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The base of a railing for a set of steps leading up to the front door of a house makes an angle of a degrees with he horizontal. Let d(x) be the horizontal distance between the two ends of the base of the railing. If the upper end of the railing is 4 feet higher than the lower end, find the positive number A such that d(x) = A cot x, and ise your function to find the length of the base of the railing if x = 35°. Round your answer to the nearest tenth of a foot. d (x) Base of railing ft

The base of a railing for a set of steps leading up to the front door of a house makes an angle of a degrees with he horizontal. Let d(x) be the horizontal distance between the two ends of the base of the railing. If the upper end of the railing is 4 feet higher than the lower end, find the positive number A such that d(x) = A cot x, and ise your function to find the length of the base of the railing if x = 35°. Round your answer to the nearest tenth of a foot. d (x) Base of railing ft

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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d(x) = ________

d(35 degrees) = _____ ft

The base of a railing for a set of steps leading up to the front door of a house makes an angle of \( x \) degrees with the horizontal. Let \( d(x) \) be the horizontal distance between the two ends of the base of the railing. If the upper end of the railing is 4 feet higher than the lower end, find the positive number \( A \) such that \( d(x) = A \cot x \), and use your function to find the length of the base of the railing if \( x = 35^\circ \). Round your answer to the nearest tenth of a foot. **Diagram Explanation:** The diagram shows a side view of a set of stairs with a railing. - The railing is diagonal, extending upwards from left to right. - The bottom of the railing forms an angle \( x \) with the horizontal ground. - The height of the rise from the bottom to the top of the railing is 4 feet. - The horizontal distance of the base of the railing is denoted as \( d(x) \). - The diagram represents a right triangle formed by the rise, the horizontal base (\( d(x) \)), and the railing as the hypotenuse.
Transcribed Image Text:The base of a railing for a set of steps leading up to the front door of a house makes an angle of \( x \) degrees with the horizontal. Let \( d(x) \) be the horizontal distance between the two ends of the base of the railing. If the upper end of the railing is 4 feet higher than the lower end, find the positive number \( A \) such that \( d(x) = A \cot x \), and use your function to find the length of the base of the railing if \( x = 35^\circ \). Round your answer to the nearest tenth of a foot. **Diagram Explanation:** The diagram shows a side view of a set of stairs with a railing. - The railing is diagonal, extending upwards from left to right. - The bottom of the railing forms an angle \( x \) with the horizontal ground. - The height of the rise from the bottom to the top of the railing is 4 feet. - The horizontal distance of the base of the railing is denoted as \( d(x) \). - The diagram represents a right triangle formed by the rise, the horizontal base (\( d(x) \)), and the railing as the hypotenuse.
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