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
amid [387]
3 years ago
8

The number of students in a cafeteria is modeled by the function p that satisfies the logistic differential equation dp/dt = 1/2

000 p(200-p), where t is the time in seconds and p(0) = 25. what is the greatest rate of change, in students per second, of the number of students in the cafeteria?
Physics
2 answers:
Sergio [31]3 years ago
7 0
The function that we are given represents the rate of change. If p is the number of students in the cafeteria and you take the first derivative with respect to time you get the rate of change. Now we have to find the maxima of this function. This is usually done by finding the first derivate and then finding its roots. In this case, we are not explicitly given the function p(t) so we can't do that. You could solve the given differential equation and then find the second derivative. However, there is an easier way. We know that parabola has its maximum in the vertex. So all we have to do is find the vertex of the parabola we are given.
p'(t)=\frac{1}{2000}p(200-p)\\ p'(t)=\frac{1}{2000}(200p-p^2)\\ p'(t)=-\frac{p^2}{2000}+\frac{p}{10}
So we are given parabola with the following parameters:
a=-\frac{1}{2000}\\ b=\frac{1}{10}\\ c=0
The x (or in our case p coordinate) coordinate of the vertex is given with this formula:
p_v=\frac{-b}{2a}\\ p_v=100
We plug this back into the original equation to obtain the maximum rate of change:
p'_{max}=-\frac{100^2}{2000}+\frac{100}{10}=5$students/s
You can check out the graph of the first derivative on this link: https://www.desmos.com/calculator/tgmnxqb7fd

lina2011 [118]3 years ago
4 0

Answer:

Maximum rate of change will be

(\frac{dp}{dt})_{max} = 5 at p = 100

Explanation:

As we know that rate of change in students per second is given by

r = \frac{dp}{dt} = \frac{1}{2000} p(200 - p)

here we need to find the greatest rate of change in the number of students

So in order to find the greatest value of the rate of students we have to put the differentiation of of the above function to be zero

so we have

\frac{dr}{dp} = 0

0 = \frac{1}{2000} (200 - 2p)

by solving above equation we have

p = 100

so maximum rate of students will be at the condition when p = 100

so the value of maximum rate will be

\frac{dp}{dt} = \frac{1}{2000}(100)(200 - 100)

\frac{dp}{dt} = 5

You might be interested in
Which of the following is a way in which earth material is returned to the surface?
kvv77 [185]

Answer:

Explanation:

soil

4 0
3 years ago
Read 2 more answers
a boat takes off from the dock at 2.5 ms in speed up at 4:.2 ms² for 6 seconds. how far has the boat traveled?
Eva8 [605]

Answer:

d=91m

Explanation:

<em />

7 0
3 years ago
When the distance between two stars decreases by one-third, the force between them
pashok25 [27]

Answer:

the force will increase by a factor 2.25

Explanation:

The gravitational force between the two stars is given by:

F=G\frac{m_1 m_2}{r^2}

where

G is the gravitational constant

m1, m2 are the masses of the two stars

r is the distance between the stars

If the distance is decreased by one-third, it means that the new distance is 2/3 of the previous distance

r'=\frac{2}{3}r

So the new force will be

F'=G\frac{m_1 m_2}{(\frac{2}{3}r)^2}=\frac{9}{4} G\frac{m_1 m_2}{r^2}=2.25 F

So, the force will be 2.25 times the previous value.

4 0
3 years ago
Elaborate on the reason(s) that matter is said to move even as in a solid state.
Pepsi [2]
1) The correct answer is
<span>C) The particles are not able to move out of their positions relative to one another, but do have small vibrational movements.
In solids, in fact, particles are bound together so they cannot move freely. However, they can move around their fixed position with small vibrational movements, whose intensity depends on the temperature of the substance (the higher the temperature, the more intense the vibrations). For this reason, we say that matter moves also in solid state.

2)  The correct answer is
</span><span>A) increase the concentration of both solutions
In fact, when we increase the concentration of both solutions, we increase the number of particles that react in both solutions; as a result, the speed of the reaction will increase.

3)  The correct answer is
</span><span>C) gas → liquid → solid
In gases, in fact, particles are basically free to move, so the intermolecular forces of attraction are almost negligible. In liquids, particles are still able to move, however the intermolecular forces of attraction are stronger than in gases. Finally, in solids, particles are bound together, so they are not free to move and the intermolecular forces of attraction are very strong. </span>
3 0
3 years ago
When going from a fast speed to a slow speed how is light bent?
Zolol [24]
Toward the normal line
4 0
3 years ago
Read 2 more answers
Other questions:
  • A non conducting sphere of radius 0.04 m has a charge of 5.0 × 10^-9 C deposited on it. CalculateThe magnitude of the electric f
    11·1 answer
  • Which one of the following statements concerning superconductors is false? A constant current can be maintained in a superconduc
    15·1 answer
  • A 0.40 kg mass hangs on a spring with a spring constant of 12 N/m. The system oscillated with a constant amplitude of 12 cm. Wha
    14·1 answer
  • Please help on this one somebody?
    6·1 answer
  • Liz rushes down onto a subway platform to find her train already departing. she stops and watches the cars go by. each car is 8.
    5·1 answer
  • When the play button is pressed, a CD accelerates uniformly from rest to 450 rev/min in 3.0 revolutions. If the CD has a radius
    13·1 answer
  • A projectile proton with a speed of 500 m/s collides elastically with a target proton initially at rest. The two protons then mo
    13·1 answer
  • The Nucleus of the Atom is in the center of the Atom, not in the outer rings &amp; orbitals.
    13·1 answer
  • If a dog ran at 5 m/s how far would it run in 45 s
    15·2 answers
  • Which of these is at thermal equilibrium?<br>A- 25° 5°<br>B- 25° 25°<br>C- 5° 5°<br>D- 5° 25°​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!