An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to
be 16.5 and 10.5 respectively. How long is the island ?
1 answer:
Answer:
154.10 Feets
Step-by-step explanation:
Given the following :
Height (h) of cliff = 320 feet
Angle of depression of near side = 16.5°
Angle of depression of far side = 10.5°
Using trigonometry :
We can obtain x and y as shown in the attached picture :
Tanθ = opposite / Adjacent
Adjacent = height of cliff = 320 Feets
For the near side :
Tanθ = opposite / Adjacent
Tan (16.5°) = x / 320
0.2962134 = x / 320
x = 0.2962134 * 320
x = 94.788318 Feets
For the far side :
Tanθ = opposite / Adjacent
Tan (10.5°) = x / 320
0.1853390 = x / 320
x = 0.1853390 * 320
x = 59.308494 Feets
Length of island = (59.308494 + 94.788318) feet
= 154.10 Feets
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Answer:
The expected amount for a duration of 20 weeks is $9.4
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Step-by-step explanation:
Read attachment to understand the complete question
From the question, we have the following given parameters:
x = Amount paid for a second movie
--- Expected value of x
--- Standard deviation of x
Required
Determine the total amount paid for a second movie for 20 weeks
The required implies that we calculate the expected value for a duration of 20 weeks.
i.e.
If
Then:
Substitute 20 for n
Substitute 0.47 for E(x)
<em>Hence, the expected amount for a duration of 20 weeks is $9.4</em>
Let
Find an integrating factor:
Multiply both sides of the ODE by
The left side can be consolidated as a derivative:
Integrate both sides with respect to
where the right side can be computed with a simple substitution. Then
Back-substitute to solve for