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Math Knowledge

A(n) __________ is to a parallelogram as a square is to a rectangle.

rhombus

A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

General Science

The four planets closest to the Sun are called terrestrial. What does terrestrial mean?

the planets are Earth-like

The four planets closest to the Sun (Mercury, Venus, Earth, and Mars) are called terrestrial (Earth-like) planets because, like the Earth, they're solid with inner metal cores covered by rocky surfaces.

Word Knowledge

Futile most nearly means:

hopeless

Without purpose, completely ineffective.

Mechanical Comprehension

If the green box is 8 ft. from the fulcrum and a certain force applied 7 ft. from the fulcrum at the blue arrow balances the lever, what is the mechanical advantage?

0.88

Because this lever is in equilibrium, we know that the effort force at the blue arrow is equal to the resistance weight of the green box. For a lever that's in equilibrium, one method of calculating mechanical advantage (MA) is to divide the length of the effort arm (E_a) by the length of the resistance arm (R_a):

MA = \( \frac{E_a}{R_a} \) = \( \frac{7 ft.}{8 ft.} \) = 0.88

When a lever is in equilibrium, the torque from the effort and the resistance are equal. The equation for equilibrium is R_ad_a = R_bd_b where a and b are the two points at which effort/resistance is being applied to the lever.

In this problem, R_a and R_b are such that the lever is in equilibrium meaning that some multiple of the weight of the green box is being applied at the blue arrow. For a lever, this multiple is a function of the ratio of the distances of the box and the arrow from the fulcrum. That's why, for a lever in equilibrium, only the distances from the fulcrum are necessary to calculate mechanical advantage.

If the lever were not in equilibrium, you would first have to calculate the forces and distances necessary to put it in equilibrium and then divide E_a by R_a to get the mechanical advantage.

Math Knowledge

If a = c = 3, b = d = 8, and the blue angle = 58°, what is the area of this parallelogram?

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 3 x 8
a = 24

General Science

Secondary consumers that also eat producers are known as:

omnivores

Secondary consumers (carnivores) subsist mainly on primary consumers. Omnivores are secondary consumers that also eat producers. Examples are rats, fish, and chickens.

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.

Math Knowledge

Solve for c:
2c + 2 < 8 - 8c

c < \(\frac{3}{5}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

2c + 2 < 8 - 8c
2c < 8 - 8c - 2
2c + 8c < 8 - 2
10c < 6
c < \( \frac{6}{10} \)
c < \(\frac{3}{5}\)

Electronics Information

Which of the following is the formula for calculating electrical power?

P = IV

Electrical power is measured in watts (W) and is calculated by multiplying the voltage (V) applied to a circuit by the resulting current (I) that flows in the circuit: P = IV. In addition to measuring production capacity, power also measures the rate of energy consumption and many loads are rated for their consumption capacity. For example, a 60W lightbulb utilizes 60W of energy to produce the equivalent of 60W of heat and light energy.

Arithmetic Reasoning

What is \( \sqrt{\frac{16}{4}} \)?

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{4}} \)
\( \frac{\sqrt{16}}{\sqrt{4}} \)
\( \frac{\sqrt{4^2}}{\sqrt{2^2}} \)
\( \frac{4}{2} \)
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