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- Find equations for the planes The plane through (2, 4, 5), (1, 5, 7), and (-1, 6, 8)Find the equation of the plane that passes through the points P1 = (2, 3, 1), P2 = (5, 4, 3), P3 = (3, 4, 4)Find an equation of the plane that passes through the points P, Q, and R. P(5, 6, 7), Q(3, 4, 5), R(8, 4, 7)
- Find an equation for the plane through the points (5,4,5),(−2,0,−1),(0,1,2).Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be a cable connecting Centerville to both towns. The idea is to save on the cost of the cable by arranging the cable in a Y-shaped configuration.Centerville is located at (10,0)(10,0) in the sexy-plane, Springfield is at (0,7)(0,7), and Shelbyville is at (0,−7)(0,-7). The cable runs from Centerville to some point (x,0)(x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x,0)(x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of xx:f(x)= We find that f(x)f(x) has a critical number at x=To verify that f(x)f(x) has a minimum at this critical number we compute the second derivative f''(x)f′′(x) and find that its value at the…Find the distance the point P(0, -6, -8), is to the plane through the three pointsQ(2, -3, -4), R(-3, 2, -2), and S(5, -5, -6).