SOLUTION: an engineer is designing a parabolic arch must be 15 m high and 6 m wide at a height of 8 m.
what is the width of the arch at its base
Determine a quadratic function that s
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Question 663248: an engineer is designing a parabolic arch must be 15 m high and 6 m wide at a height of 8 m.
what is the width of the arch at its base
Determine a quadratic function that satisfies these condition.
What is the width of the arc at its base?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Since the shape of the desired parabola is constant under any arbitrary translation of axes, you can pick any point with an ordinate of 8 as the point where the width of the arch must be 6 units. It will be convenient to select the point (0,8) as one of the points on the parabloa at the level where the width is 6. Given that desired width, there must also be a point on the parabola at (6,8). Using symmetry and the requirement that the arch be a 15 units high at apex, the vertex of the parabola has to be at the point (3,15).
A parabola can be described by the following funcition:
\ =\ ax^2\ +\ bx\ +\ c)
Using the coordinates of the three points:
\ =\ a(0)^2\ +\ b(0)\ +\ c\ =\ 8)
\ =\ a(3)^2\ +\ b(3)\ +\ c\ =\ 15)
\ =\ a(6)^2\ +\ b(6)\ +\ c\ =\ 8)
From the first equation we get
The other two equations become:
Solve the 2X2 system for 
and 
; you already know 
.
Then substitute into
To create the desired function.
Find the two zeros of the function, then calculate the absolute value of the difference between the two zeros.
John
My calculator said it, I believe it, that settles it
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