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Word Knowledge

Frank, who was wounded by Sally's remark, made a bitter recrimination.

counterclaim

A retaliatory accusation.

Mechanical Comprehension

What is work?

The movement of an object by a force

Work is accomplished when force is applied to an object: W = Fd where F is force in newtons (N) and d is distance in meters (m). Thus, the more force that must be applied to move an object, the more work is done and the farther an object is moved by exerting force, the more work is done. By definition, work is the displacement of an object resulting from applied force.

Arithmetic Reasoning

A factor is a positive __________ that divides evenly into a given number.

integer

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

Math Knowledge

Breaking apart a quadratic expression into a pair of binomials is called:

factoring

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

Word Knowledge

Heidi's grandfather was gruff, barking stern orders and hardly smiling.

surly

Rough or stern in manner or speech.

Arithmetic Reasoning

4! = ?

4 x 3 x 2 x 1

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

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.

General Science

Which of the following would be found on a reflecting telescope?

concave mirror

A concave (or converging) mirror bulges inward and focuses reflected light on the mirror's focal point where the mirror's angles of incidence converge. In contrast, a convex (or diverging) mirror bulges outward and diffuses the light waves that strike it. A common use of a concave mirror is in a reflecting telescope, a common use of a convex mirror is in the side view mirror of a car.

Mechanical Comprehension

What defines the mechanical advantage of a first class lever?

position of the fulcrum

A first-class lever is used to increase force or distance while changing the direction of the force. The lever pivots on a fulcrum and, when a force is applied to the lever at one side of the fulcrum, the other end moves in the opposite direction. The position of the fulcrum also defines the mechanical advantage of the lever. If the fulcrum is closer to the force being applied, the load can be moved a greater distance at the expense of requiring a greater input force. If the fulcrum is closer to the load, less force is required but the force must be applied over a longer distance. An example of a first-class lever is a seesaw / teeter-totter.

General Science

-40°F is how many °C?

-40

The formula to convert from F° to C° is:

\(C° = {5 \over 9} (F° - 32)\)

plugging in our values gives:

\(C° = {5 \over 9} (-40 - 32)\)

\(C° = {5 \over 9} (-72) = {{-72 \times 5} \over 9}\)

\(C° = {-360 \over 9}\)

\(C° = -40\)