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Core 1, integration, help!

I'm confused over the following question:
A road hump is 40 cm wide and 10 cm high at its peak. The cross section is modelled by a function of the form kx(w-x), where k and w are constants.

a) find the values of w and k

b) Use algebriac integration to estimate the volume of the hump, given that the road is 6m wide

Any help is much appreciated, thank you :smile:
Reply 1
Avatar for J@tko
J@tko
So basically the hump is y=kx(w-x), and you know the co-ordinates (0,0), (20,10) and (0,40) are on the hump.

(0,0) doesn't really help you very much, because you can tell that from just looking at the equation.

For (0,40), plug the values into the equation:
0=40k(w-40)
=40wk-1600k -> wk=40

Then for (20,10):
10=20k(w-20)
=20kw-400k

But we know wk is 40 so substitute that into the bottom equation to find k, then find w, then integrate the original equation :smile:
Reply 2
Avatar for Crazy_meerkat
Crazy_meerkat
OP
Original post by J@tko
So basically the hump is y=kx(w-x), and you know the co-ordinates (0,0), (20,10) and (0,40) are on the hump.

(0,0) doesn't really help you very much, because you can tell that from just looking at the equation.

For (0,40), plug the values into the equation:
0=40k(w-40)
=40wk-1600k -> wk=40

Then for (20,10):
10=20k(w-20)
=20kw-400k

But we know wk is 40 so substitute that into the bottom equation to find k, then find w, then integrate the original equation :smile:


Hey thanks for the reply, in the back of the textbook it says that w = 40 and k = 1/40 so wk = 1 :s, I'm still a little confused lol. Are they expecting you to see that w = 40 because it says the hump is 40cm wide? If so, I can see how you can get k with the method you shown :smile:
(edited 12 years ago)
Reply 3
Avatar for TenOfThem
TenOfThem
18
kx(w-x)= 0 gives you 2 answers

x = 0 (0,0)
x = w (w,0)

since you are told that these 2 points are (0,0) and (40,0) w = 40
(edited 12 years ago)
Reply 4
Avatar for Crazy_meerkat
Crazy_meerkat
OP
Original post by TenOfThem
kx(w-x)= 0 gives you 2 answers

x = 0 (0,0)
x = w (w,0)

since you are told that these 2 points are (0,0) and (40,0) w = 40


Oohh of course, it make a lot more sense now, thanks a lot :smile:
Reply 5
Avatar for TenOfThem
TenOfThem
18
you can then use the point (20,10) to find k

10 = 20k(40-20)

k = 1/40

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