functions

[travel]

So this is a story problem that I wanted to see if I did it correctlly.
A rancher has 20 miles of fencing to fence a rectangular piece of grazing land along a straight river. If no fence is required along the river and the sides perpendicular to the river are x miles long, find a formula for the area A of the rectangle in the terms of x. What is the domain of the function A that makes sense on this problem?

Well I know that the formula for Area is A=l*w
the w is x
A=l+2w since there is only one l that needs to be counted but two w's.
A-L=2w
(A-L)/2=x
20=l+2w
w=9.5 miles
This answer changes the shape though, so I think I made a mistake.

 

[mmm4444bot]

Well I know that the formula for Area is A=l*w

the w is x

You need to express the length in terms of x, too.

A=l+2w L + 2W is an expression for the perimeter of the fence line.

Are you using the symbol A to represent the area ?


A-L=2w
(A-L)/2=x
20=l+2w

Be careful with your symbols. L and l do not mean the same thing.

w = 9.5 miles Why are you trying to assign a length to the width?

Do you understand the exercise ?

Did you draw a picture and label it ?

This is what they ask for:

"a formula for the area A of the rectangle in the terms of x"



I mean, the answer looks like this:

Area = some polynomial containing the variable x

Once you find that, you need to state the domain of x.

You are not asked to find any values for the area, the length, or the width. Just the formula and the domain.

Area = x * (length goes here)

What is the length ? It's the amount left over after you use two x-mile sections of fence for the widths.

So, subtract two x from the total of 20, and that expression is the length.

Multiply that by x, and you have the polynomial that defines the area.

What values of x make sense ? Those values comprise the domain.

I welcome specific questions.

Cheers ~ Mark

 

[lookagain]

So this is a story problem that I wanted to see if I did it correctlly.
A rancher has 20 miles of fencing to fence a rectangular piece of grazing land along a straight river. If no fence is required along the river and the sides perpendicular to the river are x miles long, find a formula for the area A of the rectangle in the terms of x. What is the domain of the function A that makes sense on this problem?

Well I know that the formula for Area is A=l*w
the w is x
A=l+2w since there is only one l that needs to be counted but two w's. . . . .
No, P (perimeter) = l + 2w . . . "A" is for area.

A-L=2w . . . . . Then P - l = 2w . . . I don't see this fact (my correction) as helping.

(A-L)/2=x . . . . . (P - l)/2 = w, or (P - l)/2 = x. . . . I don't see this fact (my correction) as helping.

20=l+2w . . . or 20 = l + 2x . . . Solve for x, and substitute that in A = lw. \(\displaystyle **\) See below.
w=9.5 miles . . . . . You are not solving for A, but you are to be expressing A in terms of x.

Don't use lower case and upper case to represent the same variable (for example, the length).
Spread out your characters in each expression and/equation. Also, put in vertical spaces
between certain lines. Both of these points are for more readability.

\(\displaystyle **\) 20 = l + 2x ---> l = 20 - 2x, and w = x

Substitute these in A = lw:

\(\displaystyle A = (20 - 2x)(x) = 20x - 2x^2 = -2x^2 + 20x\)

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Domain of the function A that makes sense here:

The width and the length must each be positive, or greater than zero, in other words.

20 - 2x > 0 and x > 0 must be true together. Solve this system for your
"real world problem" domain.