# Mathematical Help needed with rational exponents and complex numbers

**Question description**

*Answers and explanations

1. Write as a single power of 2. Carefully show each step of your work.

2. Police departments find it very useful to be able to approximate driving speeds in skidding accidents. If the road surface is wet concrete the function is *S*(*x*) = is used, where *S*(*x*) is the speed of the car in miles per hour and *x* is the distance skidded in feet.

a. Fill out the table for each of the distances shown below. Round to the nearest whole number:

b. Find the distance the car will skid if the speed of the car is 60 miles per hour.

Round to two decimal places.

3. Complex numbers are used by engineers and physicists to measure electrical circuits. To measure voltage, they use the formula E = *I* • *Z*, where *E* is voltage in volts, *I* is the current in amps, and *Z* is impedance, or resistance, in ohms.

a. Find the voltage for an electrical circuit if the current is 3 - 4*i* amps and the impedance is 2 + *i*ohms. Simplify your answer completely.

b. Find the Impedance for an electrical circuit if the voltage is 18 - 24*i* and the current is 6 - 3*i*amps. Simplify your answer completely.

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