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
olasank [31]
2 years ago
11

Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t

ower equidistant from the other three, and write an equation for the circle.
Mathematics
1 answer:
Marat540 [252]2 years ago
3 0

Answer:

The location of the new cell phone tower is (h,k) = (3,4), and the equation of the circle is x^{2}+y^{2} -6\cdot x - 8\cdot y = 0.

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0 (1)

Where:

x - Independent variable.

y - Dependent variable.

A, B, C - Circunference constants.

Given the number of variable, we need the location of three distinct points:

(x_{1},y_{1}) = (6,0)

36 +6\cdot A + C = 0

(x_{2},y_{2}) = (8,4)

80 + 8\cdot A + 4\cdot B + C = 0

(x_{3},y_{3}) = (3,9)

90 + 3\cdot A + 9\cdot B + C = 0

Then, we have the following system of linear equations:

6\cdot A + C = -36 (2)

8\cdot A +4\cdot B + C = -80 (3)

3\cdot A + 9\cdot B + C = -90 (4)

The solution of this system is:

A = -6, B = -8, C = 0

By comparing the general form with the standard form of the equation of the circunference is:

A = -2\cdot h (5)

B = -2\cdot k (6)

C = h^{2}+k^{2}-r^{2} (7)

Where:

h, k - Coordinates of the center of the circle.

r - Radius of the circle.

If we know that A = -6, B = -8 and C = 0, then coordinates of the center of the circle and its radius are, respectively:

h = -\frac{A}{2}

k = -\frac{B}{2}

r = \sqrt{h^{2}+k^{2}-C}

h = 3, k = 4, r = 5

The location of the new cell phone tower is (h,k) = (3,4), and the equation of the circle is x^{2}+y^{2} -6\cdot x - 8\cdot y = 0.

You might be interested in
What is the GCF of 24,48m
Phoenix [80]
24
It goes into 24 once and into 48 twice
3 0
3 years ago
Read 2 more answers
The sum of two numbers is 6565. the larger number is fivefive more than threethree times the smaller number. find the two number
Nimfa-mama [501]
~You would set up the equation x+(3x+5)=6565
~Combine like products so 3x+x=4x.
~Now you have 4x+5=6565.
~Isolate the variable by subracting the 5 from both sides, so you have 4x=6560.
~Since you multiply x by 4, divide both sides by 4, and 6560 divided by 4 is 1,640.
*The first number is 1,640.
~Now to find the second number you simply plug in 1,640 to (3x+5), with 1,640 being x.
~That would become [3(1,640)+5].
~3 times 1, 640 is 4,920, and add the 5 so you get 4,925.
*The second and larger number is 4,925.
If you wanna check just add the two numbers, and you get 6565.

3 0
3 years ago
Find the value of x so that the function has the given value. f(x) = 3 – 2x; f(x) = -5
Brrunno [24]
F(-5)= 3-2(-5)
= 3+10
= 13

Hope it helps :))
4 0
3 years ago
A 16-ounce bottle of orange juice says that it contains 200 milligrams of vitamin C, which is 250% of the daily recommended dosa
Andrei [34K]

80 milligrams is the amount of vitamin C that is considered to be 100% of the daily recommended requirement for adults.

<h3>What is the daily recommended dosage of vitamin C for adults? </h3>

Parameter

  • The amount of liquid included in the bottle is 16 ounces.
  • The vitamin C content of the bottle comes to a total of 200 milligrams.

Since the orange juice container that has a capacity of 16 ounces states that it has 200 milligrams of vitamin C, this means that it fulfills 250% of an adult's recommended daily requirement for vitamin C. Then, for one hundred percent of the daily allotment,

As a result, we are able to draw the conclusion that the amount of vitamin C that is considered to be 100% of the daily recommended requirement for people is 80 milligrams.

Read more about vitamin C

brainly.com/question/15080220

#SPJ1

8 0
1 year ago
You decide to sell each of your toys for $25. Costs are how much you pay your supplier($11 to make each toy plus a one-time fee
patriot [66]

Answer:

I dont know

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • How to solve radical numerator fractions
    7·1 answer
  • What is the greatest common factor of 90,54 and 130?
    5·1 answer
  • What is the area of the triangle shown below ​
    8·2 answers
  • A theatre ticket costs £37 plus a booking fee of 4%.<br>What is the total price of the ticket?​
    8·1 answer
  • If a pattern starts with one and doubles each term(1,2,4,8,16...) what is the algebraic pattern rule from y(term value) to x(ter
    13·1 answer
  • Find the missing length. Round your answer to the nearest tenth.
    9·2 answers
  • It takes about fifteen minutes walk one dog. How many hours does it take to walk 25 dogs separately?
    6·2 answers
  • Graph and label each figure in its image under the given counterclockwise rotation about the origin. Give the new coordinates. p
    8·1 answer
  • Evaluate the expression. 3/4 x (1 - 1/9) *
    5·1 answer
  • Select the set of equations that is NOT equivalent to 8k = 20
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!