 20 centimeters. Therefore, into the equation D A over DT is 1/2 HDB over DT. So it's 10 times D B over DT plus B times D H over DT 20 times one was just 20. Simplify this. We got a DP over. DT is negative 1.6 centimeters her minutes. So clearly the rate is decreasing since native.

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