An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower
Answers
Answer:
415 ft/s
Step-by-step explanation:
I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.
From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.
The constant elevation remains 4090 ft while the value of x and s varies with time.
Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.
Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s
Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.
This means that we want to find ds/dt when x = 3010 ft
From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;
s = √(4090² + 3010²)
s = √25788200
s ≈ 5078.21 ft
Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;
x² + 4090² = s²
Differentiating x and s with respect to t, we have;
2x(dx/dt) = 2s(ds/dt)
2 will cancel out to give;
x(dx/dt) = s(ds/dt)
ds/dt = (x/s)(dx/dt)
Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;
ds/dt = (3010/5078.21) × 700
ds/dt ≈ 415 ft/s
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Answer:
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Answer:
$5400
Step-by-step explanation:
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Answer:parallel
Step-by-step explanation:
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Answers
Answer:
The minimum sample size required is 79.
Step-by-step explanation:
The following are given in the question:
e = Margin of error = 110
σ = Standard deviation = 500
Confidence level = 95%
n = Minimum sample size = ?
Therefore, we have:
Zσ = 1.96 at 95% confidence level
s.e. = Standard error = σ / [tex]\sqrt{n}[/tex] = 500 /
Alternatively, margin of error can be calculated as follows:
e = s.e. * Zσ = 110 ................... (1)
Substituting the other values into equation (1) and solve for n, we have:
500 / [tex]\sqrt{n}[/tex] * 1.96 = 110
500 / [tex]\sqrt{n}[/tex] = 110 / 1.96
500 / [tex]\sqrt{n}[/tex] = 56.1224489795918
500 = 56.1224489795918 * [tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex] = 500 / 56.1224489795918
[tex]\sqrt{n}[/tex] = 8.90909090909092
[tex]n^{\frac{1}{2}[/tex] = 8.90909090909092
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What do you know about the slope of two parallel lines? *
They have the opposite sign of each other
They are reciprocals of each other
They have the same slope
They have negative reciprocal slopes
Answers
Answer:
same slope
Step-by-step explanation:
if it has the same slope then the you will know the two lines are parallel
hope this helps
brainliest?
The sales tax rate in Connecticut is 6.35%. Megan wants to buy a jacket with a $45.00 price tag. She has a gift card to the store she wants to use. What amount needs to be on the gift card for Megan to be able to buy the jacket using only the gift card? Select all that apply. A. $2.86 B. $47.86 C. $45.00 D. $47.70 E. $35.29 F. $48.25
Answers
Answer:
B C A
Step-by-step explanation:
Divide: 3/8 ÷ 5/12 = ?
Answers
flip 5/12 to be 12/5 to make this equation multiplication
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The solution of expression is,
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We have to given that;
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⇒ 3/8 ÷ 5/12
Now, We can divide the numbers as;
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⇒ 9 / 10
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BI
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Answers
Answer:
Area of the circle = pi * r^2 = pi * (x+1) ^ 2
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Answers
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The prime factorization of 56 is: 2 x 2 x 2 x 7.
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2.0 × 10–7
0.2 × 10–6
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Answers
Answer:
2.0 * 10^-6
Step-by-step explanation:
Because both numbers have the same scientific notation, you can just subtract the 9.1 from the 8.9 and keep the scientific notation.
(9.1*10^-6) - (8.9*10^-6)
(9.1 - 8.9)*10^-6
(2)*10^-6
Now that you have the answer, you need to use scientific notation, which is
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If anything is unclear, please let me know!
Answer:
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Step-by-step explanation:
THIS IS THE ANSWER ON EDU
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Answers
Answer:
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Answers
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Step-by-step explanation:
Please see the attached picture for the full solution.
Further explanation:
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Answers
Answer:
1800
Step-by-step explanation:
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Answer:
1,800
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90 x 20
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Use PEMDAS.
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Answers
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Answers
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Answers
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Answers
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Answers
Answer:
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Step-by-step explanation: