## Mimi_x3 4 years ago Only for Kaffeine, easy one first. The cost to run a vehicle is a + v^2/a dollars per hour where v is the average speed of the vehicle in km/h. Show thatt the cost for a trip of Dkm is lowest if the vehicle travels at v=a km/h

1. KatrinaKaif

Do you want the work to? O_o

2. Mimi_x3

nope, wait its a show question. Just show the working if you're bothered.

3. KatrinaKaif

Okay sorry, the stupid thing said server lost connection C = a + v2/a => dc/dv = 0 + 2v/a => dc/dv = 2v/a => 2v /a = 0 2v = 0(a) v = 0 => d2c / dv2 = d/v(2v/a)= 2/a (Postive value so cost is lowest for all values of v ) ??

4. Mimi_x3

Sorry, its wrong.

5. KatrinaKaif

K give me a moment.

6. Mimi_x3

You can ask for help if you want, i don't mind.

7. KatrinaKaif

Omfg Mimi.

8. Mimi_x3

lols, what's wrong ? Archaic Mathematician can help :P

9. LagrangeSon678

This is basic calc (calc 1), i wanna see her do this.

10. Mimi_x3

Isn't calc 1 ? college ? >_<

11. LagrangeSon678

she can do it, i am sure. She solved harder ones before

12. Mimi_x3

ok, i'll give a little hint, it involved d s t

13. Mimi_x3

involves*

14. KatrinaKaif

c(a) = 2v?? don't tell me I am wrong again. -_-

15. Mimi_x3

lols, yeah sorry. Want me to type up the solution ?

16. KatrinaKaif

Lol Give me the answer and I ll figure the solution

17. LagrangeSon678

no way

18. Mimi_x3

It's a show.

19. Mimi_x3

No way ?

20. KatrinaKaif

Lagrange, stay out of it, and go away.

21. KatrinaKaif

Mimi, type.

22. Mimi_x3

23. KatrinaKaif

I ll figure it out myself.

24. LagrangeSon678

25. Mimi_x3

lols, and stubborn -_-

26. KatrinaKaif

Shut up featheres.

27. LagrangeSon678

lets get some soap for that mouth

28. Mimi_x3

Please refrain from swearing, don't get angry man.

29. KatrinaKaif

Lol You have no control over my fingers, so no use in stating stop :P Please feel free to hit the report abuse button =) It will be a donation

30. Mimi_x3

Hm...dw about the problem, I'll type up the solution if you want.

31. LagrangeSon678

yeah, put her out her misery

32. Mimi_x3

33. KatrinaKaif

Didn't I say I ll figure it out on my own?

34. Mimi_x3

It'll take a while, it took me a while.

35. KatrinaKaif

Doesn't matter. I have a brain gifted to me for it.

36. Mimi_x3

Okay, do it as you wish, don't need to give me the solution straight away.

37. LagrangeSon678

yeah, let her use "her" brain to find the solution

38. KatrinaKaif

Lagrange, how many effing times Have I told you to stay away from me? Gosh damn.

39. Mimi_x3

lols, dont be mean :P

40. Mimi_x3

Kaffeine is pissed off

41. LagrangeSon678

woah, relax buddy

42. LagrangeSon678

take a chill pill

43. KatrinaKaif

Get a life dude, other than critizing me each time I solve a calc problem.

44. KatrinaKaif

You crossed the limits a while ago, and I told you to STAY AWAY

45. LagrangeSon678

nobody is criticizing you, i just find it weird that you can solve problems i give you, that are straight from calc 2, but you cant solve this one

46. Mimi_x3

You are making it sound so serious. Don't worry about it. I'll take up the solution.

47. KatrinaKaif

Lol Does a person have be good at calc 1 to get into calc bc? Your derivative questions are easy as hell.

48. Mimi_x3

Time to travel D km T = D / S = D / V (hours) Cost to travel D km C = T * ( a + v^2/a ) = D / v ( a + v^2 / a ) = D ( a/v + v/a) dC / dt = D( -a/v^2 + 1/a) = 0 -a/v^2 + 1/a = 0 1/a = a/v^2 v^2 = a^2 -> a km/h check for minimum: (using second derivative) d^2C/dt^2 = D(2a/v^3 + 0) = D * 2a/a^3 = 2D/a^2 > 0 yes, the cost at v=a is the lowest. Therefore v=a km/h for lowest cost.

49. KatrinaKaif

Damn. forgot to plug it into the equation

50. Mimi_x3

Yeah and you forgot about the distance.

51. KatrinaKaif

Pellet >.>

52. KatrinaKaif

I used the distance to get my 2 values in the first one..Forgot all about it

53. Mimi_x3

Yeah, when i did it I forgot about the other one as well xD

54. LagrangeSon678

it was a nice try

55. Mimi_x3

Want an easier one kaffeine ?

56. Hero

This is all hilarious @Mimi_x3 @LagrangeSon678 @KatrinaKaif