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.)

Answers

Answer 1

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]

A Plane Flying Horizontally At An Altitude Of 1 Mile And A Speed Of 460 Mi/h Passes Directly Over A Radar

Related Questions

Which statement best describes the values of x and y in the table

Answers

is this 5th grade work?

Answer:

Answer A

Step-by-step explanation:

As the value of x increases by 2 the value of y increases by 4

PLEASE I NEED HELP CLICK ON THIS IMAGE

Answers

Answer:

Mean: 10

Median: 10.5

Mode: none

Step-by-step explanation:

there is no mode, mean is 10 and median is 10.5

It is desired to compare the hourly rate of an entry-level job in two fast-food chains. Eight locations for each chain are randomly selected throughout the country, the selections for each chain being independent. The following hourly rates are recorded:
Chain A 4.25 4.75 3.80 4.50 3.90 5.00 4.00 3.80
Chain B 4.60 4.65 3.85 4.00 4.80 4.00 4.50 3.65
Under the assumption of normality and equal variances, can it be concluded at the 5% significance level that chain A pays more than chain B for the job under consideration?

Answers

Answer:

It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration

Step by Step Solution:

The given data are;

Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80

Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65

Using the functions of Microsoft Excel, we get;

The mean hourly rate for fast-food Chain A, [tex]\overline x_1[/tex] = 4.25

The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478

The mean hourly rate for fast-food Chain B, [tex]\overline x_2[/tex] = 4.25625

The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649

The significance level, α = 5%

The null hypothesis, H₀:  [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ:  [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The pooled variance, [tex]S_p^2[/tex], is given as follows;

[tex]S_p^2 = \dfrac{s_1^2 \cdot (n_1 - 1) + s_2^2\cdot (n_2-1)}{(n_1 - 1)+ (n_2 -1)}[/tex]

Therefore, we have;

[tex]S_p^2 = \dfrac{0.457478^2 \cdot (8 - 1) + 0.429649^2\cdot (8-1)}{(8 - 1)+ (8 -1)} \approx 0.19682[/tex]

The test statistic is given as follows;

[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{S_{p}^{2} \cdot \left(\dfrac{1 }{n_{1}}+\dfrac{1}{n_{2}}\right)}}[/tex]

Therefore, we have;

[tex]t=\dfrac{(4.25-4.25625)}{\sqrt{0.19682 \times \left(\dfrac{1 }{8}+\dfrac{1}{8}\right)}} \approx -0.028176[/tex]

The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14

At 5% significance level, the critical t = 2.145

Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration

If 3 inches of rain fell in 5 hours, how much rain fell each hour? *

Answers

Answer:

Step-by-step explanation:

you can divide 5 divided by 3 and your answer will be 0.6

A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct in
your answer

Answers

Answer:

59.5 cm

Step-by-step explanation:

Find the area of the entire rectangle first. Formula is base times height: [tex]9*8[/tex]

=72

Next, find the missing sides by subtracting [tex]8-3[/tex] and [tex]9-4[/tex].  

=5 and 5

Then find the area of the triangle. Formula is base times height divided by 2: [tex]\frac{5*5}{2}[/tex]

=12.5

Then subtract to find only the shaded section: [tex]72-12.5[/tex]

=59.5 cm

Help help thank you

Answers

Meter is 0.5 and the fraction is I think 1/2

Explain why a variable's coefficient is 1 unless you see another number in front of it.

Answers

when you add variables you have to have something to add so instead of it being x^2 it would be x+x=2x

For adding variables we use the coefficient as 1 if there is no number infront of variable.

What is Expression?

An expression is combination of variables, numbers and operators.

A coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression.

Let us consider a algebraic expression

ax+by+z=0

In the given expression a, b are coefficients of x and y respectively.

We use coefficient as one when there is no number before a variable because when we add variables there should be some number before varibales. So we consider 1 as coefficient for those variables which does not have any coefficient.

Hence, for adding variables we use the coefficient as 1 if there is no number infront of variable.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ2

Victor buys four chairs to place around his dining room table. He pays a total of $88. What is the unit
price?

Answers

The unit price is $22.00. This is because if there are four chairs you just take
$88(total)/4(chairs)=22

Please help me :) I will give Brainiest to whoever does! PLEASE HURRY

Answers

Answer:

18.33

Step-by-step explanation:

Show your work: 1/2x = 10

Answers

1/2x = 10
think of it as 1/2 • x = 10
then multiple both sides by 2
1 • x = 20
so x=20

Find the missing angle of each triangle.

Answers

Answer:

1 is 64

2 is 85

3 is 56 hope this helps  

Step-by-step explanation:

also how give brainly i want to give u brainly

someone please help thanks

Answers

Answer:

Don't take my word for it because I havent dont this in a while but I believe it is the top right

The answer to this question is 1/2

An architect’s blueprint for a new house shows the kitchen being 7 inches wide. If the scale used to create the blueprint is 0.5 in. = 1 ft, what is the actual width of the kitchen?

