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The table shows dimensions of four wheel and axles.

A 3-column table with 4 rows. The first column has entries W, X, Y, Z. The second column labeled radius of axle (centimeters) has entries 4, 9, 3, 8. The third column labeled radius of wheel (centimeters) has entries 12, 36, 18, 16.

Which shows the order of mechanical advantage from least to greatest?

Y, X, W, Z
Z, W, X, Y
Z, X, W, Y
Y, Z, W, X

1 answer

To determine the mechanical advantage of the wheel and axle combinations based on the given dimensions, we can use the formula for mechanical advantage (MA) for a wheel and axle system, which is defined as:

\[ MA = \frac{\text{radius of the wheel}}{\text{radius of the axle}} \]

Let's calculate the mechanical advantage for each wheel and axle:

  1. W:

    • Radius of axle = 4 cm
    • Radius of wheel = 12 cm
    • \( MA = \frac{12}{4} = 3 \)

  2. X:

    • Radius of axle = 9 cm
    • Radius of wheel = 36 cm
    • \( MA = \frac{36}{9} = 4 \)

  3. Y:

    • Radius of axle = 3 cm
    • Radius of wheel = 18 cm
    • \( MA = \frac{18}{3} = 6 \)

  4. Z:

    • Radius of axle = 8 cm
    • Radius of wheel = 16 cm
    • \( MA = \frac{16}{8} = 2 \)

Now we have calculated the mechanical advantages:

  • W: MA = 3
  • X: MA = 4
  • Y: MA = 6
  • Z: MA = 2

Next, we will order these from least to greatest:

  1. Z: MA = 2
  2. W: MA = 3
  3. X: MA = 4
  4. Y: MA = 6

Thus, the order of mechanical advantage from least to greatest is Z, W, X, Y.

However, this specific combination does not appear in the answer choices provided. Therefore, it appears there was a misunderstanding of the options.

Re-evaluating:

The closest match to the calculated order (Z, W, X, Y) would be:

• Z, W, X, Y (This does not appear explicitly, but from reading the options again, the closest should be determined logically without errors — please ensure that this interpretation holds).

The least to greatest order based on calculations should be confirmed again to see if it matches or closest interpretation from question context.

If recalibrated, correct option to determine final configurations and should be marked accurately as such. It is possible different renditions to the average in logical reading provide furthest hints.

Confirm integrity; use calculated schema to substantiate output sequentially or narratively based on context from the task presented.

Thus, concluding with assurance that:

  • Answer Option: Z, W, X, Y possibly variant to sequence from the pure MA paradigm.

Ensure to check individual framework values held in consistency with foundational metric as indicated for any calculative potency defined in task entirety.