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Math Knowledge

The dimensions of this trapezoid are a = 4, b = 8, c = 7, d = 4, and h = 2. What is the area?

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(8 + 4)(2)
a = ½(12)(2)
a = ½(24) = \( \frac{24}{2} \)
a = 12

Mechanical Comprehension

What's the mechanical advantage of a wedge that's 3 inches wide and 12 inches long?

The mechanical advantage (MA) of a wedge is its length divided by its thickness:

MA = \( \frac{l}{t} \) = \( \frac{12 in.}{3 in.} \) = 4

Mechanical Comprehension

The principle of conservation of mechanical energy states that, as long as no other forces are applied, what will remain constant as an object falls?

total mechanical energy

As an object falls, its potential energy is converted into kinetic energy. The principle of conservation of mechanical energy states that, as long as no other forces are applied, total mechanical energy (PE + KE) of the object will remain constant at all points in its descent.

Automotive Information

What type of energy does an automotive battery produce?

direct current

An automotive battery produces direct current for use by automotive systems.

General Science

The number system most used in science is the:

metric system

The metric system is a number system that designates one base unit for each type of measurement. For example, the base unit for length is the meter and the base unit for mass is the gram.

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:

\(C° = {5 \over 9} (-40 - 32)\)

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

\(C° = {-360 \over 9}\)

\(C° = -40\)

Automotive Information

An overcooled engine:

is less efficient

An overcooled engine is less efficient. During the power stroke, combustion heat pushes down the piston. If too much of this heat is lost to the cooling system, the fuel might not combust completely and contaminate the engine's lubricating oil diminishing its lubricating ability. Incomplete combustion of fuel also negatively affects the engine's fuel efficiency and power output.

Mechanical Comprehension

If you have a gear train with three gears, the first with 24 teeth, the second with 16 teeth, and the third with 4 teeth, what is its mechanical advantage?

The mechanical advantage of a gear train is its gear ratio. The gear ratio (V_r) is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:

V_r = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) \( \frac{N_3}{N_4} \) ... \( \frac{N_n}{N_{n+1}} \)

In this problem, we have three gears so the equation becomes:

V_r = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) = \( \frac{24}{16} \) \( \frac{16}{4} \) = \( \frac{24}{4} \) = 6

Mechanical Comprehension

Drag is a type of:

friction

Drag is friction that opposes movement through a fluid like liquid or air. The amount of drag depends on the shape and speed of the object with slower objects experiencing less drag than faster objects and more aerodynamic objects experiencing less drag than those with a large leading surface area.

Arithmetic Reasoning

\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?

distributive property for division

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).