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anonymous
 5 years ago
The mechanics at Lincoln Automotive are reboring a 6in deep cylinder to fit a new piston. The machine they are using increases the cylinders radius onethousandth of an inch every 4min. How rapidly is the cylinder volume increasing when the bore (diameter) is 3.800in
anonymous
 5 years ago
The mechanics at Lincoln Automotive are reboring a 6in deep cylinder to fit a new piston. The machine they are using increases the cylinders radius onethousandth of an inch every 4min. How rapidly is the cylinder volume increasing when the bore (diameter) is 3.800in

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay, you can write it down like this in every 4 mins > radius increase = 1000in in every x mins? > radius increase R= D/2 =1.504 after finding the answer in mins, convert to seconds :) give it a try now :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait, I misread the question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0they want how much is the volume increasing right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0at what rate is the volume increasing, supposed to use derivitives (this is calculus)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then find the derivative of Volumeof Cylinder

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0all you have to do is find h from the original equation which is Vol = 1/3 pi r^2 h using r = 1.504

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[Vol = 1/3 \pi r^2h , Vol' = 2/3 \pi rr'h'\] I guess

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you have r' = 1000 r= 1.504 you'll have to find h'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0am I making any sense lol?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0jmcwhs2012, if you allow, may I say a few words

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it's given, it says that the radius is increasing 1000 in every 4 mins so r' = 1000in/min

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0iam please go ahead :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0"onethousandth of an inch"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, as far as I understand, the rate at which the radius is increasing is equal to the radius bored in a second

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you have the original radius, you can computer r' I guess it's 1000(1.504)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we can write dr/dt= (2.54/100000)/(60*4)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now all we need to find is dv/dt

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I dont understand where you got dr/dt?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we can use the result (dr/dt)x(dv/dr)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(dr/dt)x(dv/dr)=dv/dt

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0@jmcwhs2012 the thing is coming like this 2.54 cm is equal to one inch,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Why do we have to use cm?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I later convert it into m

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You see for that I divide it by 100000

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok let me explain the whole thing

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The machine is working at the rate of 1/1000 inch per 60*4 secs

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait @iam , he wants to find V'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thats what I am doing, if you all allow me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, sorry, proceed :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The machine is working at the rate of 1/1000 inch per 60*4 secs, is that thing clear?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Which means 2.54/100000 m per 240 secs

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So now we can find dr/dt from there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But we need to find dv/dt

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we can use the formula dv/dt=(dr/dt)x(dv/dr)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0honestly, no, why are you multiplying them?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Write that thing on a piece of paper, and try to cancel the commong terms, you will get why I am doing that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, got you! okay then what?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we have already found dr/dt which is 2.54/100000/240

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now we need to find dv/dr

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For that we will have to differenciate 6 x pi x r^2 with respect to r

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oops I am sorry, it would be 6*2.54*pi*r^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.06 is the length of the cylinder given on the problem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't get where you got 6?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So now just we will have to multiply both the things

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but isn't the vol = 1/3 pi r^2 h?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which will be 2 pi r^2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we just need to multiply both the things

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then differentiate with respect to r :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But unfortunately the person who gave this problem is not much interested

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No no no need to differenciate again

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, he'll come back later :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wouldn't you derive to V' then substitute r = 1.504 and r' in the equation and then u are done?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No not 1.504, we will have to substitute 1.900

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then by then you have found V' which is the volume rate

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, 1.900 and r' the one you have found which is dr/dt, then you're done

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually I am not getting you at all

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0{(2.54/100000)/240}*2.54*6*pi*2*1.900=dv/dt Thats it and thats all

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the given is: r = 1.900 r' = dr/dt = 2.54 so V' = 15.34(2) pi rr' = 30.68 pi (1.900)(2.54) = 465.15 m / secs So the volume is increasing = 465.15m/sec right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dr/dt = 2.54 this is not right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so then it's 2.54 /1000/240?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dr/dt ={(2.54/100000)/240} dv/dr= 2.54*6*pi*2*1.900

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so: V' = dv/dr = 2.54*12 pi *1.900 = 181.94 m/secs
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