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The hours of daylight, y, in Utica in days x from January 1, 2013 can be modeled by the equation y = 2.89sin(0.0145x-1.40) + 10.99. How many hours of daylight, to the nearest tenth, does this model predict for February 21, 2013?

Respuesta :

MrRoyal

Answer:

9.3 hours

Step-by-step explanation:

Given

[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]

Required

Hours of sunlight on Feb 21, 2013

First, calculate the number of days from Jan 1, 2013 to Feb 21, 2013

[tex]days = 52[/tex]

So:

[tex]x = 52[/tex]

So, we have:

[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(0.0145*52-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(0.754-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(-0.646) + 10.99.[/tex]

[tex]y = 2.89*-0.6020 + 10.99.[/tex]

[tex]y = -1.740 + 10.99.[/tex]

[tex]y = 9.25[/tex]

[tex]y = 9.3[/tex] --- approximated