Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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![**Problem: Ladder Sliding Down a Wall**
Consider a ladder sliding down a wall as shown in the figure.
The variable \( a \) is the length of the ladder. The variable \( h \) is the height of the ladder’s top at time \( t \), and \( x \) is the distance from the wall to the ladder’s bottom.
Suppose that the length of the ladder is 5.5 meters and the top is sliding down the wall at a rate of 0.7 m/s.
Calculate \( \frac{dx}{dt} \) when \( h = 2.4 \).
(Use decimal notation. Give your answer to three decimal places.)
\[ \frac{dx}{dt} \bigg|_{h=2.4} \approx \_\_\_\_\_\_\_\_ \, \text{m/s} \]
---
**Explanation of the Diagram:**
The diagram illustrates a right triangle formed by the ladder (labeled \(a\)), the wall (height labeled \( h \)), and the ground (distance from the wall labeled \( x \)). The ladder is represented as the hypotenuse of the right triangle, while \( h \) and \( x \) are the legs of the triangle.
The hypotenuse, \( a \), has a fixed length of 5.5 meters, while \( h \) and \( x \) change over time as the ladder slides down the wall.](https://content.bartleby.com/qna-images/question/8f96e7e7-1e0c-47dd-ab8a-07b078e3d874/d5b1fb2c-3044-4585-bd3c-7383b389a40b/vvzn2z.png)
Transcribed Image Text:**Problem: Ladder Sliding Down a Wall**
Consider a ladder sliding down a wall as shown in the figure.
The variable \( a \) is the length of the ladder. The variable \( h \) is the height of the ladder’s top at time \( t \), and \( x \) is the distance from the wall to the ladder’s bottom.
Suppose that the length of the ladder is 5.5 meters and the top is sliding down the wall at a rate of 0.7 m/s.
Calculate \( \frac{dx}{dt} \) when \( h = 2.4 \).
(Use decimal notation. Give your answer to three decimal places.)
\[ \frac{dx}{dt} \bigg|_{h=2.4} \approx \_\_\_\_\_\_\_\_ \, \text{m/s} \]
---
**Explanation of the Diagram:**
The diagram illustrates a right triangle formed by the ladder (labeled \(a\)), the wall (height labeled \( h \)), and the ground (distance from the wall labeled \( x \)). The ladder is represented as the hypotenuse of the right triangle, while \( h \) and \( x \) are the legs of the triangle.
The hypotenuse, \( a \), has a fixed length of 5.5 meters, while \( h \) and \( x \) change over time as the ladder slides down the wall.
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