The resistance of blood flowing through an artery is R = C L r4 where L...

The resistance of blood flowing through an artery is

R = C

r⁴

where L and r are the length and radius of the artery and C is a positive constant. Both L and r increase during growth. Suppose

r = 0.1 mm,

L = 1 mm,

and

C = 1.

(a) Suppose the length increases 10 mm for every mm increase in radius during growth. Use a directional derivative to determine the rate at which the resistance of blood flow changes with respect to a unit of growth in the r-L plane.

Cr4

(b) Use a directional derivative to determine how much faster the length of the artery can change relative to that of its radius before the rate of change of resistance with respect to growth will be positive.

(c) Illustrate your answers to parts (a) and (b) with a sketch of the directional derivatives on a plot of the level curves of R. (Use u for the unit change described in part (a) and v for the unit change described in part (b).)

Solutions

Expert Solution

Kindly give a positive feedback

Colby Messinger answered 7 months ago

Next > < Previous

Related Solutions

During the process of charging a capacitor C through a resistance R ; the physical quantity...

During the process of charging a capacitor C through a resistance R ; the physical quantity that decreases exponentially with time is : Select one: A. the time constant of the RC circuit B. the charge on the capacitor C. the potential difference across the capacitor D. the charging current

Decreased blood flow through the renal artery stimulates the release of renin into the blood. What...

Decreased blood flow through the renal artery stimulates the release of renin into the blood. What happens next? Describe the process until it has influenced renal function.

Blood flows through a section of a horizontal artery that is partially blocked by a deposit...

Blood flows through a section of a horizontal artery that is partially blocked by a deposit along the artery wall. A hemoglobin molecule moves from the narrow region into the wider region. What happens to the pressure acting on the molecule? There is no change in the pressure. The pressure increases. The pressure decreases.

1. The loans provided by banks have three elements: (L, r, C). Where L is the...

1. The loans provided by banks have three elements: (L, r, C). Where L is the amount of the loan, r is the interest rate on the loan and C is the security for the loan. At this time, businessman X received a loan (500 million, 10%, 200 million) from the bank. At this time, businessman X is a person who wants to maximize the expected rate of return, and there are two types of projects X can invest in,...

The turbulent blood flow through the renal artery, narrowed due to atherosclerosis, led to the sound...

The turbulent blood flow through the renal artery, narrowed due to atherosclerosis, led to the sound detected upon examination. Why did the differential renal vein renin test show an increased in the blocked renal artery side secretion of renin, yet a drop in renin levels on the other (normal) side?

Describe magnetic inductance and give examples. Describe R-L, L-C, and L-R-C series circuits, and give examples....

Describe magnetic inductance and give examples. Describe R-L, L-C, and L-R-C series circuits, and give examples. ( NOT by hand)

Describe magnetic inductance and give examples. Describe R-L, L-C, and L-R-C series circuits, and give examples....

Describe magnetic inductance and give examples. Describe R-L, L-C, and L-R-C series circuits, and give examples. PLEASE DO NOT WTITE IT BY HAND .

Consider the Potential V(r) =Vo (c/r) exp (-r/c) (where c is a constant) and a deutron...

Consider the Potential V(r) =Vo (c/r) exp (-r/c) (where c is a constant) and a deutron of reduced mass m moving in this potential . (a) Using a trial wave function R(r) = exp (- d *r / c) (d is constant ) find the ground state energy if Vo= 1.35 (b) If one bound state energy is -2.2 find Vo

In a series R-L-C circuit, R= 360 ohm , L= 0.410 H and C= 1.1*10^-2 micro...

In a series R-L-C circuit, R= 360 ohm , L= 0.410 H and C= 1.1*10^-2 micro F. 1.What is the resonance angular frequency of the circuit? 2. The capacitor can withstand a peak voltage of 550 V. If the voltage source operates at the resonance frequency, what maximum voltage amplitude can it have if the maximum capacitor voltage is not exceeded?

A 8.0 µF capacitor is charged by a 11.0 V battery through a resistance R. The...

A 8.0 µF capacitor is charged by a 11.0 V battery through a resistance R. The capacitor reaches a potential difference of 4.00 V at a time 3.00 s after charging begins. Find R in kO. I've been using , but I'm not sure if that is right since I just CAN'T get the right answer...I keep getting 370.7 kO (incorrect).

Subjects