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Solve the given problems by finding the appropriate differential.The volume $V$ of blood flowing through an artery is proportional to the fourth power of the radius $r$ of the artery. Find how much a$5 \%$ increase in $r$ affects $V$.

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 8

Differentials and Linear Approximations

Derivatives

Harvey Mudd College

Baylor University

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:13

Solve each problem.Acc…

01:01

When blood flows along a b…

03:44

Blood Flow As blood moves …

04:18

0:00

[T] The velocity $V$ (in c…

02:11

As blood moves through a v…

01:22

Unclogging arteries The fo…

09:39

Let $v(r)$ be the velocity…

04:15

The volume $V$ of a sphere…

03:15

The volume of a right circ…

according to presently lost the resistance to flow. Hear that assistance to flow a blood vessel rd directly proportional to length So assistance to directly proportional to length. And it is inversely proportional to the fourth power off the radius and inversely proportional to for power of the radius. That's now the biophysics office talk, American scientist. It is the difference if our request to 25. So that was our equals to some constant K Elly, divided with power for our power. For now, if all this 25 any questions will and Ari questo point here goingto that is your key elite will. And at this point to now we have to find the value off. Okay, so K equals two 25 multiplied with 2.2 power food divide which, well, don't solo here now and now we have to ask that to find the new Alu off our if you that is, I am saying that artists And now if our becomes 0.3 and l becomes until so for this artist will be OK here. L did until and our power for so now. Okay. Close to 25 multiplied with 0.2 powerful, divided with here. Develop felt that this will. And now our becomes 0.3 to power for now. So let's a moment in here now. By following this, we get our value that is here. 25 multiplied with here. Well, it will be expensive. And, you know, point toe you had with Europe 13 power. Whole power for that is the newly off RS equals two 25 multiplied with So he had the new value is 4.93 or approximately four. So this is a relation and this is

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