MATHS NERD HELP! (pleeease. don't make me beg)

Found 23rd May 2011
A group of students are researching the rate at which ice thickens on a frozen pond. They have experimental evidence that when the air temperature is –T °C, the ice thickens at a rate T/14000x cm s^-1, where x cm is the thickness of the ice that has already formed.

On a particular winter day the air temperature is constant at –7 °C. At 12.00 noon the students note that the ice is 2 cm thick. Time t seconds later the thickness of the ice is x cm.

(a) Show that dx/dt = 1/2000x

(b) Solve the differential equation and hence find the time when the students predict the ice will be 3 cm thick.

Between me and my girlfriend we can't do it. And we're supposed to be clever.

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Stop trying to cheat in your maths exam :0)

Sloth/Mod

Between me and my girlfriend we can't do it. And we're supposed to be … Between me and my girlfriend we can't do it. And we're supposed to be clever.

You and your girlfriend have homework and you are actually doing it!!!! What's the matter with the youth of today?? This time should be sexy time X)

Disclaimer - If any babies are born as a result of this comment i am not liable.

Original Poster

Syzable

You and your girlfriend have homework and you are actually doing it!!!! … You and your girlfriend have homework and you are actually doing it!!!! What's the matter with the youth of today?? This time should be sexy time X)Disclaimer - If any babies are born as a result of this comment i am not liable.

Later! Maths now, 'work' later...

Disclaimer - If any babies are born as a result of my actions tonight i am not liable.

Not sure the in-laws would agree with that!!

Original Poster

sancho1983

Not sure the in-laws would agree with that!!

Shh you.

Original Poster

A group of students are researching the rate at which ice thickens on a frozen pond. They have experimental evidence that when the air temperature is –T °C, the ice thickens at a rate T/14000x cm s^-1, where x cm is the thickness of the ice that has already formed.

On a particular winter day the air temperature is constant at –7 °C. At 12.00 noon the students note that the ice is 2 cm thick. Time t seconds later the thickness of the ice is x cm.

(a) Show that dx/dt = 1/2000x

(b) Solve the differential equation and hence find the time when the students predict the ice will be 3 cm thick

a/ Yes

b/ Tea time ...

the last time i did anything remotely this hard was ... wait i've never done anything this hard ..

Original Poster

arcangel111

A group of students are researching the rate at which ice thickens on a … A group of students are researching the rate at which ice thickens on a frozen pond. They have experimental evidence that when the air temperature is –T °C, the ice thickens at a rate T/14000x cm s^-1, where x cm is the thickness of the ice that has already formed. On a particular winter day the air temperature is constant at –7 °C. At 12.00 noon the students note that the ice is 2 cm thick. Time t seconds later the thickness of the ice is x cm. (a) Show that dx/dt = 1/2000x (b) Solve the differential equation and hence find the time when the students predict the ice will be 3 cm thicka/ Yesb/ Tea time ... the last time i did anything remotely this hard was ... wait i've never done anything this hard ..

thanks.

A group of students are researching the rate at which ice thickens on a frozen pond. They have experimental evidence that when the air temperature is –T °C, the ice thickens at a rate T/14000x cm s^-1, where x cm is the thickness of the ice that has already formed.

On a particular winter day the air temperature is constant at –7 °C. At 12.00 noon the students note that the ice is 2 cm thick. Time t seconds later the thickness of the ice is x cm.

(a) Show that dx/dt = 1/2000x

(b) Solve the differential equation and hence find the time when the students predict the ice will be 3 cm thick

(a) It says it right there

(b) I pick the lightest student to stand on it, when she stops falling through it is 3 cm

Done

Original Poster

sancho1983

A group of students are researching the rate at which ice thickens on a … A group of students are researching the rate at which ice thickens on a frozen pond. They have experimental evidence that when the air temperature is –T °C, the ice thickens at a rate T/14000x cm s^-1, where x cm is the thickness of the ice that has already formed. On a particular winter day the air temperature is constant at –7 °C. At 12.00 noon the students note that the ice is 2 cm thick. Time t seconds later the thickness of the ice is x cm. (a) Show that dx/dt = 1/2000x (b) Solve the differential equation and hence find the time when the students predict the ice will be 3 cm thick(a) It says it right there(b) I pick the lightest student to stand on it, when she stops falling through it is 3 cmDone

