As an odometer check, a special counter measures the miles a car travels modulo 7. explain how this counter can be used to determine whether the car has been driven 49,335; 149,335; or 249,335 miles when the odometer reads 49,335 and works modulo 100,000.

249335 miles

Step-by-step explanation:

Let x be the number of miles the car has travelled.

The odometer can only tell us that x≡49335(mod 100000).

If we also know the value of c where x≡c(mod 7)and 0≤c<7 by the Chinese remainder theorem we know the congruence satisfied by x modulo 100000•7 = 700000.

As long as the car has been driven less that 700000 this uniquely determines the number of miles driven.

In particular, we easily see that if x≡6 (mod 7)then the car was driven 49335 miles, if x≡4 (mod 7)then the car was driven 149335 miles, and if x≡2 (mod 7)then the car was driven 249335 miles

6. 104

7. 52/37

8. 2704

9. 140608

10. -52

11. |52|=52

12. 1/52

13. 156

14. 26

15. 40

16. 37

17. -364

18. 53 1/3

19. 50.96

20. 43 2/3

21. 78

22. 50.75

23. 47.63

24. 163.28

25. 10400

26. 338

27. 208

28. 2704 square inches

29. 312 square meters

30. don't know what its asking, tell me so i can tell you

31. 8490.56

32. 52 degrees would be an acute angle

33. 128 degrees

34. 20.8

35. 39

36. 208

noncoplanar points are points that do not lie on the same line.