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A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) 9 cos 0 + 3 sin 0 L(0) o [use function notation - use cos(theta) instead of costheta]. sin 0 cos 0 b) Now, find the derivative, L'(0). -2 cos (20)(3 sin(0) + 9 cos 0) + sin(20) (3 cos(0) – 9 sin(0))) 2 cos (0) sin (0) L'(0) = [use function notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) - feet

A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) 9 cos 0 + 3 sin 0 L(0) o [use function notation - use cos(theta) instead of costheta]. sin 0 cos 0 b) Now, find the derivative, L'(0). -2 cos (20)(3 sin(0) + 9 cos 0) + sin(20) (3 cos(0) – 9 sin(0))) 2 cos (0) sin (0) L'(0) = [use function notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) - feet

Calculus: Early Transcendentals
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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A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) L(0) = 9 cos 0 + 3 sin 0 sin 0 cos 0 o [use function notation - use cos(theta) instead of costheta]. b) Now, find the derivative, L'(0). -2 cos (20) (3 sin(0) + 9 cos 0) + sin(20) (3 cos (0) – 9 sin(0))) L'(0) [use function 2 2 cos“ (0) sin (0) notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) feet
Transcribed Image Text:A fence 9 feet tall runs parallel to a tall building at a distance of 3 ft from the building as shown in the diagram. Find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. LADDER 9 ft 3 ft a) First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) L(0) = 9 cos 0 + 3 sin 0 sin 0 cos 0 o [use function notation - use cos(theta) instead of costheta]. b) Now, find the derivative, L'(0). -2 cos (20) (3 sin(0) + 9 cos 0) + sin(20) (3 cos (0) – 9 sin(0))) L'(0) [use function 2 2 cos“ (0) sin (0) notation - use cos(theta) instead of costheta]. c) Lastly, find the length of the shortest ladder. In other words, minimize the length of the ladder. (Round the answer to 3 decimal places.) L(0min ) feet
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