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Controlling Air PollutionThe Chief Minister of Delhi launched the, "Switch Delhi, an electric vehicle mass awareness campaign in the National Capital. The government has also issued tenders for setting up 100 charging stations across the city. Each station will have five charging points. For demo charging station is set up along a straight line and has charging points at A(-7/3,0), B(0,7/4), C(3, 4), D(7, 7) and F(x, y). Also, the distance between C and E is 10 units. Based on the above information, answer the following questions. (i) The distance DE is (a) 5 units (b) 10 units (c) 4 units (d) 6 units (ii) The value of x + y is (a) 20 (b) 21 (c) 22 (d) 23 (iii) Which of the following is true? (a) The points C, D and E are vertices of a triangle (b) The points C, D and E are collinear (c) The points C, D and E lie on a circle (d) None of these (iv) The ratio in which B divides AC is (a) 9:7 (b) 4:7 (c) 7:4 (d) 7:9

Question

Controlling Air PollutionThe Chief Minister of Delhi launched the, "Switch Delhi, an electric vehicle mass awareness campaign in the National Capital. The government has also issued tenders for setting up 100 charging stations across the city. Each station will have five charging points. For demo charging station is set up along a straight line and has charging points at A(-7/3,0), B(0,7/4), C(3, 4), D(7, 7) and F(x, y). Also, the distance between C and E is 10 units. Based on the above information, answer the following questions. (i) The distance DE is (a) 5 units (b) 10 units (c) 4 units (d) 6 units (ii) The value of x + y is (a) 20 (b) 21 (c) 22 (d) 23 (iii) Which of the following is true? (a) The points C, D and E are vertices of a triangle (b) The points C, D and E are collinear (c) The points C, D and E lie on a circle (d) None of these (iv) The ratio in which B divides AC is (a) 9:7 (b) 4:7 (c) 7:4 (d) 7:9

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Solution

(i) The distance DE can be found using the distance formula. The coordinates of point D are (7, 7) and the coordinates of point E are not given. However, it is mentioned that the distance between C and E is 10 units. Since point C has coordinates (3, 4), we can use the distance formula to find the distance between C and E. Let the coordinates of point E be (x, y). The distance formula is given by:

√((x - 3)^2 + (y - 4)^2) = 10

Simplifying the equation, we get:

(x - 3)^2 + (y - 4)^2 = 100

Since point F has coordinates (x, y), the distance DE is the distance between points D and F. Using the distance formula, we have:

√((x - 7)^2 + (y - 7)^2)

Therefore, the distance DE is given by the equation:

√((x - 7)^2 + (y - 7)^2)

To find the value of DE, we need to know the coordinates of point F.

(ii) The value of x + y can be found by substituting the coordinates of point F into the equation x + y.

(iii) To determine whether the points C, D, and E form a triangle, are collinear, or lie on a circle, we need to know the coordinates of point E.

(iv) The ratio in which B divides AC can be found using the section formula. The section formula states that if a point divides a line segment with endpoints (x1, y1) and (x2, y2) in the ratio m:n, then the coordinates of the point are given by:

(x, y) = ((mx2 + nx1)/(m + n), (my2 + ny1)/(m + n))

In this case, B divides AC. The coordinates of point A are (-7/3, 0) and the coordinates of point C are (3, 4). Let the ratio in which B divides AC be m:n. The coordinates of point B are (0, 7/4). Using the section formula, we have:

(x, y) = ((n3 + m(-7/3))/(m + n), (n4 + m0)/(m + n))

Comparing the coordinates of point B with the coordinates obtained from the section formula, we can find the ratio m:n.

This problem has been solved

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use this format "Another problem with electric vehicles is the high purchase price. In addition, the spread of coronavirus and, consequently, the possibility of epidemics in the coming years can lead to a sharp increase in the use of vehicles in municipal services, including waste collection and road cleaning. This paper proposes a mathematical optimization model for locating charging stations with different technologies and vehicle arc routing for waste collection. However, implementing the model proposed in this paper is challenging due to (1) the lack of comprehensive technical knowledge in some countries to provide charging infrastructure, (2) limited electric vehicle companies, and (3) energy supply problems. Some knowledge-based companies and start-ups have succeeded in designing and making charging devices for electric vehicles, reducing the required time to charge vehicles. Nevertheless, the lack of financial resources for research and development is one of the main problems in these companies and start-ups, which can be solved through government subsidies. In addition, allocating government budgets to leading start-ups and companies with electric vehicle production can create a competitive environment, increase competition, and reduce prices. As the cost of electric vehicles decreases, more people can purchase them, increasing the demand for charging. Services will increase. The charging infrastructure development can also increase the demand for electricity generation, which ultimately leads to an increase in the production capacity of power plants that often use fossil fuels—expanding the use of electric vehicles results in producing more bio-pollutants by power plants. One of the best ways to solve this problem is to invest in renewable energy sources, which have received attention recently. In many countries worldwide, suitable conditions are provided for energy production from renewable sources. Therefore, government resources, private sector investment, and public-private partnerships can be useful management solutions." and write a managerial insight on "Routing optimization of an electric vehicle in municipal solid waste using genetic algorithm"

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