Question

A fluid flows along a straight shallow channel with parallel sides. At point x cm from one side of the channel, the speed v cm s ^-1 of the fluid is given by; v=3.4+0.051x-0.0003x^2.
i) Find by differentiation the maximum speed of the fluid as x varies, giving your answer correct to 2 s.f
ii) Assuming that the speed of the fluid is greatest at the point half-across the channel find the width of the channel.

Answer 1

http://mathforum.org/t2t/message.taco?thread=3879&message=2 <--- this might help :D

Answer 2

What should i don next as i click on the link and thank you :')

Answer 3

np! xD

Answer 4

and wdym "what should i don next as i click the link?"

Answer 5

Could anyone help me to solve ii)

Answer 6

ohhhhhhh

Answer 7

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations/cc-8th-linear-equations/v/solving-equations-2

Answer 8

^ that i hope helps. I looked up solve ii) and that came up

Answer 9

thank you again but thats not related to my question, the link you gave is intended for eighth grade.

Answer 10

\[v=3.4+0.051x-0.0003x^2.\]
\[v'=0.051-.0006x\] set it equal to zero and solve

Answer 11

not that you need calculus to find the max of a quadratic
you can find the max or min of any quadratic at the vertex
use \(x=-\frac{b}{2a}\)

Answer 12

i found the differentiation of v which is 85

Answer 13

and subsititute into the equation of v=3.4+0.051x-0.0003x^2

Answer 14

i cant figure out the 2nd part of the question

Answer 15

You just found that the maximum speed occurs at x = 85 cm.
They tell you "the speed of the fluid is greatest at the point half-across the channel"
So 85 cm is half-across the channel. So the channel must be twice 85 cm.

Answer 16

oh your right so 85 is supposed to be for one side out of the two parallel sides

Answer 17

Yes, 85 cm is the midpoint of the two parallel sides. So double that will be the width of the channel.

Answer 18

thank you :D

Answer 19

you are welcome.