City A is due north of City B. Find the distance between City A ​( north​ latitude) and City B ​( north​ latitude). Assume that the radius of Earth is 3960 miles.


The distance between City A and City B is ___miles.


Can someone help?! Show me step by step how this is done that I can understand it better.

City A Is Due North Of City B. Find The Distance Between City A ( North Latitude) And City B ( North

Answers

Answer 1
Answer:  1679

=========================================================

Explanation:

The notation [tex]47^{\circ}4'[/tex] means "47 degrees, 4 minutes". The "minutes" isn't referring to a time value, but instead they are arc minutes. If we divide one degree into 60 equal pieces, then we form 60 arc minute slices. So in a sense, we are using a round analogue clock to help connect the two ideas.

We can convert to purely degrees through using this formula here

[tex]a^{\circ}b' = a + \frac{b}{60}[/tex]

So,

[tex]47^{\circ}4' = 47 + \frac{4}{60} \approx 47.06667^{\circ}[/tex]

and similarly,

[tex]22^{\circ}46' = 22+ \frac{46}{60} \approx 22.76667^{\circ}[/tex]

Now subtract the two results we got

47.06667-22.76667 = 24.3

The angular distance between the two cities is 24.3 degrees. By "angular distance" I basically mean how far you need to rotate your viewing angle when looking from city A to city B. Imagine that you're able to be situated at the center of the earth.

The circumference of the earth is

C = 2*pi*r

C = 2*pi*3960

C = 24,881.4138164311

which is approximate and the units are in miles. We multiply by the fraction 24.3/360 to find the arc distance along the curve that corresponds to the angle 24.3 degrees. This is because we don't want the whole circumference, but just a small fraction of it.

So (24.3/360)*24,881.4138164311 = 1,679.4954326091

This rounds to 1679

The distance between the two cities is about 1679 miles.

Answer 2

9514 1404 393

Answer:

  1679 miles

Step-by-step explanation:

One minute is 1/60 of a degree, so the difference in latitudes is ...

  47 4/60 -22 46/60 = 24 18/60 = 24.3 . . . degrees

The arc length is given by ...

  s = rθ . . . . . . r = radius, θ = angle in radians

180° is π radians, so the surface distance between the two cities is ...

  s = (3960 mi)(24.3×π/180) = 534.6π mi ≈ 1679.495 mi

The distance between City A and City B is about 1679 miles.

_____

Additional comment

As a good approximation, the distance is about 60 nautical miles per degree of latitude. Using that approximation, and converting from nautical miles to statute miles would give a distance of 1678 miles.


Related Questions

Help please this question is hard!

Answers

9514 1404 393

Answer:

  B, C, A, D

Step-by-step explanation:

The depths are easier to compare if they are all in the same form. Here, it is convenient to use decimal numbers rounded to hundredths. Your calculator can help with the fractions if you are not familiar with decimal equivalents.

  A: -1.6 m = -1.60 m

  B: -4/3 m ≈ -1.33 m

  C: -1.36m = -1.36 m

  D: -17/9 m ≈ -1.89 m

Then the least deep site is the one with the depth number closest to 0.

In order from least to greatest depth, the sites are ...

  B (-1.33) > C (-1.36) > A (-1.60) > D (-1.89)

Answer:

yeah

Step-by-step explanation:

The 8th term of an arithmetic sequence is 3 and the 100th term is 49. What is the recursive formula for the sequence?

Answers

Answer:

uₙ₊₁ = uₙ + ¹/₂

Step-by-step explanation:

uₙ₊₁ = uₙ + d

u₈ = 3

u₁₀₀ = 49

We can establish the following:

u₉ = 3 + d

u₁₀ = (3 + d) + d = 3 + 2d

u₁₁ = (3 + 2d) + d = 3 + 3d

so...

u₈₊ₐ = 3 + ad

u₁₀₀ = u₈₊₉₂ = 3 + 92d

3 + 92d = 49

92d = 46

d = ¹/₂

∴ uₙ₊₁ = uₙ + ¹/₂

Which statement or inequalities describe the number line graph?

Answers

Answer:

Step-by-step explanation:

( - ∞ , - 3 ) ∪ [ - 1 , ∞ )

needed help here
1. If m angle 2 =58°and m angle 3 =52° then m angle 4=_
2. If m angle 4 =125°and m angle 2 =64° then m angle 3=_
3. If m angle 3 =50°and m angle 5=108° then m angle 1=_
4. If m angle 1=53° and m angle 3 =88° then m angle 5=_
5. If m angle 6 =125°and m angle 1=
59° then m angle 2=_​

Answers

60jqajjahaahahaabanaahaahan

HELP ME PLZ WILL MARK U AS BRAINLIEST

Answers

Answer:

1.33

Step-by-step explanation:

so mean is the average

so what you have to do is add the numbers for each person and then divide by the amount of numbers present. the question is asking for the difference so subtract the numbers for each from person.

mia's mean= 34.33

sophia's mean= 35.667

sophia-mia= 1.33

(check my work, and if you need help just comment)

what is the end behavior of function h(x)=-4x^2+11

Answers

Answer:

[tex]-4x^{2} +11[/tex] is a parabola. The coefficient in front of the highest term (-4 in front of the [tex]x^{2}[/tex]) is negative, meaning both of the ends go towards negative infinity (point downward). So, as x approaches positive or negative infinity, y approaches negative infinity.