I sincerely hope this isn't how the thread is going to go. I don't want to have a disappointed and upset girlfriend...

lol - you want sincere - check the Charlie Scene thread

Sloth/Mod

When i was a lad we got a Gold Star if we knew the 7 times table. Good luck. lol

Original Poster

F**k

tomwatts

I sincerely hope this isn't how the thread is going to go. I don't want … I sincerely hope this isn't how the thread is going to go. I don't want to have a disappointed and upset girlfriend...

That will come later when the sexy time starts X)

tomwatts

I sincerely hope this isn't how the thread is going to go. I don't want … I sincerely hope this isn't how the thread is going to go. I don't want to have a disappointed and upset girlfriend...

Thought you were doing that later?

tomwatts

F**k

Syzable

When i was a lad we got a Gold Star if we knew the 7 times table. Good … When i was a lad we got a Gold Star if we knew the 7 times table. Good luck. lol

this isn't going to end well ... i suggest you turn the pc off, solve it yourself then service your missus before she sees what you been writing

A) T is constant at 7

therefore dx/dt = 7/14000x = 1/2000x

b) you want dx to equal 1 cos 2 cm already exist.
therefore simply sub and solve for dt which gives 4000 seconds = 66.6 mins.

Therefore time is 13.06:67 (round to required accuracy)
Edited by: "amzmalhotra" 23rd May 2011

I'm enjoying the banter a bit much to help now....

Ok then a) Just substitute the temperature T(=7) in to the formula given as it relates to the rate of change of thickness.

b) 12:33 (Edit: Wrong! Dropped x when integrating)
Edited by: "james132" 23rd May 2011

Original Poster

tomwatts

F**k

Syzable

When i was a lad we got a Gold Star if we knew the 7 times table. Good … When i was a lad we got a Gold Star if we knew the 7 times table. Good luck. lol

She's currently playing Limbo and is unaware I'm on HUKD...

And shh sancho and micoo ):

Hubby says that part:
a) is putting the info into a mathematical form i.e. recognise that the ice thickens as a rate dx/dt is shorthand for that.
dx/dt= -T/1400x, subsitute for T = -7
b) answer is 5000seconds after. The proof is short but dificult to type on here!

a/ = 7
b/ = 13:23

Original Poster

Thank you all!!! Still having fun with it though as we keep getting different answers for the last bit, but we're going to settle on 13:23

I'm off for now (:D), thank you once again

chesso

Hubby says that part: a) is putting the info into a mathematical form … Hubby says that part: a) is putting the info into a mathematical form i.e. recognise that the ice thickens as a rate dx/dt is shorthand for that. dx/dt= -T/1400x, subsitute for T = -7 b) answer is 5000seconds after. The proof is short but dificult to type on here!

Screwed up my first time but this is what I get now too. Quick proof:

dx/dt = 1/2000x

2000xdx = dt

Integrating gives:

t = 1000x^2 + C

We know when t = 0 x = 2 therefore subbing in:

t = 1000*(2)^2 +C

C = - 4000

t = 1000x^2 - 4000

We want to know when x = 3 therefore

t = 1000*3^2 - 4000
= 5000 seconds (Approx 13:23)

tomwatts

Thank you all!!! Still having fun with it though as we keep getting … Thank you all!!! Still having fun with it though as we keep getting different answers for the last bit, but we're going to settle on 13:23 :)I'm off for now (:D), thank you once again

thats cos i is cleva

I'm not going to lie. I couldn't do it, only a year after doing my A-Level and still doing some maths at uni.

It's easy when you see the answer though... as always with maths.
Edited by: "emhaslam" 23rd May 2011