A plane flying horizontally at an altitude of 1 mile and a speed of 510 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.) mi/h

Answers

Answer 1

Answer:

442 miles

Step-by-step explanation:

Given

To properly solve this question, I illustrate some given parameters using attached image

From the image, apply Pythagoras theorem

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

Differentiate w.r.t time (t)

[tex]2x\frac{dx}{dt} + 0 = 2y\frac{dy}{dt}[/tex]

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

Divide both sides by 2

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

From the question, we have that the plan travels are 510mi/h.

This implies that:

[tex]\frac{dx}{dt} = 510mi/h[/tex]

So, we then calculate the value of x when the distance (y) is 2mi i.e.:

[tex]y = 2mi[/tex]

Apply Pythagoras theorem

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

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

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

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

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

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

So, the expression becomes:

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

[tex]\sqrt 3 * 510 = 2* \frac{dy}{dt}[/tex]

[tex]\frac{\sqrt 3 * 510}{2} = \frac{dy}{dt}[/tex]

[tex]\sqrt 3 * 255 = \frac{dy}{dt}[/tex]

[tex]\frac{dy}{dt} = 255\sqrt 3[/tex]

[tex]\frac{dy}{dt} = 255 * 1.7321[/tex]

[tex]\frac{dy}{dt} = 441.655[/tex]

[tex]\frac{dy}{dt} = 442[/tex]

Hence, the distance is 442 miles


Related Questions

Can someone please help me with this?

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1 or 2 or both ?????????

help this is due today​

Answers

Answer:

A

Step-by-step explanation:

A market researcher analyzing the fast-food industry noticed the following: The historical average amount spent at an upscale restaurant was $150.30, with a standard deviation of $50. The researcher wishes to have a sampling error of $5 or less and be 95 percent confident of an estimate to be made about average amount spent at an upscale restaurant from a survey. What sample size should be used (round the number up)

Answers

Answer:

A sample size of 385 should be used.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

What sample size should be used (round the number up)

A sample of n should be used.

n is found when M = 5.

We have that [tex]\sigma = 50[/tex]

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 1.96\frac{50}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 1.96*50[/tex]

Simplifying by 10

[tex]\sqrt{n} = 1.96*10[/tex]

[tex]\sqrt{n} = 19.6[/tex]

[tex](\sqrt{n})^2 = (19.6)^2[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample size of 385 should be used.

Please help!!!!!!!!!!!!

Answers

Answer:

a) 5 cm b) 12in c) 7yd

I think it's so simple. Anyways

This is your answer. If I'm right so,

Please mark me as brainliest. thanks!!!

Answer:

5 cm, 12in, 3.5 yrds

Step-by-step explanation:

to find the radius you divide the diamenter by 2.

Fill in the blank so that the ordered pair is a solution of y = 22 – 9x.
( ,4)

Answers

The answer of this equation is (2,4) I’m glad to help

Can someone help me please?

Answers

Answer:

uh i dont know lol im new how do i use this thing bahahaha

Step-by-step explanation:

From the set {1, 4, 6}, use substitution to determine which value of x makes the equation true. 10 x + 8 = 48

Answers

X=4 makes it true

Thank you hope this helps

PLEAS HELP THERE IS PIC drag the tiles to the correct boxes to complete the pairs. how many solutions does each equations have ?

Answers

Answer:

|2x+1|=0 has one solutions

2|x+1|=-2 has no solution

|x+21|=2 has two solution

Step-by-step explanation:

A trawler caught 2/3 ton of fish on Monday and 1/2 on Tuesday. What was the total amount of fish caught?

Answers

Answer:

1 1/6 ton

Step-by-step explanation:

wx=?
please i need help asap!

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Answer:

24 because hsbs. hwhvw w Whelan has w hahaha

Allison and Megan were at track practice. The track is 3/8 kilometers around.
- Allison ran 1 lap in 3 minutes.
- Megan ran 4 laps in 6 minutes.
How many minutes does it take Allison to run one kilometer?

Answers

Allison ran 3/8 km (0.375 km) in 3 minutes.

