To find: The exact location of the ship tracked by

Falak Kinney 2021-08-18 Answered
To find: The exact location of the ship tracked by the tracking system.
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comentezq
Answered 2021-08-19 Author has 106 answers

Procedure used:
An Application of a Nonlinear System:
"Step 1: Write a system of equations modeling the conditions in the problem.
Step 2: Solve the system and answer the question asked in the problem.
Step 3: Check the proposed solution in the original wording of the problem."
Calculation:
It is given that the ship lies on a path described by 2y2x2=1 but the boat located on a different path is described by 2x2y2=1 when the process is repeated.
Use the above procedure to find the exact location of the ship.
Multiply 2y2x2=1 by 2 and obtain the equation 4y22x2=2.
Add the both equations and obtain the result as follows.
(4y22x2)+(2x2y2)=2+1
(4y2y2)+(2x22x2)=3
3y2=3
y2=1
y=±1.
Substitute y=1 in the equation 2x2y2=1 and obtain the value of x as follows.
2x2(1)2=1
2x21=1
x2=1+12
x2=1
x=±1
Substitute y=1 in the equation 2x2y2=1 and obtain the value of x as follows.
2x2(1)2=1
2x21=1
x2=1+12
x2=1
x=±1.
Thus, for y=1, x=±1 and for y=1,x=±1.
Thus, the solution set is {(1,1),(1,1),(1,1),(1,1)}
However, the ship is located in the first quadrant of the coordinate system.
Hence, the point is (1,1).
Check the result, by substituting the obtained solutions in the given original equations 2y2x2=1 and 2x2y2=1.
Substitute (1,1) in the given system and check.
2(1)2(1)2=1
1=1
2(1)2(1)2=1
1=1
Therefore, the exact location of the ship is (1,1).

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