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
Related Questions
PLEASE HELP Line A is represented by the equation, y = 1/4x + 5 . (a) Write in slope-intercept form, the equation of a line that is steeper than line A. (b) Write in slope-intercept form the equation of a line that is a vertical shift down 4 units from line A.
Answers
Answer:
a) y= 2x +3
b) y= ¼x +1
Step-by-step explanation:
Please see the attached picture for the full solution.
Further explanation:
b) y-intercept of A= 5
y-intercept of line= 5 -4= 1
Since the gradient of the line is equal to the gradient of line A, gradient of line= ¼.
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?
Divide: 3/8 ÷ 5/12 = ?
Answers
flip 5/12 to be 12/5 to make this equation multiplication
3/8*12/5 = 36/40 = 18/20 = 9/10
The solution of expression is,
⇒ 9 / 10
We have to given that;
To Divide,
⇒ 3/8 ÷ 5/12
Now, We can divide the numbers as;
⇒ 3/8 ÷ 5/12
⇒ 3/8 × 12/5
⇒ 36 / 40
⇒ 18/20
⇒ 9 / 10
Thus, The solution of expression is,
⇒ 9 / 10
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ6
please I need help!!!
Answers
Answer:
Equation is P=4s
Step-by-step explanation:
There is a pattern here:
8 is 4 times as much as 2
12 is 4 times as much as 3
20 is 4 times as much as 5
40 is 4 times as much as 10
Since P varies directly with s, we can make an equation: P=4s where k=4 in the form of y=kx
Mental math what is 90 x 20
Answers
Answer:
1800
Step-by-step explanation:
90*20=1800 because 9*2=18 add two zeroes and ur done
Hope this helps
Answer:
1,800
Step-by-step explanation:
90 x 20
9 x 2=18
18+00
1,800
Plz give Brainiest
BI
Challenge 2
A: Can you find the
area of the circle?
r=x +1
B: Can you find the
circumference of
the circle?
Answers
Answer:
Area of the circle = pi * r^2 = pi * (x+1) ^ 2
Circumference of the circle = 2* pi * r = 2*pi*(x+1)
What is the slopeWhat is the slope of this
linear equation:
2x+3y= -4x+9 of this linear equation: 2x+3y= -4x+9
Answers
Answer:
Slope = -2
Step-by-step explanation:
Equation in slope intercept form:
y = -2x + 3
Meaning slope equals -2
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
Answers
Answer:
#2
Even though the graph dips down, x is still increasing, and y will increase as will .
As x is decreasing, y is also decreasing.
I need help like serious help
Answers
Answer:
AB is equal to AD because if you move from A to B, you would have to go 3 points toward the B, and then move one point toward B. Same for D. You must move 3 points toward D, then move one down.
Step-by-step explanation:
Which of the following options have the same value as 25\%25%25, percent of 646464?
Choose 2 answers:
Answers
Answer:
25/100 *64
0.25*64
Step-by-step explanation:
Answer:
25/100 times 64 and 0.25 times 64
Step-by-step explanation:
Aaron can buy 4 tickets for $33. How much will it cost for 11 tickets?
Answers
Answer:
$90.75
Step-by-step explanation:
$33 dollars divided by 4 tickets is $8.25 (original price) so then $8.25 x 11 is $90.75
2. Determine all the common factors and two
common multiples of 12 and 56. Show
your work.
Answers
Alternatively, the gcf of 12 and 56 can be found using the prime factorization of 12 and 56:
The prime factorization of 12 is: 2 x 2 x 3.
The prime factorization of 56 is: 2 x 2 x 2 x 7.
The prime factors and multiplicities 12 and 56 have in common are: 2 x 2.
2 x 2 is the gcf of 12 and 56.
gcf(12,56) = 4.
find the distance between points P ( 7,8 ) and Q ( 6,2 )
Answers
Answer:
6/1
Step-by-step explanation:
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:
Find the difference. Express the answer in scientific notation.
(9.1 × 10–6) – (8.9 × 10–6)
2.0 × 10–7
0.2 × 10–6
2.0 × 10–6
2.0 × 10–5
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
2*10^-6, or 2.0*10^-6.
If anything is unclear, please let me know!
Answer:
it’s A / 2.0 x 10^-7
Step-by-step explanation:
THIS IS THE ANSWER ON EDU
i know because i just took it
Please help
Which of these triangles is NOT possible?
Answers
Answer:
B
Step-by-step explanation:
The sides must be greater than 13 for a triangle to even exist
Answer:
B
Step-by-step explanation:
I Just took the test
Undefined slope, (0,-8)
Answers
Solve the proportion. 3/4=m/6
Answers
Answer:
9/2=m
Step-by-step explanation:
3/4=m/6
m/6×3/4
18/4m
9=2m
m=9/2
An athlete eats 75 g of protein per day while training. How much protein will she eat during 21 days of training? Write your answer in kilograms.
Answers
Answer:
1.575 kg
Step-by-step explanation:
75g x 21
1575 g
convert to kg
1.575 kg
Brainliest Appreciated!
What is f(3)?
o 9
0 -1
O 1
O 9
Answers
Answer:
C.
Step-by-step explanation:
f(3) is referring to 3 on the left side and it is beside 1 which is on the left so it's 1.
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Answers
Answer:parallel
Step-by-step explanation:
Maria incorrectly placed the decimal
point when she wrote 0.65 inch for the
width of her tablet computer. What is the
correct decimal number for the width?
Answers
Answer: 6.5 inches
Step-by-step explanation:
this measurement makes the most sense for the width of a tablet computer
(5/9)^2
Order of operation
Answers
Answer:
Use PEMDAS.
Parenthesis.
(5 times 9) That's 45.
Exponents.
45^2
45x45
2025
The answer is 2025.
To download movies off the internet, you must pay $1.99 per movie, plus a onetime fee of $5.50. Write an expression to show the total cost to download n movies.
Answers
Answer:
7.49
Step-by-step explanation:
just add it up
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Answers
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Answers
Evaluate for x = 3
|(3) (3) - 4| = 5
|(3) (3) - 4| = 5
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ir
Coffee costs $9 per pound. How much does 600 pounds of coffee cost?
Answers
Answer:
11.400 dollars... is the answer
Answer:
$5400
Step-by-step explanation:
9 x 600 = 5400
What is the x-value in the solution to this system of linear equations?
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x + 3y = -5
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0 -1
O 2
O4
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Answers
Solving Steps:
2x-y=11
x+3y=-5
-2x-y=11
-2x-6y=10
-7y=21
y=-3
x+3(-3)=-5
x=4
You are playing a video game. For each diamond you collect, you earn 110 points. You also earn 80 bonus points by completing the level in less than 2 minutes. You need to earn more than 1620 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.
Answers
Answer:
110d=1620
Step-by-step explanation:
110d=1620
divide by 110 on each side
d=14.2727272727
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Use the information to find the minimum sample size required to estimate an unknown population mean µ. Margin of error: $110, confidence level: 95%, σ = $500. Group of answer choices
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
Squaring both sides, we have:
([tex]n^{\frac{1}{2}[/tex])^2 = (8.90909090909092)^2
n = 79.3719008264465
Approximating to a whole number, we have:
n = 79
Therefore, the minimum sample size required is 79.