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
Papessa [141]
3 years ago
5

Six housing subdivisions within a city area are target for emergency service by a centralized fire station. Where should the new

fire station be located such that the maximum rectilinear travel distance is minimized? Assume that the total value of the homes in each sub-division is equal. The centroid locations (in miles) are as follows:
Subdivsion x-coordinate y-coordinate Total Vaue (in millions)
A 20 15 50
B 25 25 120
C 13 32 100
D 25 14 250
E 4 21 300
F 18 8 75
Engineering
1 answer:
Marina86 [1]3 years ago
5 0

Answer:

Explanation:

Since there are six points, the minimum distance from all points would be the centroid of polygon formed by A,B,C,D,E,F

To find the coordinates of centroid of a polygon we use the following formula. Let A be area of the polygon.

C_{x}=\frac{1}{6A} sum(({x_{i} +x_{i+1})(x_{i}y_{i+1}-x_{i+1}y_{i}))     where i=1 to N-1 and N=6

C_{y}=\frac{1}{6A} sum(({y_{i} +y_{i+1})(x_{i}y_{i+1}-x_{i+1}y_{i}))

A area of the polygon can be found by the following formulaA=\frac{1}{2} sum(x_{i} y_{i+1} -x_{i+1} y_{i}) where i=1 to N-1

A=\frac{1}{2}[ (x_{1}  y_{2} -x_{2}  y_{1})+ (x_{2}  y_{3} -x_{3}  y_{2})+(x_{3}  y_{4} -x_{4}  y_{3})+(x_{4}  y_{5} -x_{5}  y_{4})+(x_{5}  y_{6} -x_{6}  y_{5})]

A=0.5[(20×25 -25×15) +(25×32 -13×25)+(13×21 -4×32)+(4×8 -18×21)+(18×14 -25×8)

A=225.5 miles²

Now putting the value of area in Cx and Cy

C_{x} =\frac{1}{6A}[ [(x_{1}+x_{2})(x_{1}  y_{2} -x_{2}  y_{1})]+ [(x_{2}+x_{3})(x_{2}  y_{3} -x_{3}  y_{2})]+[(x_{3}+x_{4})(x_{3}  y_{4} -x_{4}  y_{3})]+[(x_{4}+x_{5})(x_{4}  y_{5} -x_{5}  y_{4})]+[(x_{5}+x_{6})(x_{5}  y_{6} -x_{6}  y_{5})]]

putting the values of x's and y's you will get

C_{x} =15.36

For Cy

C_{y} =\frac{1}{6A}[ [(y_{1}+y_{2})(x_{1}  y_{2} -x_{2}  y_{1})]+ [(y_{2}+y_{3})(x_{2}  y_{3} -x_{3}  y_{2})]+[(y_{3}+y_{4})(x_{3}  y_{4} -x_{4}  y_{3})]+[(y_{4}+y_{5})(x_{4}  y_{5} -x_{5}  y_{4})]+[(y_{5}+y_{6})(x_{5}  y_{6} -x_{6}  y_{5})]]

putting the values of x's and y's you will get

C_{y} =22.55

So coordinates for the fire station should be (15.36,22.55)

You might be interested in
3. When starting an automatic transmission
Alexxandr [17]

Answer:

It should be in Park or Neutral.

Explanation:

4 0
4 years ago
Explain the conductivity results observed for ionic compounds in the solid state and in aqueous solution.i.Solid ionic compounds
Svetach [21]

Answer:

Aqueous solution of ionic compounds conduct electricity while solid ionic compounds don't.

Explanation:

Ionic compound conduct electricity when liquid or in aqueous solution that is resolved in water because the ionic bonds of the compound become weak and the ions are free to move from place to place.

Ionic compounds don't conduct electricity while in solid state because the ionic bonds are to strong and ions cannot move around with lack of space for movement which makes the electric conductivity zero.

8 0
3 years ago
Which of the following is an activity of daily living? jogging cleaning weightlifting all of the above
Mrrafil [7]

Answer:

cleaning

Explanation:

4 0
4 years ago
QUESTION:
pentagon [3]
74 cycles it’s what u need
7 0
3 years ago
Water vapor at 1.0 MPa, 300°C enters a turbine operating at steady state and expands to 15 kPa. The work developed by the turbin
Andre45 [30]

Answer:

a) isentropic efficiency = 84.905%

b) rate of entropy generation = .341 kj/(kg.k)

Please kindly see explaination and attachment.

Explanation:

a) isentropic efficiency = 84.905%

b) rate of entropy generation = .341 kj/(kg.k)

The Isentropic efficiency of a turbine is a comparison of the actual power output with the Isentropic case.

Entropy can be defined as the thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

Please refer to attachment for step by step solution of the question.

5 0
3 years ago
Other questions:
  • The displacement volume of an internal combustion engine is 3 liters. The processes within each cylinder of the engine are model
    10·1 answer
  • Given a series of numbers as input, add them up until the input is 10 and print the total. Do not add the final 10. For example,
    7·1 answer
  • The mechanical properties of a metal may be improved by incorporating fine particles of its oxide. Given that the moduli of elas
    5·1 answer
  • What is your employer required to have on fixed ladders that extend more than 24 feet in the workplace?
    15·2 answers
  • The equation for the velocity V in a pipe with diameter d and length L, under laminar condition is given by the equation V=Δpdsq
    10·1 answer
  • What are common names assigned to instruction addresses in a PLC program called
    8·1 answer
  • How to solve circuit theory using mesh analysis<br>​
    11·1 answer
  • A cylindrical 1040 steel rod having a minimum tensile strength of 865 MPa (125,000 psi), a ductility of at least 10%EL, and a fi
    7·1 answer
  • Underground water is to be pumped by a 78% efficient 5- kW submerged pump to a pool whose free surface is 30 m above the undergr
    10·1 answer
  • Draw a surface development of a truncated cone
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!