### Suspension Bridge Cable Length EstimationThe function \[ f(s) = 400 + 0.0066667s^2 - 0.0000001s^4 \]approximates the length of the cable between the two vertical towers of a suspension bridge, where $ s $ is the sag in the cable. Estimate the length of the cable of the bridge in the next column if the sag is $ 28.3 $ feet. (Round your answer to the nearest foot.)$ \_\_\_\_\_\_ $ ft**Illustration Explanation:**The diagram below the function represents a suspension bridge:1. **Horizontal Span**: The distance between the two vertical towers is illustrated as $ 400 $ feet.2. **Sag**: The vertical distance from the lowest point of the sagging cable to the imaginary line connecting the tops of the towers is represented as $ s $.In this example, given $ s = 28.3 $ feet, you are asked to use the provided function to estimate the length of the cable, rounding the final answer to the nearest foot.### Steps to Calculate the Length1. Substitute $ s = 28.3 $ feet into the function $ f(s) $.2. Calculate each term of the function.3. Sum the results to get the total length of the cable.4. Round the result to the nearest foot and input the value in the provided blank section. This practical application demonstrates how mathematical modeling and functions can be used to solve real-world engineering problems such as estimating the length of cables in suspension bridges.

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The function f(s) = 400 + 0.0066667s2 - 0.0000001s4 approximates the length of the cable between the two vertical towers of a suspension bridge, where s is the sag in the cable. Estimate the length of the cable of the bridge in the next column if the is 28.3 feet. (Round your answer to the nearest foot.) 400 ft

The function f(s) = 400 + 0.0066667s2 - 0.0000001s4 approximates the length of the cable between the two vertical towers of a suspension bridge, where s is the sag in the cable. Estimate the length of the cable of the bridge in the next column if the is 28.3 feet. (Round your answer to the nearest foot.) 400 ft

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Suspension Bridge Cable Length Estimation

The function
\[ f(s) = 400 + 0.0066667s^2 - 0.0000001s^4 \]
approximates the length of the cable between the two vertical towers of a suspension bridge, where $ s $ is the sag in the cable. Estimate the length of the cable of the bridge in the next column if the sag is $ 28.3 $ feet. (Round your answer to the nearest foot.)

$ \_\_\_\_\_\_ $ ft

**Illustration Explanation:**

The diagram below the function represents a suspension bridge:

1. **Horizontal Span**: The distance between the two vertical towers is illustrated as $ 400 $ feet.
2. **Sag**: The vertical distance from the lowest point of the sagging cable to the imaginary line connecting the tops of the towers is represented as $ s $.

In this example, given $ s = 28.3 $ feet, you are asked to use the provided function to estimate the length of the cable, rounding the final answer to the nearest foot.

### Steps to Calculate the Length
1. Substitute $ s = 28.3 $ feet into the function $ f(s) $.
2. Calculate each term of the function.
3. Sum the results to get the total length of the cable.
4. Round the result to the nearest foot and input the value in the provided blank section.

This practical application demonstrates how mathematical modeling and functions can be used to solve real-world engineering problems such as estimating the length of cables in suspension bridges.

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