Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?
2 answers:
<h2>Answer:</h2>
The sequence that could be partially defined by the given recursive formula is:
-10, -7.5 , -5 , -2.5 ,........
<h2>Step-by-step explanation:</h2>We are given a recursive formula as:
for n≥1
Hence, from the given options we will check the difference of which sequence is: 2.5
A)
2.5, 6.25, 15.625, 39.0625, …
6.25-2.5=3.75
15.625-6.25=9.375
As we could see that the common difference is not 2.5
Hence, option: A is incorrect.
B)
2.5, 5, 10, 20
5-2.5=2.5
10-5=5
20-10=10
As the common difference is not 2.5.
Hence, option: B is incorrect.
C)
–10, –7.5, –5, –2.5, …
-7.5-(-10)=-7.5+10=2.5
-5-(-7.5)=5+7.5=2.5
and -2.5-(-5)=-2.5+5=2.5
As the common difference is 2.5.
Hence, option: C is correct.
D)
-10, -25 , 6.25 , 156.25
-25-(-10)=-25+10= -15
As the common difference is not 2.5
Hence, option: D is incorrect.
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Answer: The angle of elevation is 18.4 degrees (Approximately)
Step-by-step explanation: Please refer to the picture attached for more details.
The pole from top to bottom is 20 feet tall and is depicted as line FB. An observer is standing at a distance of 20 feet from the base of the pole, and that is depicted as line BA. The observer who is at point A looks up to the top of the flagpole at an angle of elevation shown as angle A.
Using angle A as the reference angle, line FB which is 20 feet would be the opposite (facing the reference angle), while line BA which is 60 feet would be the adjacent (that lies between the right angle and the reference angle).
Therefore, to calculate angle A;
Tan A = Opposite/Adjacent
Tan A = 20/60
Tan A = 1/3
Tan A = 0.3333
Checking with your calculator or table of values,
A = 18.4349°
Rounded to the nearest tenth,
A ≈ 18.4°
