Sure! I'll guide you through each part of the problem step-by-step.
Part A
Write the submarine’s initial elevation as a rational number.
The submarine is at 502.5 feet below sea level. This can be expressed as a rational number:
\[ -502.5 \text{ feet} \]
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 find the change in elevation, you will need to subtract the additional depth from the initial depth. The relevant words in the problem are "dives down" which imply an increase in negative elevation (further below sea level).
Part C
Write an expression to represent the submarine’s elevation after its final dive. Then simplify the expression to find its elevation.
The initial elevation is \(-502.5\) feet and it dives down an additional 115 feet. The expression is:
\[ -502.5 - 115 \]
Now simplify this:
\[ -502.5 - 115 = -617.5 \text{ feet} \]
Part D
Write the temperature at 502.5 feet below sea level as a rational number.
The water temperature at this depth is \(63 \frac{1}{4} °F\). As a rational number, this can be expressed as:
\[ 63.25 °F \]
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 final temperature, you will need to subtract the drop in temperature from the initial temperature. The relevant words here are "drops by" which indicates a decrease.
Part F
Write an expression to represent the water temperature after the submarine’s final dive. Then simplify the expression to find the temperature.
The initial water temperature is \(63.25 °F\) and it drops by \(2 \frac{1}{5} °F\). First, convert \(2 \frac{1}{5}\) to a decimal:
\[ 2 \frac{1}{5} = 2.2 \]
Now the expression for the final temperature is:
\[ 63.25 - 2.2 \]
Now simplify this:
\[ 63.25 - 2.2 = 61.05 °F \]
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.
Convert \(63 \frac{1}{4}\) into decimal form:
\[ 63 \frac{1}{4} = 63.25 \]
Convert \(2 \frac{1}{5}\) into decimal form:
\[ 2 \frac{1}{5} = 2.2 \]
Part H
Find the water temperature after the submarine’s final dive in decimal form. Show your work.
Using the values from Part G, compute:
\[ 63.25 - 2.2 = 61.05 °F \]
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.
Yes, both results are the same: \(61.05 °F\). This shows that the calculation method (whether using fractions or decimals) yields the same temperature result.
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.
Feel free to fill out the self-evaluation part based on your understanding and experience with the problem. If you have any additional questions or need further clarification, let me know!
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