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Mechanical Comprehension

Gear ratio indicates which of the following about two connected gears?

mechanical advantage

The mechanical advantage (amount of change in speed or torque) of connected gears is proportional to the number of teeth each gear has. Called gear ratio, it's the ratio of the number of teeth on the larger gear to the number of teeth on the smaller gear. For example, a gear with 12 teeth connected to a gear with 9 teeth would have a gear ratio of 4:3.

Mechanical Comprehension

If you have a gear train with two gears, the first with 32 teeth and the second with 4 teeth, how many revolutions does the second gear make for each revolution of the first gear?

The gear ratio (V_r) of a gear train is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:

V_r = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) \( \frac{N_3}{N_4} \) ... \( \frac{N_n}{N_{n+1}} \)

In this problem, we have only two gears so the equation becomes:

V_r = \( \frac{N_1}{N_2} \) = \( \frac{32}{4} \) = 8

Math Knowledge

If the length of AB equals the length of BD, point B __________ this line segment.

bisects

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

General Science

All surface water is part of the:

hydrosphere

The biosphere is the global ecological system integrating all living beings and their relationships. This includes their interactions with the lithosphere (the rigid outer part of the earth, consisting of the crust and upper mantle), hydrosphere (all surface water), and atmosphere (the envelope of gases surrounding the planet).

Arithmetic Reasoning

What is 7\( \sqrt{4} \) x 6\( \sqrt{4} \)?

168

To multiply terms with radicals, multiply the coefficients and radicands separately:

7\( \sqrt{4} \) x 6\( \sqrt{4} \)
(7 x 6)\( \sqrt{4 \times 4} \)
42\( \sqrt{16} \)

Now we need to simplify the radical:

42\( \sqrt{16} \)
42\( \sqrt{4^2} \)
(42)(4)
168

Arithmetic Reasoning

What is the least common multiple of 6 and 12?

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 have in common.

Word Knowledge

Augment most nearly means:

enhance

To make greater.

Automotive Information

Which of the following is a relay that connects the battery to the starter motor when the ignition key is turned?

solenoid

The cylindrical solenoid is a relay that safely connects the high amperage battery to the starter motor when the ignition key is turned. This current then allows the engine to turn at a high enough speed to start.

Mechanical Comprehension

If the handles of a wheelbarrow are 1.5 ft. from the wheel axle, how many pounds of force must you exert to lift the handles if it's carrying a 130 lbs. load concentrated at a point 0.5 ft. from the axle?

43.3

This problem describes a second-class lever and, for a second class lever, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance: F_ed_e = F_rd_r. In this problem we're looking for effort force:
\( F_e = \frac{F_r d_r}{d_e} \)
\( F_e = \frac{130 \times 0.5}{1.5} \)
\( F_e = \frac{65.0}{1.5} \)
\( F_e = 43.3 \)

Math Knowledge

Which of the following statements about a parallelogram is not true?

opposite sides and adjacent angles are equal

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).