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:
f=kr4(this is known as poiseuille’s law; ) a partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow. show that the relative change in f is about four times the relative change in r. how will a 5% increase in the radius affect the flow of blood?

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 .

Using this, the relative increase in F is and similarly the relative increase in R is given by .

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

thus

.

If we plug the value 5% in we get

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.