Question

HELP PLEASE!!!!
A rancher has 3300 feet of fence to enclose a rectangular region that lies along a straight river. If no fence is used along the river (see the figure), find the dimensions needed to enclose 20 acres of land. Recall that 1 acre = 43,560 ft2. (Enter your answers as a comma-separated list.)

Answer 1

Area is length times width. In this case, if we use all 3300 feet of fence, the width (distance from the river to the fence opposite can be x, and the fence opposite the river will be 3300-2x (the total amount of fence, less the amount on the other two sides) so the area as a function of x to meet the specification of the problem will be\[A(x)=x(3300-2x)=(43560)20\]It looks to me that you could turn it into a quadratic equation (ax^2+bx+c=0) and solve it....

Answer 2

Not sure, but I think there might be two possible solutions....

Answer 3

idk why webassign doesn't accept it((

Answer 4

The above isn't the answer. It is the setup. Your answer will be an ordered pair. You have to solve the quadratic equation. Look above, at my previous post. If you rearrange it, you will get\[-2x^2+3300x-871200=0\]You have to solve that to get the answer(s), then convert it into ordered pair(s) of length and width (x, 3300-2x).

Answer 5

You will probably get two solutions for x.

Answer 6

I solved a quadratic equation and got 330,1320

Answer 7

But it says: Enter your answers as a comma-separated list, not ordered pair

Answer 8

That multiplies out to give you only one acre. 330*1320=435600. You want the area to be 20 acres, which is 43560*20=8712000. It looks like I dropped a zero in my notation above The equation should read\[−2x^2+3300x−8712000=0\]

Answer 9

Isn't that just about the same thing? (x,y) Maybe the parentheses will confuse the computer, but you aren't close to the right answer yet.

Answer 10

\[−2x^2+3300x−8712000=0\implies x^2-1650x=-435600\implies \]\[x^2-1650x+825^2=825^2-435600\implies (x-825)^2=245025\implies\]\[x-825=\pm 495 \implies x=825 \pm 495 \implies x=330~or~x=1320\]That is the width of the enclosure, 330 or 1320. The length is 3300-2x to give ordered pairs (330,2640) or (1320,660)

Answer 11

Your two solutions were correct, but you interpreted them incorrectly. They were not length and width, they were the two correct choices for width, that goes with corresponding numbers for the length.

Answer 12

Get it now?

Answer 13

Oh, thanks so much)))