**Modeling With Functions 3B - Pre-Calculus** ### Area of a Kite A kite frame is to be made from six pieces of wood. The four pieces that form its border have been cut to the lengths indicated in the figure. Let \( x \) be as shown in the figure. #### (a) Show that the area of the kite is given by the function \[ A(x) = x \sqrt{25 - x^2} + \sqrt{144 - x^2} \] #### (b) How long should each of the two crosspieces be to maximize the area of the kite? --- **Diagram Explanation:** The diagram shows a kite with the following lengths: - Two sides are each labeled with a length of 5. - Two sides are each labeled with a length of 12. - The variable \( x \) is indicated to be part of the kite's geometry. The problem involves using these lengths to determine the area of the kite as a function of \( x \), and then finding the optimal lengths of the crosspieces to maximize this area.
**Modeling With Functions 3B - Pre-Calculus** ### Area of a Kite A kite frame is to be made from six pieces of wood. The four pieces that form its border have been cut to the lengths indicated in the figure. Let \( x \) be as shown in the figure. #### (a) Show that the area of the kite is given by the function \[ A(x) = x \sqrt{25 - x^2} + \sqrt{144 - x^2} \] #### (b) How long should each of the two crosspieces be to maximize the area of the kite? --- **Diagram Explanation:** The diagram shows a kite with the following lengths: - Two sides are each labeled with a length of 5. - Two sides are each labeled with a length of 12. - The variable \( x \) is indicated to be part of the kite's geometry. The problem involves using these lengths to determine the area of the kite as a function of \( x \), and then finding the optimal lengths of the crosspieces to maximize this area.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Modeling With Functions 3B - Pre-Calculus**
### Area of a Kite
A kite frame is to be made from six pieces of wood. The four pieces that form its border have been cut to the lengths indicated in the figure. Let \( x \) be as shown in the figure.
#### (a) Show that the area of the kite is given by the function
\[
A(x) = x \sqrt{25 - x^2} + \sqrt{144 - x^2}
\]
#### (b) How long should each of the two crosspieces be to maximize the area of the kite?
---
**Diagram Explanation:**
The diagram shows a kite with the following lengths:
- Two sides are each labeled with a length of 5.
- Two sides are each labeled with a length of 12.
- The variable \( x \) is indicated to be part of the kite's geometry.
The problem involves using these lengths to determine the area of the kite as a function of \( x \), and then finding the optimal lengths of the crosspieces to maximize this area.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fceb91cec-4f75-4c3e-8c99-1a314f3c1d0a%2F87e1aabf-1fce-48b2-86c6-cf3b2d2ce616%2Fn4ykzu.jpeg&w=3840&q=75)
Transcribed Image Text:**Modeling With Functions 3B - Pre-Calculus**
### Area of a Kite
A kite frame is to be made from six pieces of wood. The four pieces that form its border have been cut to the lengths indicated in the figure. Let \( x \) be as shown in the figure.
#### (a) Show that the area of the kite is given by the function
\[
A(x) = x \sqrt{25 - x^2} + \sqrt{144 - x^2}
\]
#### (b) How long should each of the two crosspieces be to maximize the area of the kite?
---
**Diagram Explanation:**
The diagram shows a kite with the following lengths:
- Two sides are each labeled with a length of 5.
- Two sides are each labeled with a length of 12.
- The variable \( x \) is indicated to be part of the kite's geometry.
The problem involves using these lengths to determine the area of the kite as a function of \( x \), and then finding the optimal lengths of the crosspieces to maximize this area.
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