Problem 70 - Beginning and Intermediate Algebra

Question

Much of New Orleans is below sea level. If George descends 12 feet from an elevation of 5 feet above sea level, what is his new elevation?

Step-by-Step Solution

Answer

George's new elevation is -7 feet.

Step 1: Understand the Problem

We need to find George's new elevation if he starts at 5 feet above sea level and descends 12 feet.

Step 2: Set Up the Equation

Since George descends from his initial elevation, we subtract the descent from his starting elevation. Let's use the equation: \( ext{New Elevation} = ext{Starting Elevation} - ext{Descent} \).

Step 3: Substitute Known Values

Substitute the known values into the equation: \( ext{New Elevation} = 5 - 12 \).

Step 4: Calculate the New Elevation

Calculate \( 5 - 12 = -7 \). This means George's new elevation is -7 feet.

Key Concepts

Below Sea Level

In geographical terms, being below sea level refers to an elevation that is less than the average level of the world's oceans. Imagine the sea as a zero point, a baseline.
Any location beneath this point is considered below sea level. This is common in certain regions, such as parts of New Orleans, which lie below the surface of the ocean.
When a place is beneath the ocean level, it carries certain risks, particularly of flooding. This makes accurate calculations of elevation crucial in city planning and construction in such areas.

• Understanding elevation helps in predicting and mitigating flood risks.
• It assists in engineering and building infrastructure like levees and drainage systems.

In the exercise we're discussing, George ends below sea level as indicated by the negative sign of his elevation (-7 feet). This means he is 7 feet beneath this imaginary zero line, or sea level point.

Subtraction in Mathematics

Subtraction is one of the basic arithmetic operations and is often understood as the process of taking one number away from another. Imagine you have a starting amount, and you remove a portion of it. The remaining amount is what subtraction gives you.
This operation is fundamental in calculating differences, like determining new elevations when changes occur.In our exercise, we're using subtraction to calculate George's descent from 5 feet above sea level. The equation we use is: \[ \text{New Elevation} = \text{Starting Elevation} - \text{Descent}\]After substituting the known values, \[ \text{New Elevation} = 5 - 12\]we solve it to find that:\[ \text{New Elevation} = -7\]This arithmetic helps students understand how subtraction can not only decrease values but also result in negative numbers, illustrating scenarios like descending below a certain point or level.

Real-Life Math Applications

Real-life math applications show how we use math concepts daily without even realizing it. They link abstract math ideas to the things we see and do regularly. Consider the example of elevation: it helps us understand locations, plan travels, and even predict weather patterns.
In the New Orleans problem, math helps in figuring out how low or high a place is relative to the sea. Such calculations can be crucial in designing flood defenses and for city planning.
To visualize, when George descends into negative elevation, it might indicate going deeper into an underground structure or below a certain threshold like sea level. Let's consider how math finds its way into daily life through:

• Construction and architecture, ensuring buildings are safe and stable.
• Navigation, helping pilots and mariners maintain correct altitudes and depths.
• Environmental science, using calculations to track climate changes and sea level rise.

Through exercises like these, students can see how numbers aren't just confined to paper but outline the world we live in, impacting crucial decisions and strategies.