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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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Rate of decrease of distance between boat and dock is $\frac{\sqrt{65}}{8} \approx 1 \mathrm{ms}^{-1}$

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Wen Zheng

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Amrita Bhasin

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Carson Merrill

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Jasmine G.

May 5, 2022

The altitude of a triangle is increasing at a rate of 8 cm/s while the area of the triangle is increasing at a rate of 12 cm2 /s. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 100 cm2?

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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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.

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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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oh this is a question in which will be using the concept of increasing and decreasing our application of derivative. We should say if this is triangle abc, this is the altitude and this is the base so Area is 1/2 and two. Base into the altitude question number one. Now various things we have been given ah that altitude is increasing at a rate of one centimeter per minute. So D. H by DT is one cm/min. An area is increasing at the rate of two centimeters Squire per minute. So we need to find the raid outfits. The basis is changing when altitude is 10 centimeter and base area and the area is 100 centimeters square. So let us differentiate equation number eight with respect to T so dear by duty is half since be an edge all our variables. So you'll be using the concept of the differentiation of the product. So be the H by DT place DB by DT into at Disability is 2 1 x two B. What should be base should be taken as okay. At what rate is the base of the triangle is changing when altitude? Okay no problem. Be into DHB oddity we have one place delivery T. We need to find out and altitude is 10 cm we have to find the value of B when area is and the centimeter and ah Altitude is 10 cm 8800 centimeter square half into base into altitude 10. So the system. So BB. is 20 cm so we'll be plugging in value of 20 over here. So this will be to equal to one x 2, 22 and 20 plus DB by detained 2 10. So this will be four Equal to 20 plus and D. V by DT So D V. But it will be cool too, -16 x 10 -8 x five. So the rate of change of the base will be minus 85 centimeter permit on minus one point six centimeter per minute. Now this negative science shows that the base is decreasing with time. Thank you.

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