Mimi_x3
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
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KatrinaKaif
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Do you want the work to? O_o
Mimi_x3
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nope, wait its a show question. Just show the working if you're bothered.
KatrinaKaif
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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 ) ??
Mimi_x3
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Sorry, its wrong.
KatrinaKaif
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K give me a moment.
Mimi_x3
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You can ask for help if you want, i don't mind.
KatrinaKaif
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Omfg Mimi.
Mimi_x3
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6
lols, what's wrong ?
Archaic Mathematician can help :P
LagrangeSon678
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This is basic calc (calc 1), i wanna see her do this.
Mimi_x3
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Isn't calc 1 ? college ? >_<
LagrangeSon678
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she can do it, i am sure. She solved harder ones before
Mimi_x3
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ok, i'll give a little hint, it involved d s t
Mimi_x3
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involves*
KatrinaKaif
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c(a) = 2v?? don't tell me I am wrong again. -_-
Mimi_x3
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lols, yeah sorry.
Want me to type up the solution ?
KatrinaKaif
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Lol Give me the answer and I ll figure the solution
LagrangeSon678
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no way
Mimi_x3
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It's a show.
Mimi_x3
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No way ?
KatrinaKaif
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Lagrange, stay out of it, and go away.
KatrinaKaif
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Mimi, type.
Mimi_x3
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Archaic mathematician can help you.
KatrinaKaif
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I ll figure it out myself.
LagrangeSon678
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hard headed ^
Mimi_x3
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lols, and stubborn -_-
KatrinaKaif
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Shut up featheres.
LagrangeSon678
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lets get some soap for that mouth
Mimi_x3
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Please refrain from swearing, don't get angry man.
KatrinaKaif
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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
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Hm...dw about the problem, I'll type up the solution if you want.
LagrangeSon678
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yeah, put her out her misery
Mimi_x3
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lols, yeah i feel bad.
KatrinaKaif
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Didn't I say I ll figure it out on my own?
Mimi_x3
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It'll take a while, it took me a while.
KatrinaKaif
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Doesn't matter. I have a brain gifted to me for it.
Mimi_x3
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Okay, do it as you wish, don't need to give me the solution straight away.
LagrangeSon678
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yeah, let her use "her" brain to find the solution
KatrinaKaif
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Lagrange, how many effing times Have I told you to stay away from me? Gosh damn.
Mimi_x3
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lols, dont be mean :P
Mimi_x3
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Kaffeine is pissed off
LagrangeSon678
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1
woah, relax buddy
LagrangeSon678
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take a chill pill
KatrinaKaif
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Get a life dude, other than critizing me each time I solve a calc problem.
KatrinaKaif
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You crossed the limits a while ago, and I told you to STAY AWAY
LagrangeSon678
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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
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You are making it sound so serious. Don't worry about it. I'll take up the solution.
KatrinaKaif
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Lol Does a person have be good at calc 1 to get into calc bc? Your derivative questions are easy as hell.
Mimi_x3
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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
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Damn. forgot to plug it into the equation
Mimi_x3
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Yeah and you forgot about the distance.
KatrinaKaif
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Pellet >.>
KatrinaKaif
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I used the distance to get my 2 values in the first one..Forgot all about it
Mimi_x3
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Yeah, when i did it I forgot about the other one as well xD
LagrangeSon678
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it was a nice try
Mimi_x3
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Want an easier one kaffeine ?
Hero
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This is all hilarious
@Mimi_x3
@LagrangeSon678
@KatrinaKaif