Math

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, as!!

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

XXX roolz!

1. 👍
2. 👎
3. 👁

Similar Questions

1. calculus

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30ft, find the dimensions of the window so that the greatest possible amount of light is admitted. I keep screwing up in

2. Calculus

A rectangular tank with a square base, an open top, and a volume of 864 ft^3 is to be constructed of the sheet steel. Find the dimensions of the tank that minimize the surface area

3. Geometry

Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 80 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of

4. math

A stained glass window is shaped like a semicircle. The bottom edge of the window is 36 inches long. What is the area of the stained glass window? Round your answer to the nearest hundredth. (2 pt) Draw and label the window:

1. Math

A figure is composed of a semicircle and a right triangle. Determine the area of the shaded region. Use 3.14 for π and round to the nearest tenth. Show all of your work. (semicircle then the right triangle with 5 ft on the top

2. 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

3. Calculus

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 window with a perimeter of 31 feet? A =

4. Calc

A rectangular tank with a square​ base, an open​ top, and a volume of 32 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.

1. math

A rectangular box with a volume of 320 cubic units is to be constructed with a square base and top. The cost per square foot of the bottom is 15 cents, for the top 10 cents, and for the sides is 2.5 cents. Find the dimensions that

2. algebra

A “sunburst” window above a doorway is constructed in the shape of the top half of an ellipse, as shown in the figure. The window is 20 in. tall at its highest point and 80 in. wide at the bottom. Find the height of the window

3. Calc

A rectangular box with a volume of 64 ftcubed is to be constructed with a square base and top. The cost per square foot for the bottom is 15cents​, for the top is 10cents​, and for the sides is 2.5cents. What dimensions will

4. Calculus

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 window with a perimeter of 40 feet?