Question

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

Answer 1

Do you want the work to? O_o

Answer 2

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

Answer 3

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 ) ??

Answer 4

Sorry, its wrong.

Answer 5

K give me a moment.

Answer 6

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

Answer 7

Omfg Mimi.

Answer 8

lols, what's wrong ?

Archaic Mathematician can help :P

Answer 9

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

Answer 10

Isn't calc 1 ? college ? >_<

Answer 11

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

Answer 12

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

Answer 13

involves*

Answer 14

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

Answer 15

lols, yeah sorry.

Want me to type up the solution ?

Answer 16

Lol Give me the answer and I ll figure the solution

Answer 17

no way

Answer 18

It's a show.

Answer 19

No way ?

Answer 20

Lagrange, stay out of it, and go away.

Answer 21

Mimi, type.

Answer 22

Archaic mathematician can help you.

Answer 23

I ll figure it out myself.

Answer 24

hard headed ^

Answer 25

lols, and stubborn -_-

Answer 26

Shut up featheres.

Answer 27

lets get some soap for that mouth

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

yeah, put her out her misery

Answer 32

lols, yeah i feel bad.

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

lols, dont be mean :P

Answer 40

Kaffeine is pissed off

Answer 41

woah, relax buddy

Answer 42

take a chill pill

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

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

Answer 48

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.

Answer 49

Damn. forgot to plug it into the equation

Answer 50

Yeah and you forgot about the distance.

Answer 51

Pellet >.>

Answer 52

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

Answer 53

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

Answer 54

it was a nice try

Answer 55

Want an easier one kaffeine ?

Answer 56

This is all hilarious
@Mimi_x3
@LagrangeSon678
@KatrinaKaif