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The transistor is the foundation of modern electronic devices. It is made entirely from semiconductor material (making it a solid state device) and can serve many different functions in a circuit including acting as a switch, amplifier, or current regulator. A transistor works by allowing a small amount of current applied at the base to control general current flow from collector to emitter through the transistor.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

c⁵ x 4c⁷
(1 x 4)c^{(5 + 7)}
4c¹²

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE linearly while an increase in speed increases KE exponentially.

Capacitors store electricity and are used in circuits as temporary batteries. Capacitors are charged by DC current (AC current passes through a capacitor) and that stored charge can later be dissipated into the circuit as needed. Capacitors are often used to maintain power within a system when it is disconnected from its primary power source or to smooth out or filter voltage within a circuit.

Resistors are used to limit voltage and/or current in a circuit and can have a fixed or variable resistance.  Variable resistors (often called potentiometers or rheostats) are used when dynamic control over the voltage/current in a circuit is needed, for example, in a light dimmer or volume control.

During the power stroke, just before the piston reaches top dead center, the spark plug fires and ignites the compressed air-fuel mixture. The resulting expansion due to combustion pushes the piston back down the cylinder toward bottom dead center.

Hydraulics is the transmission of force through the use of liquids. Liquids are especially suited for transferring force in complex machines because they compress very little and can occupy very small spaces. Hydraulic pressure is calculated by dividing force by the area over which it is applied: P = F/A where F is force in pounds, A is area in square inches, and the resulting pressure is in pounds per square inch (psi).

The Doppler effect occurs when the source or listener (or both) of sound waves is moving. If they're moving closer together, the listener perceives the sound with a higher pitch and, when they're moving apart, the listener perceives the sound with a lower pitch.

Approximately every 28 days during female ovulation an egg (ovum) is released from one of the ovaries and travels through the oviduct (fallopian tube) and into the uterus. At the same time, the endometrial lining of the uterus becomes prepared for implantation.

There are 4 5-passenger taxis available so that's 4 x 5 = 20 total seats. There are 23 people needing transportation leaving 23 - 20 = 3 who will have to find other transportation.