Find the geometric mean between 7 & 11. Select one:
1 answer:
The geometric mean is a variation on the standard arithmetic mean (where the numbers are totalled, then divided by the amount totalled). The latter of these two can be generalised as:
The difference with a geometric mean is that instead of totalling the numbers, the product is found; similarly instead of a division stage at the end, an appropriate root is found:
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Therefore for this question n = 2, since there are two numbers. Substituting in:
= 
= 8.77496438739 ≈ 8.8 (2sf)
The difference with a geometric mean is that instead of totalling the numbers, the product is found; similarly instead of a division stage at the end, an appropriate root is found:
Therefore for this question n = 2, since there are two numbers. Substituting in:
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Answer: cos(Θ) = (√15) / 4
Explanation:
The question states:
1) sin(Θ) = 1/4
2) 0 < Θ < π / 2
3) find cos(Θ)
This is how you solve it.
1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).
2) From which you can find:
3) Replace sin(α) with 1/4
=>
=>
4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:
cos(Θ) =
.
And that is the answer.
Explanation:
The question states:
1) sin(Θ) = 1/4
2) 0 < Θ < π / 2
3) find cos(Θ)
This is how you solve it.
1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).
2) From which you can find:
3) Replace sin(α) with 1/4
=>
=>
4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:
cos(Θ) =
And that is the answer.