💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
Get the answer to your homework problem.
Try Numerade Free for 30 days
Like
Report
When blood flows along a blood vessel, the flux $F$ (the vol-ume of blood per unit time that flows past a given point) isproportional to the fourth power of the radius $R$ of the bloodvessel: $$F=k R^{4}$$(This is known as Poiseuille's Law.) A partially cloggedartery can be expanded by an operation called angioplasty,in which a balloon-tipped catheter is inflated inside theartery in order to widen it and restore the normal blood flow. Show that the relative change in $F$ is about four times therelative change in $R .$ How will a 5$\%$ increase in the radiusaffect the flow of blood?
If percentage error in $R$ is $5 \%,$ then percentage error in $F$ will be $5 \times 4=20 \%$
Calculus 1 / AB
Chapter 2
DERIVATIVES
Section 8
Linear Approximations and Differentials
Derivatives
Differentiation
Applications of the Derivative
Campbell University
Baylor University
University of Nottingham
Boston College
Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
01:06
When blood flows along a b…
00:45
Relative change in blood f…
01:23
Blood flow High blood pres…
03:18
High blood pressure result…
01:22
Unclogging arteries The fo…
03:27
Blood flow The shape of a …
03:44
Blood Flow As blood moves …
04:18
0:00
Blood flow One of Poiseuil…
02:32
Relative change in blood v…
in this question were given function. F is related to our by this function, and it's differential because toe for K archeo times Thea so k is a constant a year and the relative era we'll be, yeah, f over ev. So we need we can do some cancellation here, So K disappears. We have four times t r o graph. Um so if if the relative error in our equals to 5% we can see the purity. If era you nave, we will be four times this, which is 20%.
View More Answers From This Book
Find Another Textbook
In mathematics, precalculus is the study of functions (as opposed to calculu…
In mathematics, a function (or map) f from a set X to a set Y is a rule whic…
When blood flows along a blood vessel, the flux $ F $ (the volume of blood p…
Relative change in blood flow Another law of Poiseuille says that when blood…
Blood flow High blood pressure results from constriction of the arteries. To…
High blood pressure results from constriction of the arteries. To maintain a…
Unclogging arteries The formula $V=k r^{4},$ discovered by the physiologist …
Blood flow The shape of a blood vessel (a vein or artery) can be modeled by …
Blood Flow As blood moves through a vein or an artery, its velocity $v$ is g…
Blood flow One of Poiseuille's laws states that theresistance of bl…
Relative change in blood velocity Suppose $y=f(x)$ and $x$ and $y$ change by…
If two resistors with resistances $R_{1}$ and $R_{2}$ are connectedin pa…
02:14
$1-38=$ Find the limit. Use l'Hospital's Rule where appropriate.
00:55
03:39
(a) Prove that $\sin ^{-1} x+\cos ^{-1} x=\pi / 2.$(b) Use part (a) to p…
01:46
Find the numerical value of each expression.(a) $\tanh 0$(b) tanh 1<…
12:41
Use the guidelines of this section to sketch the curve.$$y=\frac{1}{5} x…
06:16
A runner sprints around a circular track of radius 100 $\mathrm{m}$ ata …
03:21
Prove the identity.$$\frac{1+\tanh x}{1-\tanh x}=e^{2 x}$$
00:53
(a) How is the logarithmic function $y=\log _{a} x$ defined?(b) What is …
00:58
Find the derivative of the function. Simplify where possible.$y=x \sin ^…
Create an account to get free access
Join Numerade as a
By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy
or sign in with
Already have an account? Log in
