Answered

Students in Ms. Delgado's science class built machines. They measured the input and output forces. The results of four students are listed in the table.

\begin{tabular}{|l|c|c|}
\hline \multicolumn{1}{|c|}{ Student } & Input force (N) & Output force (N) \\
\hline Brian & 150 & 300 \\
\hline Lian & 400 & 350 \\
\hline Dipak & 250 & 450 \\
\hline Aida & 300 & 375 \\
\hline
\end{tabular}

Which lists the students in order from the student whose machine has the least mechanical advantage to the student whose machine has the greatest mechanical advantage?

A. Brian, Dipak, Aida, Lian
B. Lian, Dipak, Aida, Brian
C. Brian, Lian, Aida, Dipak
D. Lian, Aida, Dipak, Brian



Answer :

GinnyAnswer
To determine the order of students based on the mechanical advantage of their machines, we need to calculate the mechanical advantage for each student’s machine. Mechanical advantage (MA) is defined as the ratio of the output force to the input force. The formula for mechanical advantage is:

[tex]\[ MA = \frac{\text{Output Force}}{\text{Input Force}} \][/tex]

Let's calculate the mechanical advantage for each student:

1. Brian:
[tex]\[ MA_{\text{Brian}} = \frac{300 \text{ N}}{150 \text{ N}} = 2.0 \][/tex]

2. Lian:
[tex]\[ MA_{\text{Lian}} = \frac{350 \text{ N}}{400 \text{ N}} = 0.875 \][/tex]

3. Dipak:
[tex]\[ MA_{\text{Dipak}} = \frac{450 \text{ N}}{250 \text{ N}} = 1.8 \][/tex]

4. Aida:
[tex]\[ MA_{\text{Aida}} = \frac{375 \text{ N}}{300 \text{ N}} = 1.25 \][/tex]

Next, we will list the students in order from the least mechanical advantage to the greatest mechanical advantage:

- Lian has the least mechanical advantage: [tex]\(0.875\)[/tex]
- Aida has the next least mechanical advantage: [tex]\(1.25\)[/tex]
- Dipak has the next mechanical advantage: [tex]\(1.8\)[/tex]
- Brian has the greatest mechanical advantage: [tex]\(2.0\)[/tex]

Therefore, the correct order is:

Lian, Aida, Dipak, Brian

Hence, the correct answer is:

Lian, Aida, Dipak, Brian

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