When blood flows along a blood vessel, the flux f (the volume of blood per unit time that flows past

2 answers
Question:

When blood flows along a blood vessel, the flux f (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius r of the blood vessel.
that is, f = kr4 where k is some constant. this is known as poiseuille's law. show that the relative change in f (that is, df / f) is about four time the relative change in r.
how will a 5% increase or decrease in the radius of the artery affect the flow of blood?

Answers

just use this websites https://www.symbolab.com/

Step-by-step explanation:

[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]

So a 5% relative increase in R would mean a 20% relative increase in F

Step-by-step explanation:

First we need to remind the definition of relative increase of a variable.

For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].

Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].

Let's then start by deriving F with respect to R:

[tex]\frac{dF}{dR}=4kR^3[/tex]

thus

[tex]dF=4kR^3dR[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]

[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].

If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get

[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]

Similar Solved Works

4 answers

Evidence supporting a miami-dade county votes to keep a goung​

Evidence supporting a miami-dade county votes to keep a goung​...
3 answers

A hair stylist has three colors of hair dye. She has 4 bottles of chestnut, 7 bottles of blond, and 8 bottles of cherry.

A hair stylist has three colors of hair dye. She has 4 bottles of chestnut, 7 bottles of blond, and 8 bottles of cherry. What does the ratio 8:19 represent in this situation? Explain your reasoning. Include a model in your explanation. ​...
4 answers

Gwen commutes to work. her commute is 35 miles each day. on friday, she drives 28 miles farther than

gwen commutes to work. her commute is 35 miles each day. on friday, she drives 28 miles farther than any other day. her total commute for the week is 203 miles. what equation can be used to find the number of days, x, gwen commutes to work during the week?...
4 answers

निम्न छोलों को शुद्ध विल्यन कोलायडी निलम्बन में बोले

निम्न छोलों को शुद्ध विल्यन कोलायडी निलम्बन में बोले उ "तीनों में 5-5 अन्तर (क) ग) विशेषताएँ लिखो पानी + नमक पानी + रेत The f...
10 answers

Factor each trinomial. then match the polynomial (term) on the left with its factored form (definition)

Factor each trinomial. then match the polynomial (term) on the left with its factored form (definition) on the right. match term definition x2 – 4x – 12 a) (x – 2)(x + 6) x2 + 4x – 12 b) (x – 6)(x + 2) x2 – x – 12 c) (x – 4)(x + 3) x2 – 7x – 12 d) prime...
3 answers

. Joyce and Marianne both earn a combined income of $1,600 a week. Marianne earns $200 more than Joyce. How much income do Joyce and

. Joyce and Marianne both earn a combined income of $1,600 a week. Marianne earns $200 more than Joyce. How much income do Joyce and Marianne each earn? ( I need the equation and it needs to be solved. )...
3 answers

There are 23 students in mrs. cooper’s class and 26 students in mr. clark’s class.

There are 23 students in mrs. cooper’s class and 26 students in mr. clark’s class. the students in these two classes raised a total of $1,003.00 for the school fundraiser what is the average amount collected by each student?...
2 answers

If this trapezoid is moved through thetranslation (x+1, y-3), what will thecoordinates of B' be?BАD1-7-6-54-

If this trapezoid is moved through the translation (x+1, y-3), what will the coordinates of B' be? B А D 1 -7 -6 -54 - 3 -2 -10 1 2 3 4 -1 B' = ([?], [ 1) [tex]If this trapezoid is moved through the translation (x+1, y-3), what will the coordinates of B' be[/tex]...
10 answers

Which is an example of a positive incentives for consumers

Which is an example of a positive incentives for consumers...
6 answers

Can sum one help me please ASAP

Can sum one help me please ASAP [tex]Can sum one help me please ASAP[/tex]...
10 answers

Which statement best describes the relationship between central bankIndependence and price stability?A.

Which statement best describes the relationship between central bank Independence and price stability? A. A government with a high degree of control over its central bank is better able to promote price stability because it can directly control the growth rate of the mone supply B. When the central...
5 answers

Can someone help me with Question 13 and 14. The questions and the directions are shown in the photo attached right here:

Can someone help me with Question 13 and 14. The questions and the directions are shown in the photo attached right here: [tex]Can someone help me with Question 13 and 14. The questions and the directions are shown in the phot[/tex]...
8 answers

What was the slave fugitive act?

What was the slave fugitive act?...
8 answers

The following set of coordinates most specifically represents which figure? (−5, 6), (−1, 8), (3, 6), (−1, 4)

The following set of coordinates most specifically represents which figure? (−5, 6), (−1, 8), (3, 6), (−1, 4)...
3 answers

Simplify and if u can show ur work that would be great u​

Simplify and if u can show ur work that would be great u​ [tex]Simplify and if u can show ur work that would be great u​[/tex]...
4 answers

$400 invested with compound interest at a rate of 3% per year for 2 years.Formula: M= P(1+ i)'$3517.88O $888.15$1519.38$1788.14$424.36NEED

$400 invested with compound interest at a rate of 3% per year for 2 years. Formula: M= P(1+ i)" $3517.88 O $888.15 $1519.38 $1788.14 $424.36 NEED ANSWERS ASAP PLEASE [tex]$400 invested with compound interest at a rate of 3% per year for 2 years. Formula: M= P(1+ i) $[/tex]...
4 answers

The abundance of what minerals led to many flocking to the west in the mid-1800s?a. gold, silver, and copperb. gold and copperc. gold and silverd.

The abundance of what minerals led to many flocking to the west in the mid-1800s? a. gold, silver, and copper b. gold and copper c. gold and silver d. copper and silver...
3 answers

If the tone is informative, what would the mood be?

If the tone is informative, what would the mood be?...
4 answers

What is equal and opposite, according to Newton's third law?actionchange in velocityreactionchange

What is equal and opposite, according to Newton's third law? action change in velocity reaction change in acceleration...
3 answers

( the subject is dollars and sense) When comparing checking accounts, interest earned on the account is the most important

( the subject is dollars and sense) When comparing checking accounts, interest earned on the account is the most important factor. Agree or disagree Your friend says it’s a bad idea to have a checking account because of all the fees. Make a persuasive argument about the benefits of having a check...

-- 0.051916--