The top and bottom margins of a poster are 1 inches and the side margins are each 2 inches. The area of printed material on the poster is fixed at 9 square inches. See the image below 1 in Printed Material 2 in 9 square inches 2 in 1 in (You can click on the graphic to enlarge the image.) Let w be the width (in inches) of the poster and let h be the height (in inches) of the poster. Find the dimensions of the poster with the smallest area. (a) Write the formula for the area A(w) of the entire poster as a function of w only: A(w) = Z square in., for w E (4, 0). (b) What are the dimensions of the poster with the smallest area? w = Σ in. h = Σ in.
The top and bottom margins of a poster are 1 inches and the side margins are each 2 inches. The area of printed material on the poster is fixed at 9 square inches. See the image below 1 in Printed Material 2 in 9 square inches 2 in 1 in (You can click on the graphic to enlarge the image.) Let w be the width (in inches) of the poster and let h be the height (in inches) of the poster. Find the dimensions of the poster with the smallest area. (a) Write the formula for the area A(w) of the entire poster as a function of w only: A(w) = Z square in., for w E (4, 0). (b) What are the dimensions of the poster with the smallest area? w = Σ in. h = Σ in.
Chapter9: Math Models And Geometry
Section9.3: Use Properties Of Angles, Triangles, And The Pythagorean Theorem
Problem 108E: On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides the shown in the...
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**Understanding Poster Dimensions**
The top and bottom margins of a poster are 1 inch each, and the side margins are each 2 inches. The area of the printed material on the poster is fixed at 9 square inches. Refer to the diagram below.
[Image Description: A diagram of a poster is shown. The poster has a rectangular section labeled "Printed Material," which is highlighted in light blue and has an area of 9 square inches. The margins are labeled: 1 inch at the top and bottom, and 2 inches on the left and right sides. These dimensions are illustrated with dashed lines.]
(Note: You can click on the graphic to enlarge the image.)
**Problem Statement:**
Let \( w \) be the width (in inches) of the poster, and let \( h \) be the height (in inches) of the poster. Find the dimensions of the poster with the smallest area.
(a) Write the formula for the area \( A(w) \) of the **entire poster** as a function of \( w \) only:
\[
A(w) = \boxed{\phantom{\Sigma}} \text{ square in., for } w \in (4, \infty).
\]
(b) What are the dimensions of the poster with the smallest area?
\[
w = \boxed{\phantom{\Sigma}} \text{ in.}
\]
\[
h = \boxed{\phantom{\Sigma}} \text{ in.}
\]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4dc6df0f-8271-4cd6-974e-5ae567e8755e%2Fbea97cd2-ebd9-4765-ba11-4a7a1599d3f7%2F3z59fu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Understanding Poster Dimensions**
The top and bottom margins of a poster are 1 inch each, and the side margins are each 2 inches. The area of the printed material on the poster is fixed at 9 square inches. Refer to the diagram below.
[Image Description: A diagram of a poster is shown. The poster has a rectangular section labeled "Printed Material," which is highlighted in light blue and has an area of 9 square inches. The margins are labeled: 1 inch at the top and bottom, and 2 inches on the left and right sides. These dimensions are illustrated with dashed lines.]
(Note: You can click on the graphic to enlarge the image.)
**Problem Statement:**
Let \( w \) be the width (in inches) of the poster, and let \( h \) be the height (in inches) of the poster. Find the dimensions of the poster with the smallest area.
(a) Write the formula for the area \( A(w) \) of the **entire poster** as a function of \( w \) only:
\[
A(w) = \boxed{\phantom{\Sigma}} \text{ square in., for } w \in (4, \infty).
\]
(b) What are the dimensions of the poster with the smallest area?
\[
w = \boxed{\phantom{\Sigma}} \text{ in.}
\]
\[
h = \boxed{\phantom{\Sigma}} \text{ in.}
\]
---
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