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A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as shown in the diagram. LADDER 24 ft 6 ft. e We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) Type theta for 0. L(0) = [B] Now, find the derivative, L'(0). Type theta for 0. L'(0) = DELL Sign out

A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as shown in the diagram. LADDER 24 ft 6 ft. e We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) Type theta for 0. L(0) = [B] Now, find the derivative, L'(0). Type theta for 0. L'(0) = DELL Sign out

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter87: An Introduction To G- And M-codes For Cnc Programming
Section: Chapter Questions
Problem 23A: Write a G-code program for the counterclockwise arc with starting point (-40, -20), ending point...
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### Problem Statement **A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as shown in the diagram below:** ![Diagram](image-link) In this diagram: - The ladder leans against both the fence and the tall building. - The fence’s height (vertical distance to the ground) is 24 feet. - The horizontal distance between the fence and the building is 6 feet. - \(\theta\) represents the angle between the ground and the ladder (marked in the diagram). We aim to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. #### Tasks: **(A) First, find a formula for the length of the ladder in terms of \(\theta\). (Hint: split the ladder into 2 parts.)** \[ L(\theta) = \_\_\_\_\_\_\_ \] **(B) Now, find the derivative, \( L'(\theta) \).** \[ L'(\theta) = \_\_\_\_\_\_\_ \] ### Diagram Explanation **Diagram provided includes the following components:** 1. **Ladder:** The ladder is shown in green, leaning from the ground over the fence to the building. 2. **Fence:** The fence is depicted in blue, with a height of 24 feet. 3. **Building:** The building is shown in red with no specific height mentioned but is labeled to illustrate its position. 4. **Dimensions:** - The height of the fence is 24 feet. - The horizontal distance between the fence and the building is 6 feet. - The angle \(\theta\) is the angle formed between the ground and the ladder. To find the appropriate functions and derivatives, apply relevant trigonometric relationships and geometric properties, focusing on calculating the lengths related to the ladder’s configuration against the fence and building. Feel free to type the formulas and derivatives into the text boxes provided above the problem statement.
Transcribed Image Text:### Problem Statement **A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as shown in the diagram below:** ![Diagram](image-link) In this diagram: - The ladder leans against both the fence and the tall building. - The fence’s height (vertical distance to the ground) is 24 feet. - The horizontal distance between the fence and the building is 6 feet. - \(\theta\) represents the angle between the ground and the ladder (marked in the diagram). We aim to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. #### Tasks: **(A) First, find a formula for the length of the ladder in terms of \(\theta\). (Hint: split the ladder into 2 parts.)** \[ L(\theta) = \_\_\_\_\_\_\_ \] **(B) Now, find the derivative, \( L'(\theta) \).** \[ L'(\theta) = \_\_\_\_\_\_\_ \] ### Diagram Explanation **Diagram provided includes the following components:** 1. **Ladder:** The ladder is shown in green, leaning from the ground over the fence to the building. 2. **Fence:** The fence is depicted in blue, with a height of 24 feet. 3. **Building:** The building is shown in red with no specific height mentioned but is labeled to illustrate its position. 4. **Dimensions:** - The height of the fence is 24 feet. - The horizontal distance between the fence and the building is 6 feet. - The angle \(\theta\) is the angle formed between the ground and the ladder. To find the appropriate functions and derivatives, apply relevant trigonometric relationships and geometric properties, focusing on calculating the lengths related to the ladder’s configuration against the fence and building. Feel free to type the formulas and derivatives into the text boxes provided above the problem statement.
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