Problem 90 - Algebra A Combined Function

Question

Solve. See Example 22. The lowest elevation in Australia is -52 feet at Lake Eyre. If you are standing at a point 439 feet above Lake Eyre, what is your elevation? (Source: National Geographic Society)

Step-by-Step Solution

Answer

Your elevation is 387 feet above sea level.

Step 1: Understand the Problem

We need to find the elevation above sea level for a point that is 439 feet above Lake Eyre, which itself is at an elevation of -52 feet.

Step 2: Set Up the Equation

Let the elevation of Lake Eyre be \(-52\text{ feet}\) and you are standing 439 feet above this point. To find the absolute elevation, we need to add the two elevations: \(-52\text{ feet} + 439\text{ feet}\).

Step 3: Perform the Addition

Calculate the sum of \(-52\text{ feet} + 439\text{ feet}\). This results in an elevation of \(387\text{ feet}\) above sea level.

Key Concepts

Negative Numbers in Elevation

When we talk about elevation, we're referring to how high or low something is in relation to sea level. In the world of geography, sea level is usually considered as zero elevation. All heights above this point are positive, while all depths below are negative.

A negative elevation means that the location is below sea level. For instance, Lake Eyre in Australia has an elevation of -52 feet, indicating that it is 52 feet below sea level. This concept helps us describe places in terms of how high or low they are compared to this standard baseline.

Addition Involving Negative Numbers

When you need to perform addition with both negative and positive numbers, it’s like moving on a number line. Moving right indicates a positive direction, and moving left indicates a negative direction.

In our exercise, we started at -52 feet and moved 439 feet upward (in the positive direction) to find an elevation. Essentially, we added \(-52 + 439\). You can think of this action as starting 52 feet below, and rising up 439 feet. This results in a final elevation of 387 feet.

• Identify whether numbers are positive or negative.
• Add the absolute values first.
• Apply the sign: keep the sign of the larger absolute value.

Interpreting Geographical Data

Geographical data is critical for understanding the physical characteristics of a location. Information such as elevation, coordinates, and terrain types helps us to gain insights into climate, potential hazards, and the best areas for building.

Whenever dealing with geographical data:

• Look for context: Know whether the data is collected relative to sea level.
• Check units: Elevations might be given in feet or meters. Be ready to convert if needed.
• Understand the significance: Places below sea level might be prone to flooding.

In the context of this exercise, interpreting that Lake Eyre is -52 feet helps us understand the region's nature and how it might affect the local environment and activities.