96. Blood Flow As blood moves through a vein or artery, itsvelocity v is greatest along the central axis and decreases asthe distance r from the central axis increases (see the figurebelow). For an artery with radius 0.5 cm, v (in cm/s) is givenas a function of r (in cm) byv = g(r) = 18,500(0.25 – r²)(a) Find g!. What does g represent?(b) Find g-(30). What does your answer represent?

Answered: 96. Blood Flow As blood moves through a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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Related questions

Question

96. Blood Flow As blood moves through a vein or artery, its
velocity v is greatest along the central axis and decreases as
the distance r from the central axis increases (see the figure
below). For an artery with radius 0.5 cm, v (in cm/s) is given
as a function of r (in cm) by
v = g(r) = 18,500(0.25 – r²)
(a) Find g!. What does g represent?
(b) Find g-(30). What does your answer represent?

Expert Solution

Step 1

If a function f takes the elements of a set X to the set Y then, the inverse of f takes the elements from

the set Y to the set X.

The inverse of a function f is denoted by $f^{- 1}$ and it exists only when the function f is one-one and

onto function.

Step 2

Part a

We have $v = 18500 (0.25 - r^{2})$ .

Now,

$\begin{array}{rcl} v & = & 18500 (0.25 - r^{2}) \\ v & = & 4625 - 18500 r^{2} \\ r^{2} & = & \frac{4625 - v}{18500} \\ r & = & \frac{\sqrt{4625 - v}}{10 \sqrt{185}} \end{array}$

Therefore, $g^{- 1} (v) = \begin{array}{rcl} \frac{\sqrt{4625 - v}}{10 \sqrt{185}} \end{array}$ and this function represents the radial distance from the central axis.