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Mechanical Comprehension

Force of friction due to kinetic friction is __________ the force of friction due to static friction.

the same as

The formula for force of friction (F_f) is the same whether kinetic or static friction applies: F_{f =}μF_N. To distinguish between kinetic and static friction, μ_k and μ_s are often used in place of μ.

Arithmetic Reasoning

If $\left|a\right| = 7$, which of the following best describes a?

a = 7 or a = -7

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: $\left|-5\right| = 5$. In the case of a variable absolute value ($\left|a\right| = 5$) the value of a can be either positive or negative (a = -5 or a = 5).

Electronics Information

The conductivity of an element depends on how many electrons occupy which electron shell?

outer

All electricity is the movement of electrons which are subatomic particles that orbit the nucleus of an atom. Electrons occupy various energy levels called shells and how well an element enables the flow of electrons depends on how many electrons occupy its outer (valence) electron shell.

Mechanical Comprehension

If the green box weighs 25 lbs. and 75 lbs. of force is applied 5 ft. from the fulcrum at the blue arrow, how far from the fulcrum would the green box need to be placed to balance the lever?

15 ft.

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 d_a, our missing value, and plugging in our variables yields:

d_a = $ \frac{R_bd_b}{R_a} $ = $ \frac{75 lbs. \times 5 ft.}{25 lbs.} $ = $ \frac{375 ft⋅lb}{25 lbs.} $ = 15 ft.

General Science

This skeletal system is common in arthropods like insects, spiders, and crustaceans.

exoskeleton

An exoskeleton (external skeleton) is common in arthropods like insects, spiders, and crustaceans.

Mechanical Comprehension

Which of the following is the formula for hydraulic pressure?

P = F/A

Hydraulics is the transmission of force through the use of liquids. Liquids are especially suited for transferring force in complex machines because they compress very little and can occupy very small spaces. Hydraulic pressure is calculated by dividing force by the area over which it is applied: P = F/A where F is force in pounds, A is area in square inches, and the resulting pressure is in pounds per square inch (psi).

Math Knowledge

$2$\frac{1}{2}$$

The endpoints of this line segment are at (-2, -7) and (2, 3). What is the slope of this line?

2$\frac{1}{2}$

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -7) and (2, 3) so the slope becomes:

m = $ \frac{\Delta y}{\Delta x} $ = $ \frac{(3.0) - (-7.0)}{(2) - (-2)} $ = $ \frac{10}{4} $
m = 2$\frac{1}{2}$

Arithmetic Reasoning

What is -z² + 5z²?

4z²

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-1z² + 5z²
(-1 + 5)z²
4z²

Word Knowledge

The rancorous competition between the two chess clubs actually ended in a brawl.

bitter

Marked by deep ill–will.

General Science

Which of the following is metamorphic rock?

marble

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.