the dome over a town hall has a parabolic shape. the dome measures 48 m across and rises 12m at the centre. A vertical column needs to be attached to the dome at a point that is 4m away from its rim. How tall is the dome at this point? Also, what is the equation that models the shape of this dome?
math - MathMate, Friday, August 31, 2012 at 11:15am
Take the vertex of the parabola at x=0.
Then the equation of the parabola (opening downwards) is y=12-ax^2 where a is a constant to be found.
We know that y=0 at x=±24 (half span), so
The equation of the parabola is therefore
I will let you finish the problem.
math - Erica, Friday, August 31, 2012 at 11:23am
all these numbers kind of confuse me. Im not sure what ^ means. Right now the only equation i have learned is y= a(x-s)(x-t)
math - MathMate, Friday, August 31, 2012 at 11:39am
x^2 means x squared, or x².
If you just started with parabolas, it won't hurt to say what you've learned so far.
Let's start over:
We first assume the vertex of the parabola is at x=0.
We know that y=0 at x=±24, or
We also know that y=12 at x=0, i.e.
The equation of the parabola is therefore:
Can you then continue?
math - MathMate, Friday, August 31, 2012 at 11:41am
Correction to one of the above lines: