SOLUTION: my problem states that the shape of a supporting arch can be modeled by H(x) = -0.03x^2 + 3x where h(x) represents the height of the arch and x represents the horizontal dist

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Question 173552: my problem states that the shape of a supporting arch can be modeled by
H(x) = -0.03x^2 + 3x
where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch.
I need a step by step instruction on how to do these types of problems.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
my problem states that the shape of a supporting arch can be modeled by
H(x) = -0.03x^2 + 3x
where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch.
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I don't know what level of math you're in, but max and min problems use the 1st derivative of the function.
h(x) = -0.03x^2 + 3x
Set the 1st derivative to zero.
0 = -0.06x + 3
0.06x = 3
x = 50 meters
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h(50) = -0.03*2500 + 150
= -75 + 150
h = 75 meters

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
H(x) = -0.03x^2 + 3x
where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch.
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The shape of that equation is a parabola. It has either a maximum
point or a minimum point. Your equation has a maximum.
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That maximum occurs when x = -b/2a = -3/(2*-0.03) = 50
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So the maximum height is H(50) = -0.03(50)^2 + 3*50 = 75 ft.
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Cheers,
Stan H.