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Valentin [98]
2 years ago
12

Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memo

rized. The function L gives the number of words memorized at time t. The rate of change of the number of words memorized is proportional to the number of words left to be memorized.
1. Which of the following differential equations could be used to model this situation, where k is a positive constant?
A. dL/dt = kL
B. dL/dt = 100 - kL
C. dL/dt = k(100 - L)
D. dL/dt = kL - 100
Mathematics
1 answer:
nadezda [96]2 years ago
6 0

Answer:

C. dL/dt = k(100 - L)

Step-by-step explanation:

We have a list containing 100 words.

L = number of words memorized at time t.

At any time t, the number of words left to be memorized is 100-L.

Therefore:

\frac{dL}{dt}\propto 100-L\\ $Introducing k, a constant  of proportion$\\\frac{dL}{dt}= k(100-L)

<u>The correct option is C.</u>

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To a survey of 290 newspaper reader, 181
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Question:

To a survey of 290 newspaper readers, 181 of them read the Daily Times, 142 Read the Guardian 117 read punch and each reads at least one of the three papers if 75 read the Daily Times, and the Guardian, 60 read the Daily Times and punch, and 54 read the Guardian and punch : Draw a Venn diagram to illustrate this information How many readers read All three papers ,Exactly two of the papers The Guardian alone?

Answer:

39 read all three news papers,72 Exactly two Papers & 52 reads  Guardian Alone

Step-by-step explanation:

We have given, A survey of 290 newspaper readers.

Who read the Daily times A=181  

Who read the Guardian times B=142  

Who read the punch C=117

Who read Daily Times and the Guardian A\cap B= 75

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How many readers read All three papers, Exactly two of the papers The Guardian alone?

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Readers read all three papers is A\cap B\cap C

Total survey is given by,

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290 = 181 + 142 + 117 - 75 -60 - 54 +A\cap B\cap C

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290-251=A\cap B\cap C

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Exactly two of the papers = 36 + 21 + 15 = 72

Guardian Alone = 52

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Answer:

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