The end behavior of the function is being divergent for [tex]x \to \pm \infty[/tex].

According to theory of limits and differential calculus, all polynomial functions are continuous and differentiable function with no limits for [tex]x \to \pm \infty[/tex]. Therefore, we can conclude that function [tex]h(x) = -4\cdot x^{2}+11[/tex] diverges to [tex]-\infty[/tex] for [tex]x > 0[/tex] or [tex]x < 0[/tex].

That is,

[tex]x \to +\infty[/tex]

[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = -4 \cdot \lim_{x \to +\infty} x^{2} + \lim_{x \to +\infty} 11[/tex]

[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = N.E. + 11[/tex]

[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = N.E.[/tex]

[tex]x \to -\infty[/tex]

[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = -4 \cdot \lim_{x \to -\infty} x^{2} + \lim_{x \to -\infty} 11[/tex]

[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = N.E. + 11[/tex]

[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = N.E.[/tex]

Hence, the end behavior of the function is being divergent for [tex]x \to \pm \infty[/tex].

We kindly invite you to check this question related to limits: https://brainly.com/question/12383180

I need help with this

Answers

Answer:

Step-by-step explanation:

It was confusing

When looking at y = mx + b, y = b and x =a, explain how:
(a) Changing m affects the line.

(b) Changing b affects the line.

Answers

a) changing m affects the slope of the line
b) changing b translates the line up or down b units

Find the area of a triangle ABC when measure B = 56 degrees, a = 10 inches, and c = 7 inches.

Answers

The answer is around 29

Which is equivalent to (negative 2 m + 5 n) squared, and what type of special product is it?

4 m squared + 25 n squared; a perfect square trinomial
4 m squared + 25 n squared; the difference of squares
4 m squared minus 20 m n + 25 n squared; a perfect square trinomial
4 m squared minus 20 m n + 25 n squared; the difference of squares

Answers

Answer:

4 m squared minus 20 m n + 25 n squared; a perfect square trinomial

Step-by-step explanation:

(-2m+5n)(-2m+5n)

4[tex]m^{2}[/tex]-20mn+25[tex]n^{2}[/tex]

By expanding the given expression, we conclude that the equivalent expression will be the perfect square trinomial:

4m^2 + 20m*n + 25n^2

How to get an equivalent expression to the given binomial?

We have a polynomial given by the expression:

(2m + 5n)^2

If we expand the binomial (binomial means that it hastwo terms), we will get:

(2m)^2 + 2*(2m)*(5n) + (5n)^2

= 4m^2 + 20m*n + 25n^2

This is a perfect square trinomial (trinomial because has 3 terms and perfect square because is the square of a binomial).

If you want to learn more about polynomials, you can read:

https://brainly.com/question/4142886

Please help me figure this out. No links

Answers

Answer

x=1 +[tex]\sqrt{2} ,x=1 - \sqrt{2}[/tex]

Step-by-step explanation:

x.1,2=[tex]\frac{-(-2)+ \sqrt{(-2)^2-4.1(-1)} }{2.1}[/tex]

apply rule -(-a)=a

[tex]\sqrt{(-2)^2+4.1.1}[/tex]

[tex]x1,2=\frac{-(-2)+2\sqrt{2} }{2.1}[/tex]

x=1 +[tex]\sqrt{2} ,x=1 - \sqrt{2}[/tex]

A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. The interest rate applicable is j2=5.5% p.a applicable for the first five years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
a) Calculate the half-yearly payment required for each five-year interval

Answers

Did you manage to solve it?

Consider the polynomial 16x2 – 1.

What is the value of ac?



What is the value of b?



What two numbers multiply to get ac and add to get b?



The factored form of 16x2 – 1 is

Answers

9514 1404 393

Answer:

ac = -16b = 0-4, 4(4x -1)(4x +1)

Step-by-step explanation:

a) ac is the product of the leading coefficient (16) and the constant (-1).

  ac = (16)(-1) = -16

__

b) b is the coefficient of x. There is no x term, so ...

  b = 0

__

c) Two factors that add to give zero must be opposites. That is, they must be the square root of the opposite of -16, and the opposite of that.

  the two numbers are -4 and 4

__

d) The factored form for the two numbers p and q just found is ...

  ax^2 +bx +c = (ax +p)(ax +q)/a

  = (16x -4)(16x +4)/16

  = (4x -1)(4x +1) . . . . factored form of 16x^2 -1

Answer:

Consider the polynomial 16x2 – 1.