Set up a proportion to find how long it takes for her to run 1 km

[tex]\frac{0.375\textrm{km}}{3 \textrm{min}} = \frac{1\textrm{km}}{x \textrm{min}}[/tex]

Cross multiply to get:

[tex]3 = 0.375x[/tex]

Solve:

[tex]x = \frac{3}{0.375}[/tex]

x = 8 minutes

A jar contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the
probability that the first jelly bean will be blue and the second will be blue as well?

Answers

First jellybean:4/14
Second jellybean:3/14

Please help me with this :)

Answers

Mathspapa a website that will help.

PLEASE ANSWER QUICK

The sum of the data values divided by the number of data values is a measure of ______ and is called the _____

FIRST BLANK'S OPTIONS = CENTER/SPREAD

SECOND BLANK'S OPTIONS = MEAN/MEAN ABSOLUTE DEVIATION/MEDIAN/RANGE

Answers

Answer:

Center... Mean

Step-by-step explanation:

The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order.

Antonio constructs a model of a moon orbiting a planet along an elliptical orbit. The equation StartFraction x squared Over 342.25 EndFraction + StartFraction y squared Over 324 EndFraction = 1, with units in inches, represents the shape of the orbit. If the planet is located at one of the foci, which phrase describes a possible location of the model planet relative to the center?

approximately 0.5 in. below the center
approximately 4.3 in. above the center
approximately 0.5 in. to the left of the center
approximately 4.3 in. to the right of the center

Answers

Answer:

D

Step-by-step explanation:

edge

D. approximately 4.3 in. to the right of the center

What is problem-solving?

Problem-solving is the act of defining a problem; figuring out the purpose of the problem; determining, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a teacher may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Learn more about problem-solving here

brainly.com/question/23945932

#SPJ2

Part 1: Identify key features and graph a parabola from standard form.
Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it.
12(x + 3) = (y - 2)^2

a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.
(1 point)

b) What is the vertex of the parabola? (1 point)

c) What is the focus of the parabola? (2 points)

d) What is the directrix of the parabola? (2 points)

e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point

Answers

Answer:

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]

Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]

[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

It is given that the parabola equation is  [tex]\rm 12(x+3)=(y-2)^2[/tex]

What is a parabola?

It is defined as the graph of a quadratic function that has something bowl-shaped.

We know the standard form of a parabola is:

[tex]\rm x= a(y-k)^2+h[/tex]  .........(1)

We have the equation of parabola:

[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)

a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.

By comparing the equation (1) and (2), we get:

Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.

b) Vertex of the parabola = (h,k): (-3, 2)

c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],

[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]

∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]

The focus of the parabola is (0, 2)

d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]

[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]

The directrix of a is x = -6

e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry

Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

Know more about the parabola here:

brainly.com/question/8708520

I will mark you brainalist

Answers

Answer:

1.25 since all prices are sam e

Step-by-step explanation:

If you don’t know I don’t answer (NO LINKS ) please helllllppppp

Answers

Answer:

Step-by-step explanation:

1. 6.96 in

2. 2.6 in

3. 8.1 in

4. 5.6 m

5. 1.89 cm

6. 6 in

Please help it’s pretty easy and ikr reward brainiest

Answers

Answer:

Choice 1 is correct: 8/3 x 1/4 = 2/3

Step-by-step explanation:

DONT answer if you don’t know

Answers

Answer:

c. 8 1/4 inches.

Step-by-step explanation:

The snail crawls 2 3/4 inches in 1 minute.

In 3 minutes, it can crawl 2 3/4 x 3 inches.

= 8 1/4 inches.

Calculate the area of this trapezium.
6 cm
4 cm
5 cm
8 cm

Answers

area=1/2(AB+0A)Ac=4cm

Answer:

28cm²

Step-by-step explanation:

Area of trapezium = 1/2×(6+8)×4

= 28cm²

100 points who ever get this right!!

Answers

Answer:

3. A = (0,-3)

    B = (4,-2)

   C = (-1,1)

4. A = (0,-6)

    B = (4,-5)

   C = (-1,-2)

Step-by-step explanation:

3) Reverse coordinates (-3,0), (-2,4), (1,-1) to A=(0,-3), B=(4,-2), C=(-1,1).

