# Mathematics 1 Word Problem ... HELP!!!

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#### Haseebengineer

An irrigation engineer is designing a profile for a channel to pass through a farm that is in a shape of a square of side length 25 KM as shown in Fig 1. The proposed profile follows the following equation:

Y= Asin(X)+Bcos (X)+Cln (x)+Dx +E

1. By selecting ideal reference points from the graph determine the values of arbitrary constants A, B, C, D & E.
2. The turning points for the profile represents the locations where the pumps needs to be installed to distribute the water to the other parts of the farm. Determine the location of the pumping stations to the nearest 0.1 m.
3. Determine the length of the channel.
The channel has x-section in a form of a parabola. The maximum width of the channel at the existing ground level as shown in Figure.2 is 2 meters.
4. Determine the depth of the channel below the existing ground level if the minimum cross section area of the channel is 8 m^2 and hence determine the channel profile equation.
5. The excavated earth is used for the embankments alongside the channel. The cross section of the embankments as shown in Figure 2 is in a form of a symmetrical trapezium. The sides of the trapezium is tangential to the excavated channel at the ground level. Determine the height of the trapezium.
6. The maximum safe flow capacity of the channel is when the channel is full up to 0.8 of the full height of the channel. Determine the maximum safe area for the safe flow.
7. To reduce the scouring of the channel and the water seepage, it is suggested to use a lining material to the full height of the channel. If the lining material costs around \$50.00 per sq. meter, determine the cost of lining per meter length of the channel. 8. If the cost of excavation is \$10 per cubic meter, the cost of constructing the embankment is \$15.00 per cubic meter and the cost of lining is \$50.00, suggest an alternative profile for the channel x-section with less cost. The only constrains are the overall width of the channel should not be more than 9 meters and the minimum cross section for the water flow is 8 SQM.

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#### Debsta

MHF Helper
1. By selecting ideal reference points from the graph determine the values of arbitrary constants A, B, C, D & E.

Read some points off the graph eg (1, 4) and sub it into the equation. You'll need 5 points to get 5 equations so that you can solve for the 5 variables.

#### Haseebengineer

Can you solve it for me please ?

#### HallsofIvy

MHF Helper
Why are you not capable of even doing the arithmetic yourself? Do you know how to solve simultaneous linear equations? Do you understand that different people might choose different points and get different answers?

#### Haseebengineer

I didnt get your point that is why i asked, no worries if u dont have time for that. i will try... tell me one thing if u know ... u gave an example like 1,4. these are x and y right? so where to put these values... and how do i get all the constants... i am weak at maths so spare me.

#### Debsta

MHF Helper
Put x=1 and y=4 into the equation. You will end up with an equation involving A, B, C, D and E. Do this with 4 other points that you read off the graph. Then solve the equations simultaneously.

#### Haseebengineer

Thank you... Let me solve it.

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