3) A system for tracking ships indicates that the ship lies on the path described by 2y -x = 4. Thein the ship is found to lie on a path described by 2x-y = 4.a. If it is known that the ship is located in the second quadrant of the coordinate system,process is repdetermine its exact location.b. Graph this in your graphing program and paste into your Word documentс.How many solutions are there if you eliminate "it is known that the ship is located in thesecond quadrant of the coordinate system"?

Answered: 3) A system for tracking ships…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter81: Introduction To Computer Numerical Control (cnc)

Section: Chapter Questions

Problem 12A

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3) A system for tracking ships indicates that the ship lies on the path described by 2y -x = 4. The
in the ship is found to lie on a path described by 2x-y = 4.
a. If it is known that the ship is located in the second quadrant of the coordinate system,
process is rep
determine its exact location.
b. Graph this in your graphing program and paste into your Word document
с.
How many solutions are there if you eliminate "it is known that the ship is located in the
second quadrant of the coordinate system"?

Expert Solution

Sub-part (a)

$In the first iteration, the ship was tracked at the path described by : 2 y^{2} - x^{2} = 4 - - - (1)$

$In the second iteration, the ship was tracked at the path described by : 2 x^{2} - y^{2} = 4 - - - (2)$

$To find the exact location of ship, we must solve both equations simultaneously .$

$From eq . (1), 2 y^{2} - x^{2} = 4 \Rightarrow y^{2} = \frac{x^{2}}{2} + 2$

$substituting the value of y^{2} in eq . (2), we get$

$\Rightarrow 2 x^{2} - (\frac{x^{2}}{2} + 2) = 4 \Rightarrow 2 x^{2} - \frac{x^{2}}{2} - 2 = 4 \Rightarrow \frac{3 x^{2}}{2} = 6 \Rightarrow x^{2} = 4 \Rightarrow x = \pm 2$

$As the ship is located in second quadrant, x < 0, thus x = - 2 . ∴ y = \sqrt{\frac{x^{2}}{2} + 2} = \sqrt{\frac{{(- 2)}^{2}}{2} + 2} = \pm 2 As the ship is located in second quadrant, y > 0, thus y = 2 .$

$The ship is located at (- 2, 2) .$

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