4) These coordinates (0,-3), (4,-2), (-1,1) need to be moved 3 units down.

So number four answer is A=(0,-6), B=(4,-5), C=(-1,-2).

I hope this helped you.

Answer:

3)A = (0,-3)

B = (4,-2)

C = (-1,1)

4)A = (0,-6)

B = (4,-5)

C = (-1,-2)

(1.75)^2 in expanded form

Answers

Answer:

1.75 x 1.75

fillerfillerfiller

On Triangle ABC, Angle A measures 30 degrees, Angle B measures 90 degrees, and Angle C measures 60 degrees. List the sides of Triangle ABC in order from shortest to longest.​

Answers

Answer:

A=30  B=90  C=60

Step-by-step explanation:

A=30 C=60  B=90

Nadia bought tickets to attend a spaghetti supper fundraiser at her school. The equation can be used to find , the cost of each ticket in dollars. Which equation represents the cost of each ticket?

Answers

what are the equations??

Jenny and Buddy collected 376 plastic bottles for recycling.
They recycled 131 bottles on Monday and 114 bottles on Tuesday.
How many bottles do they have left to recycle?

Complete the equations to solve. Enter your answers in the boxes.
Let
m
=
the number of bottles left to recycle after Monday.

Answers

Answer:

151

Step-by-step explanation:

114+131= 272 376-272=104

What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
(5, 11)
(-5, -1)

Answers

9514 1404 393

Answer:

  6/5

Step-by-step explanation:

The slope formula is useful for finding the slope.

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -11)/(-5 -5) = -12/-10

  m = 6/5

The slope of the line through the given points is 6/5.

If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.

Answers

Answer:

A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)

Step-by-step explanation:

Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)

Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows:

Duration of Exposure
< 1 1 to < 5 >= 5
Diseased 12 10 18
Sensitized 14 18 13
Normal 66 142 210

Required:
a. Compute the expected frequencies of diseased workers.
b. Compute the expected frequencies of sensitized workers.
c. How many degrees of freedom are there?

Answers

Answer:

1. Has been answered below

2. Degree of freedom is 4

Step-by-step explanation:

Row 1: 12+10+18 = 40

Row 2: 14+18+13 = 45

Row 3: 66+142+210 = 418

Grand total = 40+45+418 = 503

Column 1 : 12+14+66 = 92

Column 2: 10+18+142 = 170

Column 3: 18+13+210 = 241

Total = 92+170+241 = 503

Expected frequencies of diseased workers

92x40/503 = 7.316

170x40/503 = 13.52

241 x 40/503 = 19.165

Expected frequencies of sensitized workers

92x45/503 = 8.23

170x45/503 = 15.20

241x 45/503 = 21.56

2.

Degree of freedom

= (Number of row -1)(number of column - 1)

= 3-1 * 3-1

= 2x2

= 4

b) The cost (x) for hiring and artist for a stage show for (y) hours is represente
as 2y + x = 20.
Draw the graph 2y + x = 20 on the grid below.
[4]​

Answers

The easiest way is to transform this equation to intercept form of straight line.

[tex]\\[/tex]

Intercept form of straight line:

[tex]\dfrac{x}{a}+\dfrac{y}{b}=1[/tex]

where [tex]a[/tex] is the x intercept - where the graph intersects the x axis, and [tex]b[/tex] is the y intercept - where the graph intersects the y axis.

[tex]\\[/tex]

Given that,

[tex]2y + x = 20[/tex]

[tex] \longrightarrow \: \dfrac{2}{20}y + \dfrac{x}{20} = 1[/tex]

[tex] \longrightarrow \: \dfrac{x}{20} + \dfrac{y}{10} = 1[/tex]

On comparing with [tex]\dfrac{x}{a}+\dfrac{y}{b}=1,[/tex] we get,

[tex]a=20[/tex][tex]b=10[/tex]

Hence, the graph shall cut the x axis and y axis at 20 and 10 respectively. This information is enough to plot the graph.

[tex]\\[/tex]

Graph: Refer to the attachment.

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