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Beginning from a depth of 35 feet below the surface, a whale swims upward and jumps to a height of nearly 17 feet above the surface. Nodel with Math Use an inequality to model the possible change in the number of feet, \( r \), of the whale's elevation.

Ask by Long Edwards. in the United States
Jan 22,2025

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Answer

The possible change in the whale's elevation \( r \) is modeled by the inequality: \[ -35 \leq r \leq 17 \]

Solution

To model the possible change in the whale's elevation, let's define \( r \) as the whale's elevation relative to the surface of the water: - **Initial Position:** The whale starts **35 feet below** the surface, so its initial elevation is \( -35 \) feet. - **Final Position:** The whale can jump **up to nearly 17 feet above** the surface, so its maximum elevation is \( +17 \) feet. Using an inequality to represent the range of possible elevations \( r \): \[ -35 \leq r \leq 17 \] **Explanation:** - The inequality \( -35 \leq r \) ensures that the whale does not go below 35 feet below the surface. - The inequality \( r \leq 17 \) ensures that the whale does not exceed 17 feet above the surface. **Graphical Representation:** ``` Elevation (r) | * | | | | |---------------------|--------------------- -35 0 17 ``` The asterisk (*) represents the range of possible elevations the whale can achieve, from 35 feet below to 17 feet above the surface. **Final Inequality:** \[ -35 \leq r \leq 17 \]

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The Deep Dive

To model the whale's elevation change, we can express the starting depth as -35 feet (below the surface) and the maximum height as +17 feet (above the surface). The change in elevation can be modeled with the inequality: \(-35 + r \leq 17\) This means the whale's elevation \( r \) can range from the starting point up to the point it breaches the surface. Solving for \( r \), we find \( r \leq 52 \). Therefore, the whale can change its elevation by a maximum of 52 feet in this scenario. Now, considering the whale's journey, the total vertical distance from the bottom to the surface and then above can help contextualize this. The journey starts from a deep dive and involves powerful propulsion both upward to the surface and beyond. This is a classic case of just how remarkable and dynamic marine life can be!

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