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An electric current can be represented by the functior y=2cos (2π (x-0.02)) ), with time in æ seconds. How many times is the electric current at a minimum on the interval 0 ?

a. 4
b. 6
c. 7
d. 5

User Lordoku
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1 Answer

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Final answer:

The electric current described by a cosine function will reach a minimum twice in each cycle, corresponding to each odd multiple of π/2 within the function's argument. Without the exact interval length, the exact number of minima cannot be provided.

Step-by-step explanation:

Regarding the student's question about how many times the electric current is at a minimum in the given time interval using the function y=2cos(2π(x-0.02)), we first understand this represents an alternating current (AC) which varies sinusoidally with time.

The electric current reaches its minimum value when the cosine function is at its minimum, which is -1. The cosine function completes a full cycle every time its argument changes by 2π. So, we look for the argument 2π(x-0.02) to be an odd multiple of π/2 for the current to be at a minimum.

The argument increases by 2π for every 1 second of time, so in 1 second, there will be one complete cycle, which means there are two minimums (one atcos(π) and another at cos(3π)). In the interval from 0 to Ą seconds, we will have Ą cycles and thus Ą*2 minima.

We cannot provide an exact answer without knowing the value of Ą, but with the understanding of the behavior of a cosine function, we can deduce the pattern of minima.

User Gavin Thomas
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