Problem 60 - Beginning and Intermediate Algebra

Question

Solve. See Example 8 The lowest point in Africa is \(-512\) feet at Lake Assal in Djibouti. If you are standing at a point 658 feet above Lake Assal, what is your elevation? (Source: Microsoft Encarta) (image cannot copy A negative net income results when a company's expenses are more than the money brought in.

Step-by-Step Solution

Answer

Your elevation is 146 feet above sea level.

Step 1: Determine the Elevation of Lake Assal

Lake Assal's elevation is given as -512 feet, meaning it is 512 feet below sea level.

Step 2: Calculate the Elevation Difference

If you are standing 658 feet above Lake Assal, your elevation with respect to Lake Assal is 658 feet.

Step 3: Find the Elevation Above Sea Level

To find your elevation above sea level, add the elevation of Lake Assal (-512 feet) to the height you are standing above Lake Assal (658 feet). So, your elevation above sea level is (-512) + 658 = 146 feet.

Key Concepts

Elevation Calculation

Elevation calculation is the process of determining the height of a particular location in relation to a baseline reference point, usually sea level. Understanding how to calculate elevation is essential in geography and can be applied in real-world situations like hiking or construction. In this example, we are asked to find a person's elevation above sea level when standing above a depression like Lake Assal. To do this, we begin with the known depression's elevation, which is 512 feet *below* sea level. Then, we calculate the total elevation above sea level by adding the height one is standing above this baseline. By using simple addition, we can find the overall elevation, thus demonstrating the straightforward approach to elevation calculation. This skill helps in understanding geographical features and their relationships with sea level.

Addition of Integers

When dealing with word problems in algebra, the addition of integers is often a crucial step. Integers can represent positive or negative numbers, making them useful for a range of calculations in mathematics. In this particular exercise, we add two integers: the negative integer representing the depression below sea level (-512) and the positive integer representing the height above this point (658). Addition of integers requires combining numbers, paying close attention to their signs:

• Adding a positive integer increases the value.
• Adding a negative integer decreases the value.

Understanding how to correctly add these values allows us to find the net elevation above sea level in the problem. This practice is fundamental for solving various algebra word problems.

Negative Numbers

Negative numbers, which lie to the left of zero on the number line, represent values less than zero. Often used to denote deficits, losses, depths, or other situations where a quantity is below a defined level, they're a common feature in real-world problems. In our exercise, the elevation of Lake Assal is -512 feet, indicating it's below sea level. Working with negative numbers in math involves understanding operations like addition and subtraction and how they affect results:

• Negative numbers decrease the sum when added to positive numbers or zero.
• When subtracting a negative, the operation becomes addition.

Mastering negative numbers is essential for accurately calculating differences, especially in elevation and other similar contexts.

Sea Level Measurement

Sea level measurement serves as a global baseline from which elevations and depths are determined. It acts as the reference point for both elevations above the land and depths below water, such as the elevation of landforms and depressions. In geographical and meteorological studies, variations in sea level are crucial for understanding climatic shifts and geographical changes. When identifying the elevation of a feature, like in this exercise, the height is compared to mean sea level. Using Lake Assal in the problem, identified as lying 512 feet below sea level, we can understand how the lake’s depression affects its relative elevation. Similarly, knowing a point's elevation above a depression allows one to calculate its overall height relative to sea level, resulting in better geographical context. Understanding sea level measurement is thus integral to accurate elevation readings.