Math question: Achiever 2, 14

[267862]

---

Members don't see this ad.

Achiever 2, 14

A 120 m trapping net stretched out into a rectangular corral to front a flowing river. What should width be to provide largest capturing area?

Answer is 30.

Basically... wtf is a rectangular corral? I tried to google this but nothing good came up. The solution saus its a 3-sided rectangular corral (2 widths and 1 length) but I don't get how they figure that. Help?

 

[khangreen]

If I had to gauge by the answer and not the solution you posted, I'd say rectangular corral is merely saying the net's made into a rectangle. Best area for a rectangle is when it's a square and thus 120m/4sides = one side length giving you 30m as the optimal width

 

[dshope]

you are using 120m of trapping net to set up a trap. to do this, all we need is set up a trap with 2 width(w) and one length(l) since we need one of the side opened up to catch something.

equation will be 2W + L = 120 ==> L = 120- 2W

we are trying to get max area which is W *L = W*(120-2W) = 120W - 2W^2
= -2(W-30)^2 + 1800

so the max area will be 1800 when W = 30m

 

[267862]

you are using 120m of trapping net to set up a trap. to do this, all we need is set up a trap with 2 width(w) and one length(l) since we need one of the side opened up to catch something.

equation will be 2W + L = 120 ==> L = 120- 2W

we are trying to get max area which is W *L = W*(120-2W) = 120W - 2W^2
= -2(W-30)^2 + 1800

so the max area will be 1800 when W = 30m

ooooooo. ok i get it. wow thank you.

 

[mashinka]

hey sorry,
just read this and i still dont quite understand the solution. im probably just ******ed, but can you explain this conversion....

120W - 2W^2 = -2(W-30)^2 + 1800

 

[Streetwolf]

hey sorry,
just read this and i still dont quite understand the solution. im probably just ******ed, but can you explain this conversion....

120W - 2W^2 = -2(W-30)^2 + 1800

You want to get it into the general equation of a parabola.

The general equation is:

y = a(x - h)^2 + k

You basically want to complete the square. First factor out a -2:

-2(-60W + W^2)

Now take the linear term, divide by 2, and square it to complete the square (that's the method): this value becomes (-60/2)^2 = 900.

Now add and subtract this term in the parenthesis to keep the equation the same. (Remember that x + 30 - 30 is still just 'x' for example.)

So we have -2(W^2 - 60W + 900 - 900).

We want the +900 term in the parenthesis to have a perfect square. To take the -900 out, remember that you have to multiply by the -2 outside the parenthesis:

-2(W^2 - 60W + 900) + 1800

Finally the term in parenthesis becomes:

-2(W - 30)^2 + 1800