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  3. hi i need help for part a and b please...

Question: hi i need help for part a and b please...

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Hi i need help for part a and b please

(4) The technique of triangulation in surveying is to locate a position in R3 if the distance to 3 fixed points is known. This is similar to how global position systems (GPS) work. A GPS unit measures the time differences taken for a signal to travel from each of 4 satellites to a receiver on Earth This is then converted to a difference in the distances from each satellite to the receiver and this can then be used to calculate the distance to 4 satellites in known positions. Let P (2,-1,4), 2 (3, 4, -3), P3 (4,-2,6), P (6,4, 12) We wish to find a point P (x, y, z) with r, y, z2 0 satisfying: P is distance Δ from P, P is distance (Δ-12+ 9V3) from P, P is distance A - 1 from P3, and P is distance A - 9 from P Note, its difficult - though not impossible - to do this by hand. You are welcome to use MATLAB, Mathematica, or any other software to do this Your program needs to be able to manipulate algebraic variables. If you are using MATLAB, you should consult chapters 10 and 11 of the online textbook for the MATLAB modules a) Write down equations for each of the given distances. b) Let s 2-(12 + y2 + z*). Show that the equations you have written down can be put in the form 21 -6 -8y+6z (24-18v3)As (353-216V3) 2A 18Δ 12r c) Solve the linear system. Your answer will express x, y, z, and Δ in terms of s In MATLAB, you may find the command syms useful.) d) Substitute the values you found for z, y, z, Δ into the equation s-Δ2-(12+92 + 22). Solve the resulting quadratic equation in s. (In MATLAB, use the command solve for this. You can present rounded values with the command round.) e) Substitute s back into your expressions for r, y, z to find the point P. (In MATLAB, use the command subs)

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