Explanation Given: Number of woods for the frame of the kites is 6. Formula used: Pythagorean Theorem: If c denotes the length of the hypotenuse and a and b denote the length of the other two sides of a right angle triangle, then the Pythagorean theorem can be expressed as the Pythagorean equation: a 2 + b 2 = c 2 Calculation Consider the figure In Figure 1, In triangle A B C , A C D By Pythagoras theorem, B C = a 2 − x 2 = C D In triangle B C E , C D E By Pythagoras theorem, C E = a 2 − x 2 x 2 + b 2 − a 2 Area of triangle A B C = 1 2 (base)(height) The area is A = Area of triangle A B C + area of triangle A C D + area of triangle B C E + area of triangle C D E A = 1 2 ( 2 a 2 − x 2 ) x + 1 2 ( 2 a 2 − x 2 ) x 2 + b 2 − a 2 = a 2 − x 2 ( x + x 2 + b 2 − a 2 ) Differentiate with respect to x , d A d x = a 2 − x 2 ( 1 + x x 2 + b 2 − a 2 ) + ( x + x 2 + b 2 − a 2 ) ( − x a 2 − x 2 ) For critical points, d A d x = 0 a 2 − x 2 ( 1 + x x 2 + b 2 − a 2 ) + ( x + x 2 + b 2 − a 2 ) ( − x a 2 − x 2 ) = 0 ( x + x 2 + b 2 − a 2 ) ( x a 2 − x 2 ) = a 2 − x 2 ( x 2 + b 2 − a 2 + x x 2 + b 2 − a 2 ) x a 2 − x 2 = a 2 − x 2 x 2 + b 2 − a 2 Simplify that, x ( x 2 + b 2 − a 2 ) = a 2 − x 2 x 2 ( x 2 + b 2 − a 2 ) = a 4 + x 4 − 2 a 2 x 2 x 4 + b 2 x 2 − a 2 x 2 = a 4 + x 4 − 2 a 2 x 2 b 2 x 2 + a 2 x 2 − a 4 = 0 Then¸ x 2 ( a 2 + b 2 ) = a 4 x = a 2 a 2 + b 2 Differentiate d A d x with respect to x d 2 A d x 2 = { − x a 2 − x 2 + x 2 + b 2 − a 2 ( a 2 − x 2 + − x 2 a 2 − x 2 ) − x a 2 − x 2 x x 2 + b 2 − a 2 x 2 + b 2 − a 2 + ( 1 + x x 2 + b 2 − a 2 ) ( − x a 2 − x 2 ) + ( x + x 2 + b 2 − a 2 ) ( − a 2 − x 2 + x ( − x a

Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

2nd Edition

ISBN: 9781285101552

Author: James Stewart

Publisher: Cenage

See similar textbooks

Videos

Question

Chapter 4.5, Problem 50E

To determine

To find: The length of the diagonal pieces.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 49E

Chapter 4.5, Problem 32E

Students have asked these similar questions

See image

i don't understand how to get these answers please help!

Chapter 4 Solutions

Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

Ch. 4.1 - Explain the difference between an absolute minimum...Ch. 4.1 - Suppose f is a continuous function defined on a...Ch. 4.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 4.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The length of the diagonal pieces.

Solution Summary: The author explains how the Pythagorean theorem can be expressed by the following formula: c denotes the length of the hypotenuse and a and

Videos

To find: The length of the diagonal pieces.

Want to see the full answer?

Chapter 4 Solutions