A plane flying horizontally at an altitude of 1 mile and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station. (Round your answer to the nearest whole number.)

Answer:

The rate increases at 398mi/h

Step-by-step explanation:

Given

[tex]\frac{dx}{dt} = 460mi/h[/tex] --- rate when [tex]y = 2[/tex] --- distance

The given parameters is represented with the attached figure

Using Pythagoras theorem [take the attached image as a point of reference]

[tex]y^2 = x^2 + 1^2[/tex]

[tex]y^2 = x^2 + 1[/tex]

Differentiate with respect to time (t):

[tex]2y \frac{dy}{dt} = 2x \frac{dx}{dt}[/tex]

Divide both sides by 2

[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex] --- (1)

When y = 2:

[tex]y^2 = x^2 + 1^2[/tex] --- Pythagoras Theorem

[tex]2^2 = x^2 + 1[/tex]

[tex]4 = x^2 + 1[/tex]

Collect like terms

[tex]x^2 = 4 -1[/tex]

[tex]x^2 = 3[/tex]

Solve for x

[tex]x = \sqrt 3[/tex]

So:

[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex]

Substitute: [tex]x = \sqrt 3[/tex], [tex]\frac{dx}{dt} = 460mi/h[/tex] and [tex]y = 2[/tex]

[tex]2 * \frac{dy}{dt} = \sqrt 3 * 460[/tex]

[tex]2 * \frac{dy}{dt} = 460\sqrt 3[/tex]

Divide by 2

[tex]\frac{dy}{dt} = 230\sqrt 3[/tex]

[tex]\frac{dy}{dt} = 230*1.7321[/tex]

[tex]\frac{dy}{dt} = 398.383[/tex]

[tex]\frac{dy}{dt} \approx 398[/tex]

Which of the following is in the solution set to 3x - y = 12? (hint: what
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(3,2)
(0,4)
(-4,0)
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Answer(8,12)

Use the figure to find the Volume.

Label the diagram
with
x-axis y-axis origin quadrant I quadrant II quadrant III quadrant IV
A
B
C
D

1/3 + 1/2 and I am 5 years old

Identify the sampling designs that use convenience sampling. Check all that apply.
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O A student organization interviews students in a lunch line about cafeteria meals.
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The management employees of a company, which has locations throughout the country, are asked about job
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someone please find the area of this figure.

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^ means exponents

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What number divided by 4 equals 6?
Type the correct answer, then press Enter.

Identify the distance between points (−1,7,10) and (6,−3,2), and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary.

Which equation represents "The sum of a number n and 8, subtracted from 20, is 16."
A. n + 8-20 = 16
B. 8n - 20 = 16
C. 20 - (n + 8) = 16
D. 20- 8n = 16​

6 1/5 - 4 2/4=? help I need it now pls thx u.

Не
На спортивных соревнованиях по Плаванию за первое
место боролись Вера, Ксюша, Алина
Алина и Надя. Коша
заняла
Второе место, Надя не заняла ни первое,
НИ второе место, Вера заняла четвёртое место, Алина
Не заняла первое место.
Кто из девочек стал победителем соревнований?​

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c. (3,
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Impossible Not Ukely Equslly Ukely & Unlikely Ukoly Certain Events: a. You will win the grand prize in a raffle if you purchased 2 of the 100 tickets. b. You will wait less than 10 minutes before ordering at a fast-food restaurant. c. You will get an even number when you roll a standard number cube. d. A four-year-old child is over six feet tall. e. No one in your class will be late to class next week. f. The next baby born at a hospital will be a boy, g. It will snow at our school on July 1. h. The sun will set today before 11:00 p.m. i. Spinning the spinner shown will result in green. j. Spinning the spinner shown will result in yellow.​

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U.S. Manufactured General Aviation Shipments, 2009–2015
Year Qtr 1 Qtr 2 Qtr 3 Qtr 4 Total
2009 310 408 390 477 1,585
2010 243 377 281 433 1,334
2011 268 289 286 480 1,323
2012 305 358 339 514 1,516
2013 329 413 353 520 1,615
2014 345 380 379 527 1,631
2015 296 374 378 544 1,592

Click here for the Excel Data File

(a) Plot the data on airplane shipments.


Plot A Plot B Plot C Plot D



multiple choice 1
Plot A
Plot B
Plot C
Plot D


(b) Can you see seasonal patterns?

multiple choice 2
Yes
No


(c) Use MegaStat or Minitab to calculate estimated seasonal indexes and trend. (Round your answers to 3 decimal places.)


Qtr1
Index Qtr2
Index Qtr3
Index Qtr4
Index






(d) In which quarters are shipments highest? Lowest? (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)

Highest

check all that apply 1
Q1
Q2
Q3
Q4


Lowest

check all that apply 2
Q1
Q2
Q3
Q4


(e) Is there a trend in the deseasonalized data?

There is a slight
(Click to select)
trend in the deseasonalized data.