*)   What is the value of ac?  

–16

**)     What is the value of b?  

0

***)    What two numbers multiply to get ac and add to get b?  

–4 and 4

****)    The factored form of 16x2 – 1 is  

(4x– 1)(4x+ 1)

.

Step-by-step explanation:

Edge 2021

Find the limit of the function algebraically. Lim=-5 x^2-25/x+5

Answers

Answer:

[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 0[/tex]

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Factoring

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5}[/tex]

Step 2: Evaluate

Factor:                                                                                                           [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = \lim_{x \to 5} \frac{(x - 5)(x + 5)}{x + 5}[/tex]Simplify:                                                                                                         [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = \lim_{x \to 5} x - 5[/tex]Limit Rule [Variable Direct Substitution]:                                                     [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 5 - 5[/tex]Simplify:                                                                                                         [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 0[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits


3 consecutive integers have a sum of 27. What are the integers?

Answers

Answer:

8,9,10

Step-by-step explanation:

Let x be the first integer

x+1 is the next consecutive integer

x+2 is the third consecutive integer

The sum is 27

x + (x+1) + (x+2) = 27

Combine like terms

3x+3 = 27

Subtract 3 from each side

3x+3-3 =27-3

3x =24

Divide by 3

3x/3 = 24/3

x=8

The integers are

x=8

x+1 =9

X+2 =10

Answer: three consecutive integers that add up to 27 are 8,9 and 10

Explanations: x+x+1+x+2=27
3x+3=27
3x=27-3
3x=24
X=8
Three consecutive numbers
X=8
X+1=8+1=9
X+2=8+2=10

Help me out thank u

Answers

9514 1404 393

Answer:

  (a)  145

Step-by-step explanation:

The measure of the angle marked x° is half the sum of the intercepted arcs:

  (90° +200°)/2 = x° = 145°

If P = (-4,-3) and Q = (2, 1) are the
endpoints of the diameter of a circle,
find the equation of the circle.
(x - [?])2 + (y - [ ])2 = [
]​

Answers

Answer:

[tex](x+1)^2 + (y + 1)^2 = 13[/tex]

Step-by-step explanation:

To find the centre of the circle, find the mid - point of PQ :

[tex]Centre =( \frac{x_1+x_2}{2} \ , \ \frac{y_1 + y_2}{2}) = (\frac{-2}{2} \ , \ \frac{-2}{2}) = (-1, -1)[/tex]

Diameter = 2 x Radius , To Find the diameter, find distance between P and Q:

[tex]Distance , PQ = \sqrt{(2 - (-4))^2 + (1 -(-3))^2}[/tex]

                   [tex]= \sqrt{6^2 + 4^2} = \sqrt{36+ 16} = \sqrt{52} = \sqrt{4 \times 13} = 2 \times \sqrt{13}[/tex]

PQ is the diameter , therefore radius :

                                                [tex]r = \frac{1}{2} \times 2 \sqrt{13} = \sqrt{13}[/tex]

Equation of a circle :

                              [tex](x + 1)^2 + (y + 1)^2 = 13[/tex]

Answer:

(x - 1)2 + (y - 1)2 = 13

Step-by-step explanation:

This is the answer for Acellus users

Which of the following statements represents a correct relationship?
300 < 30
547 > 574
20,007 < 20,070
6,050 = 6,060

Answers

the third one is correct, 20,007 is less than 20,070

Three rectangular prisms each have a height of 1 cm.
. Prism A has a base that is 1 cm by 11 cm
* Prism B has a base that is 2 cm by 7 cm SA +V
Prism C has a base that is 3 cm by 5 cm.
1. Find the surface area and volume of each prism. Use the dot paper to draw the prisms, if needed.

Answers

Answer:

A: SA = 46 cm^2; V = 11 cm^3

B: SA = 46 cm^2; V = 14 cm^3

C: SA = 46 cm^2; V = 15 cm^3

Step-by-step explanation:

SA = 2B + PH = 2LW + PH

where SA = total surface area,

B = area of a base

P = perimeter of the base

H = height of the prism

L = length of the base

W = width of the base

V = LWH

Prism A:

SA = 2(11 cm)(1 cm) + 2(11 cm + 1 cm)(1 cm)

SA = 46 cm^2

V = (11 cm)(1 cm)(1 cm) = 11 cm^3

Prism B:

SA = 2(7 cm)(2 cm) + 2(7 cm + 2 cm)(1 cm)

SA = 46 cm^2

V = (7 cm)(2 cm)(1 cm) = 14 cm^3

Prism C:

SA = 2(5 cm)(3 cm) + 2(5 cm + 3 cm)(1 cm)

