The formula for the nth term of a geometric sequence:
a₁ - the first term, r - the common ratio
![54, a_2, a_3, 128 \\ \\ a_1=54 \\ a_4=128 \\ \\ a_n=a_1 \times r^{n-1} \\ a_4=a_1 \times r^3 \\ 128=54 \times r^3 \\ \frac{128}{54}=r^3 \\ \frac{128 \div 2}{54 \div 2}=r^3 \\ \frac{64}{27}=r^3 \\ \sqrt[3]{\frac{64}{27}}=\sqrt[3]{r^3} \\ \frac{\sqrt[3]{64}}{\sqrt[3]{27}}=r \\ r=\frac{4}{3}](https://tex.z-dn.net/?f=54%2C%20a_2%2C%20a_3%2C%20128%20%5C%5C%20%5C%5C%0Aa_1%3D54%20%5C%5C%0Aa_4%3D128%20%5C%5C%20%5C%5C%0Aa_n%3Da_1%20%5Ctimes%20r%5E%7Bn-1%7D%20%5C%5C%0Aa_4%3Da_1%20%5Ctimes%20r%5E3%20%5C%5C%0A128%3D54%20%5Ctimes%20r%5E3%20%5C%5C%0A%5Cfrac%7B128%7D%7B54%7D%3Dr%5E3%20%5C%5C%20%5Cfrac%7B128%20%5Cdiv%202%7D%7B54%20%5Cdiv%202%7D%3Dr%5E3%20%5C%5C%0A%5Cfrac%7B64%7D%7B27%7D%3Dr%5E3%20%5C%5C%0A%5Csqrt%5B3%5D%7B%5Cfrac%7B64%7D%7B27%7D%7D%3D%5Csqrt%5B3%5D%7Br%5E3%7D%20%5C%5C%0A%5Cfrac%7B%5Csqrt%5B3%5D%7B64%7D%7D%7B%5Csqrt%5B3%5D%7B27%7D%7D%3Dr%20%5C%5C%0Ar%3D%5Cfrac%7B4%7D%7B3%7D)
a₁ - the first term, r - the common ratio
What expression is equivalent to (f+g)(4)
1 answer:
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Answer:
The horizontal distance from the plane to the person on the runway is 20408.16 ft.
Step-by-step explanation:
Consider the figure below,
Where AB represent altitude of the plane is 4000 ft above the ground , C represents the runner. The angle of elevation from the runway to the plane is 11.1°
BC is the horizontal distance from the plane to the person on the runway.
We have to find distance BC,
Using trigonometric ratio,
Here, ,Perpendicular AB = 4000
Solving for BC, we get,
(approx)
(approx)
Thus, the horizontal distance from the plane to the person on the runway is 20408.16 ft
Answer:
- Mean = 26.24
- Median = 27
- Mode = 32
- Range = 38
Step-by-step explanation:
Plotting the original data from leaf plot
<em><u>Finding Mean:</u></em>
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
= 26.24
Therefore, the range = 26.24.
<u>Finding Median:</u>
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47
So, the median is 27 .
<em><u>Finding Mode: </u></em>
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47
We see that the mode is 32.
<em><u>Finding Range:</u></em>
The range is the difference between the highest and lowest values in the data set.
Ordering the data from least to greatest, we get:
9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47
The lowest value is 9.
The highest value is 47.
The range = 47 - 9 = 38
Answer:
See below for answer and explanations (as well as an attached graph)
Step-by-step explanation:
Pay attention to the behavior of the asymptotes. If the asymptotes are approaching a certain x-value or y-value, then that value is undefined for the function.
Take for example :
- As x approaches ∞ and -∞, then y approaches 0, which is our horizontal asymptote
- As y approaches ∞ and -∞, then x approaches 0, which is our vertical asymptote
See the graph for a visual.
