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Lelechka [254]
2 years ago
14

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. Assume that the rate at which material is forgotten is proportional to the amount 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) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t).)
dA/dt =
Mathematics
1 answer:
babymother [125]2 years ago
7 0

Answer:

dA/dt = k1(M-A) - k2(A)

Step-by-step explanation:

If M denote the total amount of the subject and A is the amount memorized, the amount that is left to be memorized is (M-A)

Then, we can write the sentence "the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized" as:

Rate Memorized = k1(M-A)

Where k1 is the constant of proportionality for the rate at which material is memorized.

At the same way, we can write the sentence: "the rate at which material is forgotten is proportional to the amount memorized" as:

Rate forgotten = k2(A)

Where k2 is the constant of proportionality for the rate at which material is forgotten.

Finally, the differential equation for the amount A(t) is equal to:

dA/dt = Rate Memorized - Rate Forgotten

dA/dt = k1(M-A)  - k2(A)

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The graph of the function f(x) = (x − 3)(x + 1) is shown. On a coordinate plane, a parabola opens up. It goes through (negative
mote1985 [20]

Answer:

Correct option: first one -> all real values of x where x < −1

Step-by-step explanation:

First we need to find the roots of the function f(x):

0 = (x - 3)(x + 1)

(x - 3) = 0 -> x = 3

(x + 1) = 0 -> x = -1

The roots of the function are x = 3 and x = -1.

The vertex is between the roots (x = 1) and has a negative value of y (y = -4), so the concavity of the parabola is upwards.

So the graph is decreasing until it reaches the vertex, then the graph is increasing.

Then, we can affirm that the graph is positive and decreasing for all real values of x where x < -1 (for x > -1 and x < 3 we have negative values)

Correct option: first one

8 0
1 year ago
Mike runs for the president of the student government and is interested to know whether the proportion of the student body in fa
Alik [6]

Answer:

We conclude that the proportion of student body in favor of him is significantly less than or equal to 50%.

Step-by-step explanation:

We are given that Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent.

A random sample of 100 students was taken. Fifty-five of them favored Mike.

<em>Let p = </em><u><em>proportion of the students who are in favor of Mike.</em></u>

So, Null Hypothesis, H_0 : p \leq 50%      {means that the proportion of student body in favor of him is significantly less than or equal to 50%}

Alternate Hypothesis, H_A : p > 50%      {means that the proportion of student body in favor of him is significantly more than 50%}

The test statistics that would be used here <u>One-sample z proportion</u> <u>statistics</u>;

                        T.S. =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of students body in favor of Mike = \frac{55}{100} = 0.55

           n = sample of students taken = 100

So, <em><u>test statistics</u></em>  =   \frac{0.55-0.50}{\sqrt{\frac{0.55(1-0.55)}{100} } }

                               =  1.01

The value of z test statistics is 1.01.

<em>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</em>

<em>Since our test statistic is less than the critical value of z as 1.01 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><u><em>we fail to reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that the proportion of student body in favor of him is significantly less than or equal to 50% or proportion of the students in favor of Mike is not significantly greater than 50 percent.

4 0
1 year ago
List the next three numbers for the sequence:<br><br> 34, 102, 408, 2040, ...
stiv31 [10]

Answer:

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Step-by-step explanation:

We know that the sequence is growing rapidly

To see how rapidly divide the second term by the first term

102/34 =3

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Check the fourth term divided by the third term

2040/408=5

To get the second term, multiply by 3,  to get the third term multiply by 4

to get the fourth term multiply by 5

to get the nth term multiply by (n+1)

The 5th term would be multiplied by 6

2040 *6 =12240

The 6th term by 7

12240*7=85680

The 7th term by 8

85680*8=685440

5 0
1 year ago
Jacob made a circle-shaped poster for his geometry class.
garri49 [273]
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Answer:

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Step-by-step explanation:

Given

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1 year ago
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