the regression equation ( y = 8.6sin(0.24x - 1.88)+62.8 ) models the fahrenheit temperature in a room ( x )…
the regression equation ( y = 8.6sin(0.24x - 1.88)+62.8 ) models the fahrenheit temperature in a room ( x ) hours after midnight. what is the maximum temperature in the room during the first 24 hours?\n( 54.2^{circ}f )\n( 57.0^{circ}f )\n( 62.8^{circ}f )\n( 71.4^{circ}f )
Answer
Explanation:
Step1: Analizar la función sinusoidal
La función general de una onda sinusoidal es (y = A\sin(Bx - C)+D). Aquí, (A = 8.6), (D=62.8).
Step2: Encontrar el valor máximo
El valor máximo de una función (y = A\sin(\theta)+D) se da cuando (\sin(\theta)=1). Entonces, (y_{max}=A + D). Sustituyendo (A = 8.6) y (D = 62.8) en la fórmula (y_{max}=A + D), obtenemos (y_{max}=8.6+62.8). [y_{max}=71.4]
Answer:
71.4°F