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Math Knowledge

Solve 3b + 2b = 9b - 9z + 8 for b in terms of z.

1\(\frac{5}{6}\)z - 1\(\frac{1}{3}\)

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

3b + 2z = 9b - 9z + 8
3b = 9b - 9z + 8 - 2z
3b - 9b = -9z + 8 - 2z
-6b = -11z + 8
b = \( \frac{-11z + 8}{-6} \)
b = \( \frac{-11z}{-6} \) + \( \frac{8}{-6} \)
b = 1\(\frac{5}{6}\)z - 1\(\frac{1}{3}\)

Mechanical Comprehension

If the radius of the axle is 5 and the radius of the wheel is 6, what is the mechanical advantage of this wheel and axle configuration?

1.2

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 6 and the output radius (where the resistance is being applied) is 5 for a mechanical advantage of \( \frac{6}{5} \) = 1.2

Mechanical Comprehension

An inclined plane increases ___________ to reduce ____________.

distance, force

An inclined plane is a simple machine that reduces the force needed to raise an object to a certain height. Work equals force x distance and, by increasing the distance that the object travels, an inclined plane reduces the force necessary to raise it to a particular height. In this case, the mechanical advantage is to make the task easier. An example of an inclined plane is a ramp.

Mechanical Comprehension

The mechanical advantage of a wheel and axle is equal to the:

ratio of the diameters of the wheels

A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the ratio of the diameters of the wheels. An example of a wheel and axle is the steering wheel of a car.

Mechanical Comprehension

Which of the following is not a type of simple machine?

gear

The six types of simple machines are the lever, wheel and axle, pulley, inclined plane, wedge, and screw.

Electronics Information

All electricity is the movement of which subatomic particles?

electrons

All electricity is the movement of electrons which are subatomic particles that orbit the nucleus of an atom. Electrons occupy various energy levels called shells and how well an element enables the flow of electrons depends on how many electrons occupy its outer (valence) electron shell.

General Science

When two air masses meet and neither is displaced, what kind of front is present?

stationary

When two air masses meet and neither is displaced, a stationary front is created. Stationary fronts often cause persistent cloudy wet weather.

Word Knowledge

They were ecstatic when their team won the championship game in the last second.

overjoyed

Overwhelmingly emotional.

Shop Information

Screwdrivers are most broadly classified by their:

tip

Screwdrivers come in many different handle, shaft, and tip configurations for use in a wide variety of applications. Screwdrivers are classified by their tip which is shaped to fit a corresponding screw head. Common tips are slotted (flat) and Phillips (x-shaped).

General Science

Cellular fermentation takes place:

anaerobically

If no oxygen is present, cellular respiration is anaerobic and will result in fermentation where either lactic acid or alcohol is used instead of oxygen.