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General Science

Velocity and displacement are fully described by both a magnitude and a direction. Velocity and displacement are which of the following?

vector quantities

Velocity and displacement are vector quantities which means each is fully described by both a magnitude and a direction. In contrast, scalar quantities are quantities that are fully described by a magnitude only. A variable indicating a vector quantity will often be shown with an arrow symbol: \(\vec{v}\)

Mechanical Comprehension

If A = 9 ft. and the green box weighs 30 lbs. what is the torque acting on the A side of this lever?

270 ft⋅lb

For a lever, torque is weight x distance from the fulcrum which, in this case, is: 30 ft. x 9 lbs. = 270 ft⋅lb

Word Knowledge

Sheila, who could not resist bragging, flaunted the "A" marked on her test paper.

parade

To display showily.

Automotive Information

The piston moves downward in the cylinder creating a vacuum that pulls an air-fuel mix into the combustion chamber. This describes which engine stroke?

intake

The four-stroke piston cycle of internal combustion engines starts with the piston at top of the cylinder head (top dead center or TDC) during the intake stroke. The piston moves downward in the cylinder creating a vacuum that pulls an air-fuel mix into the combustion chamber through the now open intake valve.

Mechanical Comprehension

Power is the rate at which:

work is done

Power is the rate at which work is done, P = w/t, or work per unit time. The watt (W) is the unit for power and is equal to 1 joule (or newton-meter) per second. Horsepower (hp) is another familiar unit of power used primarily for rating internal combustion engines. 1 hp equals 746 watts.

General Science

The formula for acceleration is which of the following?

\(\vec{a} = { \vec{F} \over m }\)

Newton's second law of motion leads to the formula for acceleration which is a measure of the rate of change of velocity per unit time and, if you solve for positive acceleration, reveals how much net force is needed to overcome an object's mass. The formula for acceleration is \(\vec{a} = { \vec{F} \over m }\) or, solving for force, \(\vec{F} = m\vec{a}\).

General Science

The __________ nervous system controls voluntary actions.

somatic

Part of the peripheral nervous system, the somatic nervous system is made up of nerve fibers that send sensory information to the central nervous system and control voluntary actions.

General Science

I biome is made up of naturally occurring flora and fauna. Fauna is which of the following?

animals

A biome is a large naturally occurring community of flora (plants) and fauna (animals) occupying a major habitat (home or environment).

Math Knowledge

Solve for x:
x² + 6x - 13 = -x + 5

2 or -9

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

x² + 6x - 13 = -x + 5
x² + 6x - 13 - 5 = -x
x² + 6x + x - 18 = 0
x² + 7x - 18 = 0

Next, factor the quadratic equation:

x² + 7x - 18 = 0
(x - 2)(x + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 2) or (x + 9) must equal zero:

If (x - 2) = 0, x must equal 2
If (x + 9) = 0, x must equal -9

So the solution is that x = 2 or -9

Mechanical Comprehension

An object's resistance to changes in direction is known as:

inertia

The more mass a substance has the more force is required to move it or to change its direction. This resistance to changes in direction is known as inertia.