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The voltage of the alternating current coming through an electrical outlet can be modeled by the function V(t) = 167 sin(110πt), where t is measured in seconds and V in volts. Find all times at which the voltage is at its maximum. (Let k be any integer.

Respuesta :

Answer:

[tex]t = \frac{(4k + 1) }{220 } \\[/tex] for k =0, 1,2,3............

Step-by-step explanation:

From the function [tex]V(t) = 167 sin (110\pi t)[/tex]

[tex]V_{max} = 167 V[/tex]

For [tex]V_{max} = 167[/tex],

[tex]sin (110\pi t) = 1[/tex] ...................(1)

That is, [tex]sin\frac{(4k + 1)\pi }{2}[/tex] = 1...............(2)

Comparing equations (1) and (2)

[tex]110\pi t = \frac{(4k+1)\pi }{2}[/tex]

[tex]t = \frac{(4k + 1)\pi }{2(110\pi) } \\t = \frac{(4k + 1) }{220 } \\[/tex]

For all positive integer values of k, i.e. k = 0, 1, 2, ........

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