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d1i1m1o1n [39]
3 years ago
9

An ant went 2 meters away from its nest searching for food. The next time, the ant went 3 meters away. Each successive time the

ant leaves the nest to search for food, the ant travels the sum of the two previous times. How far will the ant travel on his fifth trip?
Mathematics
1 answer:
seropon [69]3 years ago
8 0

Answer:

The first time, the ant went 2m away, then we have a₁ = 2m

The second time, the ant went 3m away, then we have a₂ = 3m

The next time, the ant went a distance equal to the sum of the two previous ones, so we can write it in a general case as:

aₙ = aₙ₋₁ + aₙ₋₂

Only if n > 2.

then the third time, we have n = 3.

a₃ = a₂ + a₁ = 2m + 3m = 5m

a₄ = a₃ + a₂ = 3m + 5m = 8m

a₅ = a₄ + a₃ = 5m + 8m = 13m

This means that in the fifth trip, the ant went 13 meters away from its nest.

And if we consider the fact that the ant must go and return, then it will move a total distance of 13 meters two times, or 2*13m = 26 meters.

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1, In a class of 80 students in Debreberhan University, 45 are good in mathematics, 15 are good in both mathematics and in Engli
Aleks [24]

Treating the data as a Venn set, it is found that:

  • 26 students are good in mathematics only.
  • 28 students are not good in any of the three courses.

---------------------------------

I am going to say that:

  • A is the number of students good in Math.
  • B is the number of students good in English.
  • C is the number of students good in Psychology.

---------------------------------

9 are good in all of the three courses.

This means that: A \cap B \cap C = 9

---------------------------------

13 are good in both mathematics and psychology

This means that:

(A \cap C) + (A \cap B \cap C) = 13

(A \cap C) + 9 = 13

(A \cap C) = 4

---------------------------------

15 are good in both mathematics and in English

This means that:

(A \cap B) + (A \cap B \cap C) = 15

(A \cap B) + 9 = 15

(A \cap B) = 6

---------------------------------

16 are good in both English and psychology

This means that:

(B \cap C) + (A \cap B \cap C) = 16

(B \cap C) + 9 = 16

(B \cap C) = 7

---------------------------------

20 are good in psychology

This means that:

c + (A \cap C) + (B \cap C) +  (A \cap B \cap C) = 20

c + 4 + 7 + 9 = 20

c = 0

---------------------------------

45 are good in mathematics

This means that:

a + (A \cap B) + (A \cap C) +  (A \cap B \cap C) = 45

a + 6 + 4 + 9 = 45

a = 26

---------------------------------

Question a:

a = 26, which means that 26 students are good in mathematics only.

---------------------------------

Question b:

At least one is:

a + (A \cap B) + (A \cap C) + (B \cap C) +  (A \cap B \cap C) = 26 + 6 + 4 + 7 + 9 = 52

Thus, 80 - 52 = 28

28 students are not good in any of the three courses.

A similar problem is given at: brainly.com/question/22003843

4 0
3 years ago
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