Respuesta :
Answer:
a). Horizontal distance = 11.1 m
b). Maximum height = 6.2 m
c). Firefighter is 13.7 m from the house
Step-by-step explanation:
Given question is incomplete; find the complete question in the attachment.
Height of the water can be determined by the expression,
h(x) = -0.026x²+ 0.577x + 3
Here x = Horizontal distance of the from the firefighter
a). Since the stream of the water will follow a parabolic path, maximum point of the parabola will be = Vertex of the parabolic path
Horizontal distance from the firefighter at which the water achieves the maximum height = -[tex]\frac{b}{2a}[/tex]
From the quadratic function,
h(x) = -0.026x²+ 0.577x + 3
a = -0.026
b = 0.577
Therefore, the horizontal distance = [tex]-\frac{0.577}{2\times (-0.02612)}[/tex] = 11.05 m
≈ 11.1 meters
b). By putting x = 11.1 in the quadratic equation,
h(x) = -0.02612(11.1)²+ 0.577(11.1) + 3
= -3.2182 + 6.4047 + 3
= 6.18 m
≈ 6.2 m
c). For h(x) = 6 m
6 = -0.02612x² + 0.577(x) + 3
0.02612x² - 0.577x + 3 = 0
From quadratic formula,
x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
x = [tex]\frac{0.577\pm \sqrt{(-0.577)^2-4(0.02612)(3))}}{2(0.02612)}[/tex]
x = [tex]\frac{0.577\pm\sqrt{0.019489}}{0.05224}[/tex]
x = [tex]\frac{0.577\pm0.1396}{0.05224}[/tex]
x = 13.7 m, 8.37 m
Therefore, the farthest distance of the firefighter from the house will be 13.7 m
