1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
balandron [24]
4 years ago
15

Coughing forces the trachea to contract, which affects the velocity v of the air passing through the trachea. Suppose the veloci

ty of the air during coughing is v = k(R-r)r2 where k and R are constants, R is the normal radius of the trachea, and r is the radius during coughing. What radius will produce the maximum air velocity?
Physics
1 answer:
Katyanochek1 [597]4 years ago
7 0
The normal radius of the trachea does not change so you can view R as a constant as well. 


Find v ' and solve v ' = 0. 

v ' = k(R-r)(2r) + k(-1)(r^2) 

v ' = 2rk(R-r) + -kr^2 

v ' = 2rkR - 2kr^2 - kr^2 

v ' = 2rkR - 3kr^2 


Set v ' = 0 and solve for r. 


0 = 2rkR - 3kr^2 

0 = rk(2R - 3r) 

rk = 0 or 2R - 3r = 0 

r = 0 or 2R = 3r 

r = 0 or r = 2R/3 


Plug 0 and 2R/3 for the orginal v and the larger value is the maximum. 


If r = 0, then v = k(R - 0)(0^2) = 0 

If r = 2R/3, then v = k(R - 2R/3)(2R/3)^2 


v = k(R/3)(4R^2 / 9) 

v = 4kR^3 / 27 


<span>Therefore, the radius of 2R/3 will produce the maximum air velocity of 4kR^3 / 27.</span>
You might be interested in
Anyone want to talk? whats photosynthesis
choli [55]
<h2>Answer:</h2>

<h2>Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's metabolic activities</h2>

<h2>MaRk mE aS braiNliest ❤️</h2>

4 0
3 years ago
Read 2 more answers
What is the main source of groundwater? A. precipitation falling into man-made wells B. precipitation seeping through pores and
Yuliya22 [10]

Answer:

B: precipitation seeping through pores and cracks in the ground

Explanation:

Man made wells aren't the main source because their isn't enough of them and morning dew doesn't go in to the ground in one main source.

5 0
3 years ago
Electrons moving back and forth through a circuit would be
yaroslaw [1]

The particles that carry charge through wires in a circuit are mobile electrons. The electric field direction within a circuit is by definition the direction that positive test charges are pushed. Thus, these negatively charged electrons move in the direction opposite the electric field.

5 0
4 years ago
If engine oil gets into the brake fluid, which of the following will happen? A. Rubber seals will swell. B. Everything should op
wlad13 [49]
The answers are A and D.

Engine oil reacts with rubber, changing its properties and causing it to expand. This will compromise rubber seals in the brake system and lead to a failure.


4 0
4 years ago
Read 2 more answers
A tightly wound 1000-turn toroid has an inner radius 1.00 cm and an outer radius 2.00 cm, and carries a current of 1.50 A. The t
V125BC [204]

Therefore, the magnitude of magnetic field at a distance 1.10cm from the origin is 27.3mT

<u>Explanation:</u>

Given;

Number of turns, N = 1000

Inner radius, r₁ = 1cm

Outer radius, r₂ = 2cm

Current, I = 1.5A

Magnetic field strength, B = ?

The magnetic field inside a tightly wound toroid is given by B = μ₀ NI / 2πr

where,

a < r < b and a and b are the inner and outer radii of the toroid.

The magnetic field of toroid is

B = \frac{u_oNI}{2\pi r}

Substituting the values in the formula:

B (1.10cm) = \frac{(4\pi X 10^-^7 ) ( 1000)(1.5)}{2\pi (1.10) } \\\\

B (1.10cm) = 27.3mT

Therefore, the magnitude of magnetic field at a distance 1.10cm from the origin is 27.3mT

7 0
3 years ago
Other questions:
  • Which electromagnetic waves emitted from the sun produce a heating effect?
    6·1 answer
  • A ball is shot straight up from the surface of the
    5·1 answer
  • How does the flatter design make sweeping the floor easier
    6·1 answer
  • How many moons does Jupiter have?<br><br> I think it is 67 but im not sure.
    6·2 answers
  • A 5.0 kg object moving at 5.0 m/s. KE = mv2 times 1/2
    12·1 answer
  • What does the diagram show about Earth’s interior? The outer core is the hottest region. The mantle is hotter than the outer cor
    14·2 answers
  • A super train is moving along a track at a speed close to the speed of light. you are watching the train from the ground. you ob
    5·1 answer
  • Can some smart person help me out here!!!!!!!
    12·2 answers
  • A 21.0 kg uniform beam is attached to a wall with a hi.nge while its far end is supported by a cable such that the beam is horiz
    9·1 answer
  • Choose the statements that correctly describe a scientific theory. Select all that apply.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!