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A few questions I need help figuring out how to do.

1. Given g(x) = 2tan4(x - pi/2) state the equation(s) of the asymptote(s) over a domain of 0 to pi

2. During an experiment, the intensity i(t) of the electric current of a device as a function of time (t) elapsed since the beginning of the expression is given by:

i(t) = 6sin((pi)(t)/12 + 2pi/3)) + 6 where t is expressed in seconds

The device emits a sound signal each time the current's intensity is equal to 9. The experiment lasts 120 seconds. How many sound signals does the device emit during the experiment?

Sorry I took so long.

1. I believe there is a vertical assymtote at x - pi/2 = pi/2. Add pi/2 to both sides and then add on the fact that it occurs every time x is this value plus or minus pi.

2. For the intensity to be exactly 9, it occurs twice every cycle of the sin().

If the function were sin(x), the cycles would be 2*pi.

Multiply this by the inverse of the multiplier on x, giving 2*pi*12/pi = 24.

To look at it another way, note that the sin() function repeats for every passage of 2*pi in the x. That would give an indication it repeats very 24 seconds. Since 120 = 5*24, this means it repeats the cycle 5 times. Since it crosses the value 9 twice in every interval,

the total number of times would be twice the number of intervals, which is 2*5 = 10.

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