Answers

You would do 7x0.5 which equals 3.5 ft :^)

Write an emergency that could happen that would have a financial cost

Answers

Answer:

Your house burning down.

Step-by-step explanation:

You would have to pay to repair it.

Answer:

Earthquake will make the building crash and people will lost their things and money. And the building need to rebuild.

The building fire will make people lost their things and the building need to rebuild.

Tsunami will make the things near beach all destroy, all the things will lost and more people will die in disaster. All the building need to rebuild in this disaster.

Bank robbery will lost money, sometimes people will kill by the gun of the thief, and the building do not need to rebuild, maybe the window need to rebuild.

Rob the shop will make the boss of the shop lose all the money in the store, the door or window might need to rebuild.

Blasting vehicle will make the things in the car lose. the car need to put the windows on again.

Terrorist attacks will lost lives more than lost money or other things.

Volcanic eruptions will make the building near burn, and so plant and many other things. The building might need to rebuild.

That is all I can think of.

an oil company bores a hole 80m deep estimate the cost of boring if the cost is £30 for drilling the first meter with an increase in cost of £2 per meter for each succeeding meter​

Answers

Answer: £188

Step-by-step explanation:

Given

The depth of the hole is 80 m

For the first meter, it is £30

After that, it is £2 per meter

after a meter, it is 79 m more

The total cost is C

[tex]\Rightarrow C=30+2\times 79\\\Rightarrow C=30+158=188[/tex]

PLEASE HELP
x + 2/3 = 9/10

Answers

Answer:

The answer is x= 7/30

HELP!!!!! WILL GIVE BRANLIEST !!!!!

Answers

Answer:

F = (-2,4); E = (-2,0); D = (2,0)

Step-by-step explanation:

F = 4 points from A, so by a scale factor of 2, it would be 2 times father away from A. The same thing applies for all of the other points; just find how much father A is from a point, then dilate that point by multiplying it by the scale factor, and settling the point closer or father from A.

EASY Work!! Please look at the picture and yes it’s easy for other people but not me for people asking.

Answers

Answer:

7()=11

8()=42

I could barely see the answer for number 9 sorry :(

Step-by-step explanation:

the 7() is 2(3)+5

2(3)=6

6+5=11

Question (8)

c^2+3a x b

c(6)^2+ 3(3) x 2/3

36+9 x 2/3

36+6=42

Answer:

(7)=11

(8)=42

Step-by-step explanation:

here

ANSWERRRRR????HELPP PSLSSSSS

Answers

Answer:

its sas side angle side plz mark me branliest

A triangle with an area of 37 units? is dilated by a scale factor of . Find the area of
the triangle after dilation. Round your answer to the nearest lenth, if necessary.

Answers

Answer:

58 units

Step-by-step explanation:

I decided that one side is 37 units and another is 2 units, since that would make the area 37 units. (you can also use 74 units and 1 unit)

Then I multiplied 37 by 5/4, which equals a new length of 46.25 units, and I also multiplied 2 by 5/4, which equals a new length of 2.5 units.

Finally, I solve for the area of the triangle:

1/2(46.25 x 2.5) ≈ 58 units (rounded to the nearest whole number)

which is an equation of a line through (7,1) and perpendicular to y=-x+3

Answers

Answer:

The answer is y=-1x+8 or you can write it this way y=-x+8 either way will work fine.

Step-by-step explanation:

y=mx+b

m=-1

y-y=m(x-x¹)

y-1=-1(x-7)

y-1=-1x+7

+1 +1

y=-x+8

I hope this helps:)

Helppppppppppp I have 3 minutes

Answers

Answer:

It definitely is linear, and it is a straight line

Step-by-step explanation:

Try using desmos, it may help

Answer:

A) it is linear and it is a straight line

Step-by-step explanation:

it is a linear equation. It will be straight

y=mx+b is linear

Solve for the length of BA and BC, round your answer to 1 decimal place

Answers

Answer:

[tex]BA = 6.0[/tex]

[tex]BC = 13.4[/tex]

Step-by-step explanation:

Given

The attached triangle

Solving (a) BA

Considering the tangent of angle C, we have:

[tex]tan\ C = \frac{BA}{AC}\\[/tex]

This gives:

[tex]tan\ 25 = \frac{BA}{12}[/tex]

Make BA the subject

[tex]BA = 12 * tan\ 25[/tex]

[tex]BA = 12 * 0.4663[/tex]

[tex]BA = 6.0[/tex] --- approximated

Solving (a) BC

Using Pythagoras theorem

[tex]BC^2 = BA^2 + AC^2[/tex]

[tex]BC^2 = 6.0^2 + 12^2[/tex]

[tex]BC^2 = 180[/tex]

Square root of both sides

[tex]BC = \sqrt{180[/tex]

[tex]BC = 13.4[/tex]

A stadium is shaped like a hemisphere with a radius of 150 feet. Last month, the owners of the stadium paid $0.05 per cubic foot to cover the cost of utilities. What was the total cost for utilities last month?

