A graphing calculator is recommended.A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 90 ft is to be constructed(a) Find a function that models the area A of the window in terms of width xх |23.1490 2xхA(x)+22X(b) Find the dimensions of the rectangular portion of the window, such that the full window admits the greatest amount of light. (Round your answers to two decimal places.)widthftX ftheightEnter a number.

Question
Asked Oct 12, 2019
A graphing calculator is recommended.
A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 90 ft is to be constructed
(a) Find a function that models the area A of the window in terms of width x
х |2
3.14
90 2x
х
A(x)
+
2
2
X
(b) Find the dimensions of the rectangular portion of the window, such that the full window admits the greatest amount of light. (Round your answers to two decimal places.)
width
ft
X ft
height
Enter a number.
help_outline

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A graphing calculator is recommended. A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 90 ft is to be constructed (a) Find a function that models the area A of the window in terms of width x х |2 3.14 90 2x х A(x) + 2 2 X (b) Find the dimensions of the rectangular portion of the window, such that the full window admits the greatest amount of light. (Round your answers to two decimal places.) width ft X ft height Enter a number.

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check_circleExpert Solution
Step 1

Diameter of the semi circle = x

So radius=r= x/2

Upper circumeference =pi*r= pi(x/2)=(pi*x)/2

Step 2

Let height of the rectangle part = h

We find h in terms of x.

-+2h=90
X+
2
2h 90-x
2
(90-x--
TTX
h=
2
2
X
h=45
2
4
180-2x-Tx
h=
4
Ks
help_outline

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-+2h=90 X+ 2 2h 90-x 2 (90-x-- TTX h= 2 2 X h=45 2 4 180-2x-Tx h= 4 Ks

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Step 3

We add the area of the semi circle with the area of the rectan...

Area=
+hx
2
2
180-2x-TX
X
Area=
4
x2
-+45x-
2
Area=
4
2
Area 45x-
2
help_outline

Image Transcriptionclose

Area= +hx 2 2 180-2x-TX X Area= 4 x2 -+45x- 2 Area= 4 2 Area 45x- 2

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