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Mechanical Comprehension

A 290 lb. barrel is rolled up a 14 ft. ramp to a platform that's 2 ft. tall. What effort is required to move the barrel?

41.4 lbs.

This problem describes an inclined plane and, for an inclined plane, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance:

F_ed_e = F_rd_r

Plugging in the variables from this problem yields:

F_e x 14 ft. = 290 lbs. x 2 ft.
F_e = \( \frac{580 ft⋅lb}{14 ft.} \) = 41.4 lbs.

Word Knowledge

Equitable most nearly means:

impartial

Fair and equal.

Word Knowledge

Lorraine was in rhapsody when she was accepte to the college of her dreams.

ecstasy

State of great happiness.

Automotive Information

What combines the suspension spring and shock absorber into one unit?

strut

Because a compressed spring will extend violently, shock absorbers must be used to dampen the spring’s compression and extension cycles. Struts combine the spring and shock into one unit

General Science

The Earth's rocks fall into three categories based on how they're formed. Which of the following is formed when existing rock is altered through pressure, temperature, or chemical processes?

metamorphic

The Earth's rocks fall into three categories based on how they're formed. Igneous rock (granite, basalt, obsidian) is formed from the hardening of molten rock (lava), sedimentary rock (shale, sandstone, coal) is formed by the gradual despositing and cementing of rock and other debris, and metamorphic rock (marble, slate, quartzite) which is formed when existing rock is altered though pressure, temperature, or chemical processes.

Arithmetic Reasoning

If \( \left|x + 9\right| \) - 3 = 7, which of these is a possible value for x?

-19

First, solve for \( \left|x + 9\right| \):

The value inside the absolute value brackets can be either positive or negative so (x + 9) must equal + 10 or -10 for \( \left|x + 9\right| \) to equal 10:

x + 9 = 10
x = 10 - 9
x = 1

x + 9 = -10
x = -10 - 9
x = -19

So, x = -19 or x = 1.

General Science

Scavengers break down the dead bodies of plants and animals into which of the following?

simple nutrients

Like decomposers, scavengers also break down the dead bodies of plants and animals into simple nutrients. The difference is that scavengers operate on much larger refuse and dead animals (carrion). Decomposers then consume the much smaller particles left over by the scavengers.

Math Knowledge

Simplify (9a)(8ab) + (7a²)(8b).

128a²b

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(9a)(8ab) + (7a²)(8b)
(9 x 8)(a x a x b) + (7 x 8)(a² x b)
(72)(a¹⁺¹ x b) + (56)(a²b)
72a²b + 56a²b
128a²b

Mechanical Comprehension

If the radius of the axle is 5 and the radius of the wheel is 6, what is the mechanical advantage of this wheel and axle configuration?

The mechanical advantage of a wheel and axle lies in the difference in radius between the inner (axle) wheel and the outer wheel. But, this mechanical advantage is only realized when the input effort and load are applied to different wheels. Applying both input effort and load to the same wheel results in a mechanical advantage of 1.

Electronics Information

Which of the following will help to prevent a short circuit?

fuse

Fuses are thin wires that melt when the current in a circuit exceeds a preset amount. They help prevent short circuits from damaging circuit components when an unusually large current is applied to the circuit, either through component failure or spikes in applied voltage.