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Mechanical Comprehension

If the green box weighs 30 lbs. and is 8 ft. from the fulcrum, how much force would need to be applied at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 9 ft.?

26.67 lbs.

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

Solving for R_b, our missing value, and plugging in our variables yields:

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{30 lbs. \times 8 ft.}{9 ft.} \) = \( \frac{240 ft⋅lb}{9 ft.} \) = 26.67 lbs.

Word Knowledge

Induce most nearly means:

incite

To influence or cause.

Mechanical Comprehension

What type of load acts on a relatively small area of a structure?

concentrated load

A concentrated load acts on a relatively small area of a structure, a static uniformly distributed load doesn't create specific stress points or vary with time, a dynamic load varies with time or affects a structure that experiences a high degree of movement, an impact load is sudden and for a relatively short duration and a non-uniformly distributed load creates different stresses at different locations on a structure.

Word Knowledge

Sadie's cowboy hat was incongruous with her black cocktail dress.

inappropriate

Not harmonious, incompatible.

General Science

As part of the carbon cycle, plants release carbon into the atmosphere through which process?

decomposition

The carbon cycle represents the ciruit of carbon through Earth's ecosystem. Carbon dioxide (CO₂) in the atmosphere is absorbed by plants through photosynthesis. Plants then die and release carbon back into the atmosphere during decomposition or are eaten by animals who breathe (respiration) the carbon into the atmosphere they exhale and produce waste which also releases carbon as it decays.

Electronics Information

Capacitors are charged by what type of current?

direct

Capacitors store voltage and are used in circuits as temporary batteries. Capacitors are charged by DC current (AC current passes through a capacitor) and that stored charge can later be dissipated into the circuit as needed. Capacitors are often used to maintain power within a system when it is disconnected from its primary power source or to smooth out or filter voltage within a circuit.

Math Knowledge

Solve for a:
a² - 5a - 6 = 0

-1 or 6

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

a² - 5a - 6 = 0
(a + 1)(a - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 1) or (a - 6) must equal zero:

If (a + 1) = 0, a must equal -1
If (a - 6) = 0, a must equal 6

So the solution is that a = -1 or 6

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.

Word Knowledge

Lurid most nearly means:

gruesome

Causing horror, shocking.

Mechanical Comprehension

Which of the following surfaces would have the highest coefficient of friction?

concrete

Coefficient of friction (μ) represents how much two materials resist sliding across each other. Smooth surfaces like ice have low coefficients of friction while rough surfaces like concrete have high μ.