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

- Mimi_x3

- Stacey Warren - Expert brainly.com

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- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- KatrinaKaif

Do you want the work to? O_o

- Mimi_x3

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

- 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 ) ??

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## More answers

- Mimi_x3

Sorry, its wrong.

- KatrinaKaif

K give me a moment.

- Mimi_x3

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

- KatrinaKaif

Omfg Mimi.

- Mimi_x3

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

- anonymous

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

- Mimi_x3

Isn't calc 1 ? college ? >_<

- anonymous

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

- Mimi_x3

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

- Mimi_x3

involves*

- KatrinaKaif

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

- Mimi_x3

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

- KatrinaKaif

Lol Give me the answer and I ll figure the solution

- anonymous

no way

- Mimi_x3

It's a show.

- Mimi_x3

No way ?

- KatrinaKaif

Lagrange, stay out of it, and go away.

- KatrinaKaif

Mimi, type.

- Mimi_x3

Archaic mathematician can help you.

- KatrinaKaif

I ll figure it out myself.

- anonymous

hard headed ^

- Mimi_x3

lols, and stubborn -_-

- KatrinaKaif

Shut up featheres.

- anonymous

lets get some soap for that mouth

- Mimi_x3

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

- 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

- Mimi_x3

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

- anonymous

yeah, put her out her misery

- Mimi_x3

lols, yeah i feel bad.

- KatrinaKaif

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

- Mimi_x3

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

- KatrinaKaif

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

- Mimi_x3

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

- anonymous

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

- KatrinaKaif

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

- Mimi_x3

lols, dont be mean :P

- Mimi_x3

Kaffeine is pissed off

- anonymous

woah, relax buddy

- anonymous

take a chill pill

- KatrinaKaif

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

- KatrinaKaif

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

- anonymous

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

- Mimi_x3

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

- KatrinaKaif

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

- 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.

- KatrinaKaif

Damn. forgot to plug it into the equation

- Mimi_x3

Yeah and you forgot about the distance.

- KatrinaKaif

Pellet >.>

- KatrinaKaif

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

- Mimi_x3

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

- anonymous

it was a nice try

- Mimi_x3

Want an easier one kaffeine ?

- Hero

This is all hilarious
@Mimi_x3
@LagrangeSon678
@KatrinaKaif

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