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As their names indicate, a step-up transformer is used to step up or increase voltage and a step-down transformer is used to step down or decrease voltage. In a step-up transformer, the secondary voltage is higher than the primary voltage and it has more turns in the secondary winding than in the primary winding.

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

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

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.

The primary difference between internal and external combustion engines lies in where the power is developed. In an internal combustion engine fuel is ignited and burned inside the same container where the power is developed while in an external combustion engine the fuel is ignited outside the engine and the resulting power sent to it.

Wrenches are used with threaded fasteners like bolts and nuts. A bolt has external threads while a nut has internal threads and this thread pattern combination allows them to lock together and act as fasteners. Nuts come in a variety of configurations including wing nuts which provide appendages that allow tightening and loosening by hand, slotted nuts that use a cotter pin to lock the nut in place and prevent it from loosening, and lock nuts that also prevent loosening via nylon in their threads. Threads are identified by pitch which is the number of threads per inch.

Direct current flows in only one direction in a circuit, from the negative terminal of the voltage source to the positive. A common source of direct current (DC) is a battery.

A compound is a substance containing two or more different chemical elements bound together by a chemical bond. In covalent compounds, electrons are shared between atoms. In ionic compounds, one atom borrows an electron from another atom resulting in two ions (electrically charged atoms) of opposite polarities that then become bonded electrostatically.

If 68% of the town's 29,000 voters cast ballots the number of votes cast is:

(\( \frac{68}{100} \)) x 29,000 = \( \frac{1,972,000}{100} \) = 19,720

The mayor got 86% of the votes cast which is:

(\( \frac{86}{100} \)) x 19,720 = \( \frac{1,695,920}{100} \) = 16,959 votes.