Match the sequence (term) with the correct type of sequence (definition). match term definition 128, 32, 8, 2, …

1 answer:

8 0

Note that we can get 32 from 128 by mult. 32 by (32/128), or (1/4). Mult. 32 by (1/4) produces the 3rd term, 8, as expected. Thus, the common ratio, r, is 1/4.

Illustrations:

128(1/4) = 32
32(1/4) = 8
8(1/4) =2
2(1/4) = 1/2
and so on.

This is a geometric series with first term 128 and common ratio 1/4.

None of the 4 possible answers you've shared matches this outcome. Check to ensure that you've copied them down accurately. But most importantly, decide whther or not you agree that the common ratio of the given sequence is 1/4 and that the first term is 128.

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How far away can a person live from a radio station and hear its broadcast if the signal covers a circular area of 40000 square

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Answer: Approximately 112.86 miles in any direction away from the radio station

Step-by-step explanation: If the radio signal of the radio station can cover a circular area of 40,000 square miles, it simply means any direction away from the radio station that is within the coverage area. With the radio station as the center, we would have a radius that can reach any point within the area, and any distance beyond the radius would be out of coverage area. If the area has been given as 40000, then we have;

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40000 = 3.14 x r^2

By cross multiplication we now have

40000/3.14 = r^2

Add the square root sign to both sides of the equation

112.8665 = r

Therefore, the farthest a person can live away from the radio station is approximately 112.86 miles

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1. shifts the graph right 2 units

2. y = -2(x -3)² +7

Step-by-step explanation:

1) Replacing x with x-h in any function shifts the graph h units to the right. Here, you have replaced x with (x-2), so the graph will be shifted 2 units to the right.

3) The vertex form of the equation of a parabola is ...

y = a(x -h)² +k . . . . . . . . for vertex (h, k) and vertical scale factor 'a'

Here, the vertex is (h, k) = (3, 7), and the parabola opens downward. This tells us the sign of 'a' is negative.

The graph is not so clear that it is easy to read the value of 'a' directly from it, but there are several clues.

The zeros of the above function are found at h±√(k/a). This graph shows the zeros to be located such that √(7/a) is slightly less than 2. This means the magnitude of 'a' will be slightly more than 7/2² = 1.75. The y-intercept of the function is 7-9a. It is less than -7, but probably more than -14. This puts bounds on 'a':

-14 < 7-9a < -7

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If we assume that 'a' is an integer value, we have bounded its magnitude as being between 1.75 and 2.33, so a=-2 is a reasonable choice.

The equation of the graph may be ...

y = -2(x -3)² +7