Sure! Let's go through each part step by step.
Part A
Write the submarine’s initial elevation as a rational number.
The initial elevation of the submarine is -502.5 feet, since it is below sea level.
Part B
Which operation must you use to calculate the submarine’s change in elevation? Which word or words in the problem signify this operation?
To calculate the submarine's change in elevation, you need to use subtraction. The phrase "dives down" signifies that the submarine is going deeper, which involves subtracting the additional depth from the initial elevation.
Part C
Write an expression to represent the submarine’s elevation after its final dive. Then simplify the expression to find its elevation.
Initial elevation: -502.5 feet
Dive depth: 115 feet
The expression to represent the elevation after the dive is:
\[-502.5 - 115\]
Now, simplifying:
\[-502.5 - 115 = -617.5\]
So, the submarine's final elevation is -617.5 feet.
Part D
Write the temperature at 502.5 feet below sea level as a rational number.
The water temperature is a variable value that is not provided in the problem. Assuming we represent it as \(T\), we can express it as \(T\) degrees Fahrenheit at -502.5 feet.
Part E
Which operation must you use to find the water temperature after the submarine’s final dive? Which word or words in the problem signify this operation?
To find the new temperature after the submarine's final dive, you need to use subtraction. The phrase "drops by" signifies that the temperature decreases, which requires subtracting the drop in temperature from the initial temperature.
Part F
Write an expression to represent the water temperature after the submarine’s final dive. Then simplify the expression to find the temperature.
Let’s say the temperature at -502.5 feet is \(T\), and the temperature drops by \(D\) degrees. The expression is:
\[T - D\]
Since we do not have numerical values for \(T\) and \(D\), we cannot simplify further without that information.
Part G
Now you’ll complete the temperature part of the problem again, but this time using decimal numbers. Start by converting the temperatures in the problem statement from fractions to decimal numbers.
If the temperatures were provided as fractions, convert them to decimals. However, as of now, the relationship is still unspecified. For example, if it was stated that the initial temperature is \(62.5°F\) at -502.5 feet, you'd consider that number to be 62.5 in decimal form.
Part H
Find the water temperature after the submarine’s final dive in decimal form. Show your work.
If we assume an initial temperature \(T\) at -502.5 feet was \(62.5°F\) and it drops \(3.5°F\) during the dive: \[ 62.5 - 3.5 = 59.0°F \] The final temperature would then be 59.0°F.
Part I
Is the result that you obtained in part F (with fractions) the same as the result you obtained in part H (with decimal numbers)? Explain.
Without specific values in Part F, we can't directly compare them. However, if you follow the same operations, the results should mathematically match when decimals are correctly converted from fractions and vice versa.
Self-Evaluation
**Rating: ** (Scale of 1 to 5)
Let’s say I would rate my work a 4.
Evaluation: I was able to clearly articulate the process for each part, but I encountered some challenges when values were not provided. I learned the importance of specifying values for a complete answer and how to express operations in elevation and temperature changes effectively. Overall, I feel confident in understanding the concepts but would improve on ensuring all necessary information is included in problems.
Please let me know if you would like specific numerical values or if you have more details to work with!