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

A nail is a short pin-shaped shaft of steel that's typically used to fasten pieces of wood together. It has a flat head on one end and a point on the other. A rivet consists of a cylindrical shaft with a head on one end and a tail on the other. When the rivet is installed, the tail is expanded and reshaped to form another head, creating a dumbell shape that will hold two surfaces together semi-permanently.

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

Solving for d_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{55 lbs. \times 3 ft.}{70 lbs.} \) = \( \frac{165 ft⋅lb}{70 lbs.} \) = 2.36 ft.

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

38,000 fans x \( \frac{3}{4} \) = \( \frac{114000}{4} \) = 28,500 fans.

The purpose of a capacitor is to retain electric charge and it will do so even after its input voltage is removed. After the input voltage is removed, the capacitor will slowly discharge but, depending on the size and characteristics of the capacitor, discharging could take from a few minutes to a few years. So, it's never safe to touch a capacitor with your hands and you should make sure to discharge any capacitors in a circuit before working on it using an appropriately high-wattage resistor or a capacitor discharge tool.

The mechanical advantage (amount of change in speed or torque) of connected gears is proportional to the number of teeth each gear has. Called gear ratio, it's the ratio of the number of teeth on the larger gear to the number of teeth on the smaller gear.  For example, a gear with 12 teeth connected to a gear with 9 teeth would have a gear ratio of 4:3.

Cylinders act as a guide for the pistons that translate the heat energy of combustion into the mechanical energy necessary to move a vehicle. Piston rings seal the piston to the cylinder to contain combustion gases and also regulate the oil distribution between the piston and cylinder wall. A cylinder head closes in the top of the cylinder forming the combustion chamber which is sealed by a head gasket (head). The head provides space for air and fuel intake valves, exhaust valves, and mounts for spark plugs and fuel injectors.

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.