Where do I start? Finding maximums and solving for y.

[Alyssa_NetAdmin]

Not looking for the answers. However I am having difficulty solving for y. Where do I start?

1. You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?



Complete the following steps to solve the above problem:
a. Write the equation for the area of the rectangular region:
A =bh

b. Write the equation for the fencing required:

150 =10(15)

c. Solve the equation for fencing for [FONT=&quot][/FONT]y. This is where I am having trouble and I can't finish the rest of the question without finding the
answer.


d. Substitute the result of step c) into the area equation to obtain A as function of [FONT=&quot][/FONT]x.

e. Write the function in the form of [FONT=&quot][/FONT]f(x)=ax^2+bx+c..

f. Calculate [FONT=&quot][/FONT]-b/2 If a < 0, the function has a maximum at this value.

This means that the area inside the fencing is maximized when [FONT=&quot][/FONT]x = ?

g. Find the length of side [FONT=&quot][/FONT]y.

h. Find the maximum area.

 

[JeffM]

Not looking for the answers. However I am having difficulty solving for y. Where do I start?

1. You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?



Complete the following steps to solve the above problem:
a. Write the equation for the area of the rectangular region:
A =bh OK so far conceptually but ....

b. Write the equation for the fencing required:

150 =10(15) You go off the rails here.

c. Solve the equation for fencing for y. This is where I am having trouble and I can't finish the rest of the question without finding the
answer.


d. Substitute the result of step c) into the area equation to obtain A as function of x.

e. Write the function in the form of f(x)=ax^2+bx+c..

f. Calculate -b/2 If a < 0, the function has a maximum at this value.

This means that the area inside the fencing is maximized when x = ?

g. Find the length of side y.

h. Find the maximum area.

In any word problem, the best first step is to identify the relevant variables and to name each with a letter in WRITING. Usually you can pick what letters stand for what variables, but in this problem, the problem is implicitly specifying most of them (and not in the clearest way).

x = base of rectangle

y = height of rectangle.

You used b and h, which makes sense, but the problem is going in a different direction.

A = area of rectangle. The problem tells you to name the area capital A.

N = fencing needed.

a, b, and c are parameters that you are to find on the assumption that A = f(x) = ax^2 + bx + c, a quadratic in standard form. I hate it when people unnecessarily use the same letter in upper case and lower case to stand for different variables.

Usually this step is easy, but this problem has made it complicated.

The second step is, using the letters assigned in the first step to identify the relevant relationships, either based on specific information in the problem or on general information implicitly assumed by the problem.

You did this properly at first.

A = xy. This is information that the problem assumes you know.

Now how much fencing do you need. Well normally you would need fencing that equaled the perimeter of the area enclosed, right? But the problem says that you do not need fencing for one side.

So how much fencing do you need? (There are two possible ways to answer this, but that turns out to make no difference which one you choose.)

Answer this question and we can proceed.

 

[stapel]

1. You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing.

Draw the situation. Label the length L and the width w of the area. Note that only three sides (let's say, one "length" and two "widths") are fencing, because the other side (the other "length") is, I dunno, the side of a barn. What then is the length of the fencing in terms of the variables in the drawing? Construct an equation for this.

Solve the equation for one of the variables in terms of the other.

Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

Create the "area" equation in terms of the one variable, starting with "A = Lw". (Note that the area is quite unlikely to equal the length of the fencing, so assigning the fence-length value to the area that you are trying to find doesn't make much sense.) You should end up with a quadratic.

Find the vertex to locate the max/min values.

 

[Alyssa_NetAdmin]

In any word problem, the best first step is to identify the relevant variables and to name each with a letter in WRITING. Usually you can pick what letters stand for what variables, but in this problem, the problem is implicitly specifying most of them (and not in the clearest way).

x = base of rectangle

y = height of rectangle.

You used b and h, which makes sense, but the problem is going in a different direction.

A = area of rectangle. The problem tells you to name the area capital A.

N = fencing needed.

a, b, and c are parameters that you are to find on the assumption that A = f(x) = ax^2 + bx + c, a quadratic in standard form. I hate it when people unnecessarily use the same letter in upper case and lower case to stand for different variables. Am I supposed to plug in x,y,a, and n into the quadratic? If so, how do I tell where it goes?

Usually this step is easy, but this problem has made it complicated.

The second step is, using the letters assigned in the first step to identify the relevant relationships, either based on specific information in the problem or on general information implicitly assumed by the problem.

You did this properly at first.

A = xy. This is information that the problem assumes you know.

Now how much fencing do you need. Well normally you would need fencing that equaled the perimeter of the area enclosed, right? But the problem says that you do not need fencing for one side.

So how much fencing do you need? (There are two possible ways to answer this, but that turns out to make no difference which one you choose.) Will the amount of fencing required in fact be less than the fencing actually available? I keep thinking it needs to equal exactly 150 ft. of fencing.

Answer this question and we can proceed.

This problem is racking my brain Thanks for your help though

 

[Alyssa_NetAdmin]

Draw the situation. Label the length L and the width w of the area. Note that only three sides (let's say, one "length" and two "widths") are fencing, because the other side (the other "length") is, I dunno, the side of a barn. What then is the length of the fencing in terms of the variables in the drawing? Construct an equation for this.

Solve the equation for one of the variables in terms of the other.


Create the "area" equation in terms of the one variable, starting with "A = Lw". (Note that the area is quite unlikely to equal the length of the fencing, so assigning the fence-length value to the area that you are trying to find doesn't make much sense.) You should end up with a quadratic.

Find the vertex to locate the max/min values.

Thank you for help, I think I'm having trouble understanding how to convert the area equation into the quadratic.

 

[stapel]

Thank you for help, I think I'm having trouble understanding how to convert the area equation into the quadratic.

When you multiplied the "length" expression by the "width" expression, you did NOT get a quadratic? What did you get? Please be complete. Thank you!