**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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Here, the objective is to find the area function for Kite.
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