A rectangualr garden is to be enclosed usinf two different types of fencinf. one side of the garden boarders a road and the fencing for this side costs $25 per foot. The fencinf for the other sides costs $10 per foot.

x = 18.9737 ft

y = 15.8114 ft

Step-by-step explanation:

Given:

- Area of rectangle garden A = 300 ft^2

- Cost of one side fencing = $25 /ft

- Cost of second side fencing = $10 /ft

Find:

- Find the dimensions to minimize the cost.

Solution:

- Develop a total cost function for the rectangular garden as follows:

                         Total Cost = x*25 + 3*y*10

                            T.C = 25*x + 30*y

- Use the area expression to find the relationship between x and y dimensions:

                              A = x*y

                              300 = x*y

                              y = 300 / x

- Input the above relationship into the total cost function:

                              T.C = 25*x + 30*300/x

                              T.C = 25*x + 9000/x

- To minimize the function, take its derivative with respect to dimension x:

                              dC/dx = 25 - 9000/x^2

- Set derivative to 0:

                               0 = 25 - 9000/x^2

Solve for x:

                               0 = 25x^2 - 9000

                                x = sqrt(9000/25)

                               x = 18.9737 ft

- The corresponding dimension y is:

                              y = 300/18.9737 = 15.8114 ft

597

step-by-step explanation:

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068