Common household electric current is called alternating current because the current alternates direction within the wires. The voltage V in a typical 115-volt outlet can be expressed by the function V(t)=163 sin wt Upper V left parenthesis t right parenthesis equals 163 sine omega t ,

where omega=w

is the angular speed (in radians per second) of the rotating generator at the electrical plant and t is the time measured in seconds. It is essential for electric generators to rotate at precisely 60 cycles per sec.

How many times does the current oscillate in 0.30

sec?__times

n = 18 cycles

Step-by-step explanation:

To know how many times does the current oscillates in the given time, you take into account that the number of oscillation can be calculated by using the following expression:

        (1)

f: frequency of the oscillation of the current

t: time = 0.30s

The frequency is the number of cycles per second, that is, f = 60 cycles/s

You replace the values of f and t in the equation (1):

In 0.30s the current oscillates 18 times

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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