SA = 46 cm^2

V = (5 cm)(3 cm)(1 cm) = 15 cm^3

Do these ordered pairs represent a function?
(0, 1), (0, 2), (2,3), (4,8)

Answers

Answer:

No

Step-by-step explanation:

To be a function, each input can only go to one output

0 goes to 1 and 2 so it cannot be a functions

i need help on this one please help! (listing BRAINLIST and giving points) ​:D​

Answers

Answer:

sin x = a/b

cos x = c/b

tan x = a/c

Answer:

sin x = a/b

cos x = c/b

tan x = a/c

         

Step-by-step explanation:

We know,

sin(θ) = Opposite / Hypotenusecos(θ) = Adjacent / Hypotenusetan(θ) = Opposite / Adjacent

So, in this right triangle, the opposite is a

                                          "   hypotenuse is b

                                          "   adjacent is c

So, sin x = a/b

      cos x = c/b

      tan x = a/c          

The Hamilton’s are installing a new pool in their backyard .The scale drawing below represents the new pool,where 1 centimeter represents 5 feet.

Answers

4cm X 5 = 20ft
6cm X 5 = 40ft

20ft : 40ft pool

20x40 = 800 square ft

900sq ft - 800sq ft

100 square feet

y varies inversely as x. y=3 when x=10. Use the variation constant and inverse variation equation to find y when x=6.

Do not type y= in your answer.

Answers

Answer:

5

Step-by-step explanation:

Given :

Y α 1/x

Y = k/x

Where, k = constant of proportionality ;

y = 3 ; x = 10

3 = k / 10

k = 10 * 3

k = 30

Equation becomes :

Y = 30/x

Y =? ; when x = 6

Y = 30 / 6

Y = 5

Free question answer for points. If its correct ill mark brainliest ​

Answers

Answer:

[tex]14. \\841\rightarrow 800\\\\15.\\750[/tex]

Step-by-step explanation:

14:

Round the highest place means keeping the farther non-zero digit to the left, then rounding. Therefore, there should only be one non-zero digit in our final answer. The only answer choice that follows this and correctly rounds is [tex]\boxed{841\rightarrow 800}[/tex]

15:

There are 30 days in November. Therefore, the number of pages typed is equal to [tex]30\cdot 25=\boxed{750}[/tex]

Answer:

.

Step-by-step explanation:

HELP HELP HELP!!!!!!!!!!!!!!!!!!!

Answers

Answer: the top one

Step-by-step explanation:

What is the reciprocal of 8 2/5

Answers

Answer:

8 and 2/5 is 42/5 and its reciprocal is 5/42

Step-by-step explanation:

[tex]Reciprocal \: of \: \frac{42}{5} \: is \: \frac{5}{42} [/tex].

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]8 \frac{2}{5} \\ \\ = \frac{42}{5} [/tex]

[tex]Hence, \:the\: reciprocal \: of \: \frac{42}{5} \: is \: \frac{5}{42}.[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

30% of a sum of money is $234.
Use this fact to work out:
a 60%
b 90%
C 15%
d 3%
of the same amount.

Answers

Answer:

just took it, 15%

Step-by-step explanation:

I just took it online on ed

Answer:

30/100 × Y= 234

Y= 234÷30=7.8

7.8×100= 780

So the money is $780

Step-by-step explanation:

a. 60/100× 780 = $468

b. 90/100× 780 = $702

c. 15/100× 780= $117

d. 3/100 × 780= $23.4

HELP PLSSS I WILL GIVE YOU BRAINLYEST
i suck at math this is easy

Answers

OPTION C is the correct answer.

(2 1
2
-
4
-
5
) ÷
3
-
4

Answers

Answer:

[tex]63\frac{6}{9}[/tex]

Step-by-step explanation:

[tex](212-4-5)[/tex] ÷ [tex]3-4=[/tex]

[tex]203[/tex] ÷ [tex]3-4=[/tex]

[tex]67\frac{6}{9}-4=[/tex]

[tex]=63\frac{6}{9}[/tex]

Hope this helps

112 1/2 as a decimal

Answers

Answer:

[tex] \frac{1}{2} \: as \: a \: decimal = \\ 0.5[/tex]

Step-by-step explanation:

thats the answer

The decimal form, the mixed fraction can be written as 112.5.

To find out mixed fraction in the form of decimal.

What is fraction?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

The mixed fraction is a fraction whose nominator is greater than its denominator or improper fraction is a fraction in which the denominator is always less than the numerator.

 112 1/2

= (2 x 112 + 1)/2

= (224 + 1)/2

= 225/2

To divide the 225 by 2 ,we get

=112.5

So,  the decimal form, the mixed fraction can be written as 112.5

Learn more about fraction here:

https://brainly.com/question/24092047

#SPJ2

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