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- Test y2=6x for symmetry with respect to both axes and the origin.What are the coordinates of the vertices of △A′B′C′ after a reflection across a line through point P with a y-intercept at y=−2 followed by translation T3,3?What are the coordinates of the vertices of△A′B′C′after a reflection across a line through point P with a y-intercept at y=−2 followed by translation T3,3?
- 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 the 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 (7,0) in the xy-plane, Springfield is at (0,5), and Shelbyville is at (0,−5). The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. 1). To solve this problem we need to minimize the following function of x:f(x)=? a). We find that f(x) has a critical number at x=? b). To verify that f(x) has a minimum at this critical number we compute the second derivative f′′(x) and find that its value at the critical number is =? (positive…4. Trapezoid JKLM with vertices J(2, 1) , K(5, 1), L ^ n * (8, - 4) and M(1,-4);90 ° clockwise rotation about Y(- 1, 3)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 cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuration. Centerville is located at (15,0) in the xy-plane, Springfield is at (0,3), and Shelbyville is at (0,-3). The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. (Draw a picture of this situation).It costs $1000 per unit to lay cable along the x-axis and $1250 per unit otherwise. Write a function for the total cost of laying the cable in terms of x.Cost(x)=__________ Take the derivative of your cost function by carefully applying the chain rule.dCost/dx=__________ To find the x location that yields a minimum cost we need Calculus! Recall that if the derivative of the cost function is zero then the x is…
