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)

And the solution for this equation is:

Using the substitution u = M-A, we have that du = -dA and after integrate we got:

C is a constant.

Now we can apply exponential in both sides and we got:

Step-by-step explanation:

Let's define some notation first :

represent the total amount of the subject to be memorized

represent the amount memorized at time t

t represent the time

k is a constant of proportionality

For this case we know that the rate of memorizing is proportional to the amount left to be memorized.

So then we can create the following relationship:

Where k>0. We can solve this differential equation like this:

Using the substitution u = M-A, we have that du = -dA and after integrate we got:

C is a constant.

Now we can apply exponential in both sides and we got:

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225