Four towns wish to build a radio station. Suppose that the towns are located at (0,0), (10,0), (0,5) and (2, 2) on a square grid. At what point (a, b) should the station be located to minimize the sum of the squares of the distances from each town to the station?

Q: 15. You want to put a fence around a rectangular field and then subdivide the field into 4 smaller…

A: Let's find.

Q: C: rectangle with vertices (0, 0), (2, 0), (2, 3), and (0, 3)

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Q: Find the least-squares line y = bo + bịr of best fit through the points (-2,3), (-1,4), (2, 1), (3,…

A: Solve it.

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A: The slope is -2. Thus, the value of slope is -2. For every one unit increasing variable x, there…

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A: To find- Use Lagrange multipliers to find three positive numbers whose sum is 51 and the sum of…

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

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Q: Use Lagrange multipliers to find three positive numbers whose sum is 30 and the sum of whose squares…

A: We have find three numbers whose sum is 30 and whose squares is as small as possible, by lagrange…

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A: To minimise the cost, the dimensions are to be computed. we have,Area = xy = 16000now,Length of…

Q: If you wish to find the least squares line of best fit y = mx + c through the points (2, 1), (2, 3),…

A: The equation of the line is y=mx+c. The line passes through the points 2,1, 2,3, 5,4. Calculate the…

Q: 5. A rectangular poster is to contain 648 square inches of print. The margins at the top and the…

A: Given that a rectangular poster is to contain 648 square inches of print. There is a margin of 2…

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A: Let's find.

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A: For a positive integer n, the formula for n! is n(n – 1)(n – 2)…..3.2.1.

Q: Find the equation y = Bo + B₁ of the least-squares line that best fits the five points (-3, 4),…

A:

Q: 5. A farmer wants to fence an area of 9600 square feet in a rectangular field and then divide it in…

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Q: (b) A wire of length 100 centimeters is cut into two pieces. One piece is bent to form a square. The…

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Q: Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible.

A: To find a positive number for which the sum of it and its reciprocal is the smallest possible.

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

A: Using Lagrange multiplier to find the dimension of rectangle whose area is maximum

Q: A rectangular lot has a perimeter of 80m. If its lot area is to be maximized, what is its length?

A:

Q: Find the shortest tour through the points of a: a) 3 x 3 grid, b) 4 x 4 grid, c) 5 x 5 grid and d)…

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Q: A rectangular poster is to contain 200 square inches of print. The margins at the top and bottom of…

A: Given ,A rectangular poster is to contain 200 square inches of print.The margins at the top and…

Q: A farmer wants to construct a fence around an area of 726 square feet in a rectangular field and…

A: Dimensions:  33×22

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Q: If Xmin = - 6, Xmax = 10, and Xscl = 2, how should Ymin, Ymax, and Yscl be selected so that the…

A: There are many ways to answer this question. One such answer is as written below.

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Q: Find two positive integers such that their sum is 10, and minimize the sum of squares.

A: Given  two positive integers such that their sum is 10, To minimize the sum of squares

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A: Let the width of each pen be x and the length of each pen be y. As the pens are rectangular thus the…

Q: By using the method of least squares, find the best parabola through the points: (-1,–2), (1,0),…

A: Given data: x -1 1 2 0 y -2 0 3 0 The general equation of the parabola is y=c0+c1x+c2x2…

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A: Follow the procedure given below.

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Q: A rectangular corral of 726 square meters is to be fenced off and then divided by a fence into two…

A: I use second derivative test to find out dimensions where amount of required fencing minimum

Q: 6] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

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Q: 13. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then…

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Q: 17. Find two positive integers such that their sum is 10 and maximize and minimize the sum of their…

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Q: 10. A farmer has 400 feet of fencing to enclose two adjacent sheep corrals. What should be the…

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Q: 1. A rectangular plot of land is to be fenced in using only two kinds of fencing. Two opposite sides…

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Q: 2. Find the slopes of the medians of the triangle with vertices (2, 3), (5, 7), and (4, -2).

A: Given : The vertices of the triangle A2, 3, B5, 7 and C4, -2

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Q: A rectangular poster is to contain 648 square inches of print. The margins at the top and bottom of…

A: Given: The area of the poster is 648 square inches. The following diagram shows all the…

Q: 16. A farmer wants to fence an area of 2 million square feet in a rectangular field and then divide…

A: Here first we find the total length of fence in terms of the sides. Now using differentiation we…

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A: One side is covered with stream and not needed any fencing. Total area to be fenced is 800 ft².…

Q: A rectangular building covering 6,000m2 is to be built on a lot as shown in the figure. If the…

A: Minimize area