SOLUTION: 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
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Question 165510: 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. Show work.
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Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
Solve the equation for x = 0;
-.03x^2 + 3x = 0
:
Factor out -.03x
-.03x(x - 100) = 0
x = 0
and
x = 100 meters is the width of the base of the arch
:
Find the maximum height of the arch.
:
Max height occurs halfway, at x = 50 (axis of symmetry)
:
Substitute 50 for x in the original equation
:
h(x) = -.03*50^2 + 3(50) = 0
h(x) = -75 + 150
h(x) = 75 meters is the height
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