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2 years ago

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The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electric

al potential in a neuron v(t) obeys the differential equation dv dt = −v[v2 − (1 + a)v + a] where a is a positive constant such that 0 < a < 1. (a) For what values of v is v unchanging (that is, dv/dt = 0)? (Enter your answers as a comma-separated list.) v

1 answer:

tatuchka [14]2 years ago

7 0

Answer:

v = 0, 1, a

Explanation:

dv/dt = v(v² - (1 + a)v + a)

When dv/dt = 0

=> 0 = v(v² - (1 + a)v + a)

=> v = 0 and (v² - (1 + a)v + a) = 0

Open up the bracket:

v² - v - av + a = 0

v(v - 1) - a(v - 1) = 0

(v - a) (v - 1) = 0

=> v = a and v = 1

Hence, the values of v for which dv/dt can be 0 are v = 0, 1, a.

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A block moves at 5 m/s in the positive x direction and hits an identical block, initially at rest. A small amount of gunpowder h

Anestetic [448]

Answer:

Speed of 1.83 m/s and 6.83 m/s

Explanation:

From the principle of conservation of momentum

$mv_o=m(v_1 + v_2)$ where m is the mass, $v_o$ is the initial speed before impact, $v_1$ and $v_2$ are velocity of the impacting object after collision and velocity after impact of the originally constant object

$5m=m(v_1 +v_2)$

Therefore $v_1+v_2=5$

After collision, kinetic energy doubles hence

$2m*(0.5mv_o)=0.5m(v_1^{2}+v_2^{2})$

$2v_o^{2}=v_1^{2} + v_2^{2}$

Substituting 5 m/s for $v_o$ then

$2*(5^{2})= v_1^{2} + v_2^{2}$

$50= v_1^{2} + v_2^{2}$

Also, it’s known that $v_1+v_2=5$ hence $v_1=5-v_2$

$50=(5-v_2)^{2}+ v_2^{2}$

$50=25+v_2^{2}-10v_2+v_2^{2}$

$2v_2^{2}-10v_2-25=0$

Solving the equation using quadratic formula where a=2, b=-10 and c=-25 then $v_2=6.83 m/s$

Substituting, $v_1=-1.83 m/s$

Therefore, the blocks move at a speed of 1.83 m/s and 6.83 m/s

6 0

2 years ago

A professor's office door is 0.89 m wide, 2.0 m high, and 4.0 cm thick; has a mass of 25 kg ; and pivots on frictionless hinges.

taurus [48]

In order to answer this question ... strange as it may seem ...
we only need one of those measurements that you gave us
that describe the door.

The door is hanging on frictionless hinges, and there's a torque
being applied to it that's trying to close it. All we need to do is apply
an equal torque in the opposite direction, and the door doesn't move.

Obviously, in order for our force to have the most effect, we want
to hold the door at the outer edge, farthest from the hinges. That
distance from the hinges is the width of the door ... 0.89 m.

We need to come up with 4.9 N-m of torque,
applied against the mechanical door-closer.

Torque is (force) x (distance from the hinge).

4.9 N-m = (force) x (0.89 m)

Divide each side by 0.89m: Force = (4.9 N-m) / (0.89 m)

= 5.506 N .

7 0

2 years ago

An object is 6.0 cm in front of a converging lens with a focal length of 10 cm.Use ray tracing to determine the location of the

Masja [62]

As we know that

$\frac{1}{d_i} + \frac{1}{d_0} = \frac{1}{f}$

here we know that

$d_0 = 6 cm$

$f = 10 cm$

now from above equation we have

$\frac{1}{d_i} + \frac{1}{6} = \frac{1}{10}$

$d_i = -15 cm$

so image will form on left side of lens at a distance of 15 cm

This image will be magnified and virtual image

Ray diagram is attached below here

8 0

2 years ago

If you add 700 kJ of heat to 700 g of water at 70 degrees C, how much water is left in the container? The latent heat of vaporiz

makkiz [27]

Answer:A

Explanation:Find attached picture file for details

3 0

2 years ago

Fill in the blanks to correctly complete the statement. The motion of an object moving with uniform circular motion is always to

Citrus2011 [14]

The sentence can be completed as follows:

<span>The motion of an object moving with uniform circular motion is always tangential to the circle, so the speed of an object moving in a circle is known as tangential speed.

The object moves by uniform circular motion due to the presence of a force (called centripetal force) pointing toward the center of the circle. Due to the presence of this force, the object experiences an acceleration (called centripetal acceleration) that makes the object turning in a circle. This centripetal acceleration changes only the direction of the velocity of the object, not its magnitude, which is called tangential speed and it is constant.</span>

8 0

2 years ago

Read 2 more answers