differential equations pure3 Watch

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enchan
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hi ya, im really stuck on these Q's. could sum 1 help me pleaseeee!!????

(iv got my exam 2moro)

1) Water leaks slowly out of a tank. The depth of the water after t hours is h metres, and these variables are related by a differential equation of the form dh/dt= -ae-0.1t . Initially the depth of water is 6metres, and after 2 hours it has fallen to 5 metres. At what depth will the level eventually settle down??

Find an expression for dh/dt in terms of h.

ANs;0.483m; -0.1h+0.0483

2) a) the number of people, x in a queue at a travel centre t minutes after it opens is modelled by the differential equation dx/dt=1.4t-4 for values of t up to 10. Interpret the term '-4' on the right side of the equation. Solve the differential equation, given that x=8 when t=0.

b) an alternative model gives the differential equation dx/dt=1.4t-0.5x for the same values of t. Verify that x= 13.6e-0.5t +2.8t-5.6 satisfies this differential equation. Verify also that when t=0 this function takes the value 8.



Any help will be greatly appreciated!!! pleaseee!!!
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Fermat
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see attachment.
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Evolin
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i can't access the attachment!

can anyone do the above?
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Fermat
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see attachment.
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yusufu
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(Original post by Fermat)
see attachment.
id just like to say that your handwriting is fantastic .
it looks just like id imagined a mathematicians handwriting to be!!
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Fermat
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(Original post by Tazzie)
i can't access the attachment!

can anyone do the above?
I've just been able to access both of them.

They're both pretty large. You may have to wait a moment to download them if you're on dial-up.
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(Original post by Undry1)
id just like to say that your handwriting is fantastic .
it looks just like id imagined a mathematicians handwriting to be!!


Edit: it gets like that from scribbling down endless lecture notes
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