Which proportion satisfies the geometric mean (altitude) theorem for the triangle?
2 answers:
Answer:
D.
Step-by-step explanation:
We have been given an image of a triangle. We are asked to choose the proportion that satisfies the geometric mean (altitude) theorem for the triangle.
The geometric mean (altitude) theorem states that altitude drawn from the right angle to hypotenuse divides the hypotenuse into two segments such that their product is equal to the altitude times altitude.
Therefore, option D is the correct choice.
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A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or
ancestors.
In the third generation we have 8 ancestors ot
ancestors.
We can see that each succesive generation has two times more members. The sum is:
To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>
<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
For this question:
a1 = 2
r = 2
n = 40
</span>
<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years
c.
Total number of people who have ever lived = </span>
Number of ancestors in 40 generations =
The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or
In the third generation we have 8 ancestors ot
We can see that each succesive generation has two times more members. The sum is:
To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>
<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
For this question:
a1 = 2
r = 2
n = 40
</span>
<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years
c.
Total number of people who have ever lived = </span>
Number of ancestors in 40 generations =
The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.