1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Paul [167]
2 years ago
6

Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points ​(4​,5​), ​(-6​,-6​), and ​(-14​,2​

), respectively. The epicenter of an earthquake is determined to be 10 units from X​, 5 units from​ Y, and 13 units from Z. Where on the coordinate plane is the epicenter​ located?
Find the coordinates of the epicenter.

Mathematics
1 answer:
Lilit [14]2 years ago
8 0

Answer:

  (-2, -3)

Step-by-step explanation:

A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.

_____

The simultaneous equations for the circles can be solved algebraically.

The epicenter is 10 units from X, so lies on the circle ...

  (x -4)^2 +(y -5)^2 = 10^2

  x^2 -8x +16 +y^2 -10y +25 = 100

  x^2 +y^2 -8x -10y = 59

__

The epicenter is 5 units from Y, so lies on the circle ...

  (x +6)^2 +(y +6)^2 = 5^2

  x^2 +12x +36 +y^2 +12y +36 = 25

  x^2 +y^2 +12x +12y = -47

__

The epicenter is 13 units from Z, so lies on the circle ...

  (x +14)^2 +(y -2)^2 = 13^2

  x^2 +28x +196 +y^2 -4y +4 = 169

  x^2 +y^2 +28x -4y = -31

__

Subtracting the second equation from each of the other two, we get ...

  (x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)

  -20x -22y = 106 . . . . eq1 -eq2

  (x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)

  16x -16y = 16 . . . . . . . .eq3 -eq2

These simultaneous linear equations can be solved a variety of ways. We might use substitution:

  x = y+1 . . . . . from eq3 -eq2 divided by 16

  10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2

  21y = -63 . . . . . . . . . . . . simplify, subtract 10

  y = -3

  x = y+1 = -2

The epicenter is located at (x, y) = (-2, -3).

You might be interested in
In a school 3/5 of children are boys and the number of girls is 2000. Find the number of boys.
Ahat [919]

Answer:

3000

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Antoine wants to get a subscription to a local library. There are two libraries, each of which charges a monthly subscription fr
frozen [14]

Answer:

the first one is B and the second one is A

Step-by-step explanation:

I guessed and I got it right

5 0
3 years ago
Read 2 more answers
Point R is on line segment QS. Given QS= 5x-2, QR= 3x-6, and RS=4x-2, determine the numerical length of RS.
pashok25 [27]

Answer:

The numerical length of RS is 10 units

Step-by-step explanation:

* <em>Lets explain How to solve the problem</em>

- Point R is on line segment QS

- The length of QS is (5x - 2)

- The length of QR is (3x - 6)

- The length of RS is (4x - 2)

- <em>The length of QS is the sum of the lengths of QR and RS</em>

∵ QS = QR + RS

∴ (5x - 2) = (3x - 6) + (4x - 2)

- Simplify the right hand side by adding like terms

∴ 5x - 2 = (3x + 4x) + (-6 + -2)

∴ 5x - 2 = 7x + -8 ⇒ (+)(-) = (-)

∴ 5x - 2 = 7x - 8

- Add 8 for both sides

∴ 5x + 6 = 7x

- Subtract 5x from both sides

∴ 6 = 2x

- Divide both sides by 2

∴ x = 3

- <em>To find the length of RS substitute the value of x in its expression</em>

∵ RS = 4x - 2

∵ x = 3

∴ RS = 4(3) - 2 = 12 - 2 = 10

∴ The numerical length of RS is 10 units

8 0
3 years ago
Simplify 4^7/5^2 all raised to the 3rd power<br><br> 4^10/5^5<br> 4^4/5<br> 4^21/5^6<br> 12^7/15^2
zepelin [54]
[4^7/5^2]³ = 4^21/5^6

When a power is raised to an other power, you multiply these 2 powers

Answer: 4^21/5^6
5 0
3 years ago
a bakery sells packages of 10 bagels for $3.69 it's a bakery start selling the bagels in packages of 12 how much would you expec
Sophie [7]
3.69/10 = .369 x 12 = 4.428, so around 4.43
5 0
3 years ago
Other questions:
  • Marcus hired a car service to drive him to the airport. The bill came to $56.80. He gave the driver a 20% tip. How much money di
    14·2 answers
  • Please help will vote brainliest. Due soon please
    10·1 answer
  • Solve the equation using the zero-product property (2x-8)(7x+5)=0
    7·2 answers
  • Halle el valor de "h" del punto centro de la ecuación de la circunferencia cuyo diámetro es el segmento de la recta que une los
    10·1 answer
  • For which value of x is the equation 3(x + 2) + x = 2x + 16 true?
    14·1 answer
  • What is the volume of the triangle prism? ( HELP PLEASE )
    12·1 answer
  • Pls tell the value of Y pls pls
    11·2 answers
  • Jayden had $43 in his bank account. He wanted to buy a game at GameStop. The game cost $15. He made the purchase.
    12·2 answers
  • Find the value of variable X. <br><br> 16<br><br> 41<br><br> 10<br><br> 17.5
    14·1 answer
  • Write the fractions 22/100 and 22/1000 as decimal how are the values of the digit 2 related in each of the decimals
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!