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Mechanical Comprehension

If the green arrow in this diagram represents 420 ft⋅lb of work, how far will the box move if it weighs 140 pounds?

3 ft.

The Law of Work states that the work put into a machine is equal to the work received from the machine under ideal conditions. In equation form, that's:

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 420 ft⋅lb and the resistance force is 140 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
420 ft⋅lb = 140 lbs. x d_resistance
d_resistance = \( \frac{420ft⋅lb}{140 lbs.} \) = 3 ft.

Math Knowledge

Which of the following statements about parallel lines with a transversal is not correct?

same-side interior angles are complementary and equal each other

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

Word Knowledge

The teacher suggested the combative student channel his aggression into boxing.

aggressive

Eager to fight.

General Science

Examples of primary consumers include:

cows

Primary consumers (herbivores) subsist on producers like plants and fungus. Examples are grasshoppers, cows, and plankton.

Electronics Information

Use Ohm's Law to calculate the value of voltage in this circuit if resistance is 10 Ω and current is 2.5 amps.

25 V

Ohm's law specifies the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit: V = IR.

V = \( I \times R \) = \( 2.5 \times 10 \) = 25 V

Arithmetic Reasoning

Which of these numbers is a factor of 72?

The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

General Science

Which of the following is related to the Cambrian Explosion?

fossil record

The Cambrian period is one of the most significant geological time periods. Lasting about 53 million years, it marked a dramatic burst of changes in life on Earth known as the Cambrian Explosion. It is from this period that the majority of the history of life on Earth, as documented by fossils, is found. Called the fossil record, the layering of these mineralized imprints of organisms preserved in sedementary rock have allowed geologists to build a historical record of plant and animal life on Earth.

Electronics Information

The valence shell of a conductor is how full of electrons?

less than half full

Conductors are elements that allow electrons to flow freely. Their valence shell is less than half full of electrons that are able to move easily from one atom to another.

Electronics Information

A transistor works by allowing a small amount of current to control general current flow. Where is the small amount of current applied?

base

The transistor is the foundation of modern electronic devices. It is made entirely from semiconductor material (making it a solid state device) and can serve many different functions in a circuit including acting as a switch, amplifier, or current regulator. A transistor works by allowing a small amount of current applied at the base to control general current flow from collector to emitter through the transistor.

Automotive Information

Another name for a reciprocating engine is a(n):

piston engine

A reciprocating engine is an engine whose crankshaft is turned by pistons moving up and down in a cylinder.