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
Over [174]
3 years ago
13

In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to

be memorized. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t > 0. Determine a differential equation for the amount A(t). (Assume the constant of proportionality is k > 0. Use A for A(t).)
Mathematics
1 answer:
fiasKO [112]3 years ago
4 0

Step-by-step explanation:

From the statement:

M: is total to be memorized

A(t): the amount memorized.

The key issue is translate this statement as equation "rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized"

memorizing rate is \frac{dA(t)}{dt}.

the amount that is left to be memorized can be expressed as the total minus the amount memorized, that is M-A(t).

So we can write

\frac{dA(t)}{dt}=k(M-A(t))

And that would be the differential equation for A(t).

You might be interested in
10. At the end of the day, Mandy sold the rest of her hot dogs at her hot dog stand for half price. 50
vekshin1

Answer:

56

Step-by-step explanation:

Firstly, we know she sold 24 hot dogs at half price. We do not know the total number of hot dogs.

Secondly, we know that 30% of the hot dogs were sold at half of the price. This means 70% were sold at full price.

Now there are two approaches to this. I'm going to take the easier one.

What we are expressing mathematically is that 30% of a certain number equals 24. Let the total number of hot dogs she had that day at her stand be x.

This mean 30% of x = 24.

30/100 × x = 24

30x = 24× 100

30x = 2,400

x = 2,400/30 = 80.

This means she had a total of 80 hot dogs that day. Since we know the number she sold at half price, it's now easy to calculate the number she sold at full price.

This number now equals 80 - 24 = 56 hot dogs.

This mean Mandy sold 56 hot dogs at full price.

4 0
3 years ago
Rectangle MNOP is similar to rectangle WXYZ. Which is the length of segment YZ?
DanielleElmas [232]

Answer: Do it yourself!

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
HELPPPPPP!! PLEASE HELP!!
NARA [144]
The answer is 10u +3v
7 0
3 years ago
Segment YZ has endpoints (6, 3) and (3, 9). Find the coordinates of the point that divides the line segment directed from Y to Z
fenix001 [56]

Answer:

  (4, 7)

Step-by-step explanation:

The point of interest is ...

  P = (2Z +1Y)/(2+1) = ((2·3+6)/3, (2·9+3)/3)

  P = (4, 7)

__

The point that divides the segment into the ratio a:b is the weighted average of the endpoints, with the weights being "b" and "a". The weight of the first end point corresponds to the length of the far end of the segment.

8 0
3 years ago
Read 2 more answers
Brainliest to most helpful! Answer asap!
kap26 [50]

ΔAOB is a right angled triangle. Therefore the Pythagorean Theorem applies in this situation.
θ is the angle from a standard position of the line OA

The length of the y component is √(1-0)2 +(-3-(-3))2] =√(12+ 02) = 1 A(-3,1) to B(-3,0) which is opposite

Then the length of the x-component is √[(-3-0)2 +(0-0)2] = √(9+0)= 3 B(-3,0) to O(0,0) which is adjacent

The length of vector OA is √[(-3-0)2 + (1-0)2] = √(9+1) = √(10) A(-3,1) to O(0,0) which is the hypotenuse of the triangle

θ = 180 - α
sinθ = sin(180-α) = opposite/hypotenuse = 1/√10
cosθ = adjacent/hypotenuse = -3/√10
tanθ = opposite/adjacent = 1/-3 = -1/3

α= arcsin(1/√10) ≈ 18
θ =180 -18 ≈162
8 0
3 years ago
Other questions:
  • PLEASE HELP!!!!<br><br> Write the values for sin X and cos X
    10·1 answer
  • Ignore the top just answer both of the questions at the bottom plz
    5·2 answers
  • Sam must score greater than a 70 on his test to pass the class. Which inequality represents this? x &lt; 70 x &lt; 70 x &gt; 70
    14·1 answer
  • Monique uses a random number generator to simulate the results of a coin
    6·1 answer
  • What would be the answer to this question?<br> -31=26+a
    11·2 answers
  • It is a 3-kilometer hike to the river PJ Walks for 500 then he walks another 1050 how many more kilometers must PJ walk to reach
    15·1 answer
  • Prove that root6+root2 is irrational
    11·1 answer
  • 5. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of
    10·1 answer
  • Can someone help me
    9·2 answers
  • You have a bag of 63 candies you want to give to your 9 friends. The company that makes the candies guarantees that exactly 9 of
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!