# Math

posted by .

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window with maximum area if the total perimeter is 16 feet.

X = the width of the rectangle.

Y = the length of the rectangle.

X/2 = the radius of the circle.

First let's detemine one of the dimensions, length or width in terms of the other for this perimeter.
Perimeter P=x+2y+pi*x/2 so y=16-(x++pi*x/2)/2

The area Q of the semi-circle is Q=pi*(x/2)^2
The area R of the rectangle is R=x*y=x*(16-(x++pi*x/2)/2)
The total area is A=Q+R=pi*(x/2)^2 + x*(16-(x++pi*x/2)/2)
Find dA/dx and solve for x= 0, be sure to determine the max range for x and check the endpoints too.

Now, how would you find the max range?

I didn't fully understand the lesson I had on this and even though it's starting to make sense I'm still confused.

What are the max and min values for x. Most likely the answer is not at the endpoints for this problem, but when doing optimization problems they must be checked too. Frequently the optimum is at the endpoint for the domain.
I think the endpoints for the domain here are 0 and 16, so the optimum value should be somewhere in between them.
The hardest part of this problem should be trying to state it in one variable. After you have A(x), find A'(x) and solve when it's 0.

I notice I have the area of the semicircle wrong. It should be
Q=(1/2)*pi*(x/2)^2

So what would be the revised equation?

Here's the original post you gave.
"if the total perimeter is 16 feet.
X = the width of the rectangle.
Y = the length of the rectangle.
X/2 = the radius of the circle."

Perimeter P=x+2y+pi*x/2 so y=16-(x++pi*x/2)/2

I gave the wrong formula for Q, it should be half that amount.
The area Q of the semi-circle is Q=(1/2)*pi*(x/2)^2
The area R of the rectangle is R=x*y=x*(16-(x++pi*x/2)/2)
The total area is A=Q+R=(1/2)*pi*(x/2)^2 + x*(16-(x++pi*x/2)/2)

Be sure to draw a diagram and label the parts. Show what the area and perimeter of the rectangle and semicircle should be.
I 'think' I gave the correct formula for A(x) now. Simplify the right hand side, differentiate, set it to 0 and solve for x. Then go back to the perimeter formula and determine y.

Since a square encloses the maximum area for a given perimeter, let the sides of the square portion be x and then P = 3x + xPi/2 = 16.

Solve for x.

8=000o==D~~~ a

a few drops o this KUM might help ya, suckas!!

8=000o==D~~~)-: maybe a few drops o this KUM mite help ya, suckas

XXX roolz!

## Similar Questions

1. ### Math (:

My answer doesn't make sense. It's too big. A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman …
2. ### calculus - applied problems

Max area - A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet. - - - - - --------- ! ! ^ !<-x/2->! …
3. ### calculus - applied problems

Max area - A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet. - - - - - --------- ! ! ^ !<-x/2->! …
4. ### calculus

I really hate to dump a problem like this on the teachers here, but I really need to get an answer to this. Thank you and I'm sorry. A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. …
5. ### calculus

a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area it the total perimiter is 52 feet.
6. ### math collage algebra

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). The perimeter of the window is 12 feet.
7. ### AP Calculus

a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. find the dimensions of a norman window of maximum area if the total perimeter is 72 units. Base value is 21.
8. ### calculus

A Norman window is constructed by adjoining a semicircle to the top of a rectangular window . (The diameter of the semicircle is the same as the width of the rectangular) If the perimeter of the Norman window is 20 ft, find the dimensions …
9. ### Calc

A Norman window is constructed by adjoining a semicircle to the top of a rectangular window as shown in the figure below. If the perimeter of the Norman window is 24 ft, find the dimensions that will allow the window to admit the most …
10. ### calc

1.A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window find the dimensions of a Norman window of maximum area when the total permeter is 16ft. 2. A rectangle is bounded by the x axis …

More Similar Questions