# math

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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 -

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
0=12-a(24^2)
=>
a=12/576=1/48
The equation of the parabola is therefore
y=12-x^2/48.

I will let you finish the problem.

• math -

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 -

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
y=a(x-24)(x+24).
We also know that y=12 at x=0, i.e.
12=a(0-24)(0+24)=-576
so a=12/(-576)=-1/48
The equation of the parabola is therefore:
y=(x-24)(x+24)/48

Can you then continue?

• math -

Correction to one of the above lines:

12=a(0-24)(0+24)=-576a

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