Answers

Answer:

353,249 feet cubed

Step-by-step explanation:

V=(4/3)[tex]\pi (3.14)rx^{3}[/tex]/2 times 0.05

The table shows the prices for the same cereal, sold in different weights. Which size box is the best buy, in terms of price per ounce?

A. 9 oz
B.18 oz
C.28 oz
D.38 oz

Answers

Answer:

c

Step-by-step explanation:

ESPERO TE A YDUE :)

If l=3, w= 3, and h= 5, what is the volume of this box​

Answers

Answer and Step-by-step explanation:

To find the volume, we multiply the length by the width by the height for a rectangular prism (aka the box).

length = l = 3

width = w = 3

height = h = 5

Now, we multiply each together.

3 × 3 × 5

9 × 5

45

The volume of the box is 45.

#teamtrees #PAW (Plant And Water)

Answer:

the volume of the box would be 45

Step-by-step explanation:

(10y + 3) - (2y - 2)

Answers

Answer:

8y+5

Step-by-step explanation:

If 60 minutes equals one hour, which expression would you use to find the number of
hours in 240 minutes?

Answers

Answer is: 60x=240
240/60=40

Find z. Just write the number. Answer should be a whole number. PLS HELP DUE IN 10 MINS WILL GIVE BRAINLIST

Answers

Answer:

square root of 338 or 18.38

Step-by-step explanation:

since a² and b² are equal, you would do 13² plus 13² then add those and you end up with 338. then you find the square root of 338 which is 18.38477631, or 18.38

A clothing business finds there is a linear relationship between the number of shirts, n (in thousands) it can sell and the price, P, it can charge per shirt. In particular, historical data shows that 3 thousand shirts can be sold at a price of $69 each, and that 7 thousand shirts can be sold at a price of $61 each. Find the equation of the form P(n)

Answers

Answer:

The equation of the form P(n) is:

P(n)=-0.002n+75

Step-by-step explanation:

From the information provided, you have two points: (3000, 69) and (7000, 61). With this, you can find the slope using the following formula:

m=(p1-p2)/(n1-n2)

m=slope

p1=69

p2=61

n1=3000

n2=7000

m=(69-61)/(3000-7000)

m=8/-4000

m=-0.002

Now that you have the slope, you can find the the equation of the form P(n):

P(n)=-0.002(n-3000)+69

P(n)=-0.002n+6+69

P(n)=-0.002n+75

According to this, the answer is that the equation of the form P(n) is:

P(n)=-0.002n+75

Other Questions
What was the one or two reasons the colonists were willing to brave hostile Indians, diseases and starvation to come to an untamed and often harsh new word to start a new life?Please help What is the circumference of the following circle when diameter = 9 cm PLZ HELP IF ITS CORRECT I WILL MARK U BRAINLIEST Complete the equations below. Llena el espacio con la conjugacin correcta del verbo.T ________ la informacin.repetrepitrepetisterepeti 1. PART A: Which of the following best describes a central idea of the text?O A The human race is evolving beyond the need for petty fighting.OB Above all, soldiers duties are to serve and protect their country.C Soldiers should never question others or engage in politics.D The only way to ensure global peace is through waging war. What is the value of |-8| Pratibha spends 5 3/4 hours in school. He spends 4 1/4 hours for classes and 3/4 hours for lunch break. She spends the remaining time on sports. How much time does she spend on sports? Un pueblo tena 13.578 habitantes en 1970. En 1988 la poblacin se increment 1,5 veces con respecto a 1970 y en 2001 se increment 2,25 veces en relacin a 1988. Cuntos habitantes haba en el ao 2001? Which could be the measures of the interior angles of a triangle?A. 50, 45, 45B. 60, 60, 60C. 70, 70, 70D. 80, 55, 25 Consider the following reaction occurring in a 1.0 L container: H2 (g) + I2 (g) 2 HI (g) State 2 requirements for a successful collision between H2 and I2. Find the correct plugged in formula for each figure. What specific rights or conditions did these treatises, decrees, declarations and constitution ask for? The Garcias bought a washing machine for $435 and a clothes dryer for $395 bath prices include tax to deliver these items the store charges $10 plus $2 per mile if the Garcias live 15 miles from th store what is their total bill? HELP FAST THIS 6TH GRADE MATH! ANSWERRRRR????HELPP PSLSSSSS What is royal regalia?a.Jewels, scepters, and other artifacts of the reigning royal family.b.Processed thin, smooth and durable animal hide used in the pre-printing age for written works.c.Any type of royal clothing which has been individually created to display deity.d.A thin lay based liquid which is used in the production of ceramics as either a glue to hold pieces together, or as a paint. Please help. Four players from the NBA and their career 3-point percentage are listed below. 3-point percentage is calculated by dividing the number of 3-pointers the player makes by the number of 3-pointers he attempts. If Steph Curry attempted 25 3-pointers in his last game, how many can we assume he made? which are not the length of sides of a right sample 1sample 2sample 3sample 4