math
posted by Erica .
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?

Take the vertex of the parabola at x=0.
Then the equation of the parabola (opening downwards) is y=12ax^2 where a is a constant to be found.
We know that y=0 at x=±24 (half span), so
0=12a(24^2)
=>
a=12/576=1/48
The equation of the parabola is therefore
y=12x^2/48.
I will let you finish the problem. 
all these numbers kind of confuse me. Im not sure what ^ means. Right now the only equation i have learned is y= a(xs)(xt)

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(x24)(x+24).
We also know that y=12 at x=0, i.e.
12=a(024)(0+24)=576
so a=12/(576)=1/48
The equation of the parabola is therefore:
y=(x24)(x+24)/48
Can you then continue? 
Correction to one of the above lines:
12=a(024)(0+24)=576a
Respond to this Question
Similar Questions

Calc 3
The actual span of the base of the dome is 143 feet. 1) Use cylindrical coordinates to write the surface of the dome as a function of the distance from the center of the base; that is find z = f (r) . 2) Use your function to find the … 
physics
A particle of mass m is released from rest at the top of a spherical dome of radius R. how far below the starting point will the particle leave the surface of the dome? 
Science: Physics
A spherical metal dome of radius 15 cm is electrically charged. It has a positive charge of +2.5 μC distributed uniformly on its surface. a. Calculate the electric field strength on the surface of the dome. b. Explain how your … 
AP Calculus AB
Please Help! Thank you! An observatory is to be in the form of a right circular cylinder surmounted by a hemispherical dome. If the dome costs twice as much per square foot as the cylindrical wall, what are the most economical proportions … 
physics
The dome of a Van de Graaff generator has a diameter of 32.0 cm and is surrounded by dry air with a 'breakdown' electric field of 3.00 106 V/m. What is the maximum potential of the dome? 
physics (help)
A small object of mass m= 90 kg slides down a spherical dome of radius R=12 m without any friction. It starts off at the top (polar angle θ=0) at zero speed. Use g=10 m/s2. (See figure) (a) What is the magnitude of the force (in … 
Physics(IMPORTANT)
A small object of mass m= 90 kg slides down a spherical dome of radius R=12 m without any friction. It starts off at the top (polar angle Î¸=0) at zero speed. Use g=10 m/s2. (See figure) (a) What is the magnitude of the force (in … 
physics(help)
A small object of mass m= 90 kg slides down a spherical dome of radius R=12 m without any friction. It starts off at the top (polar angle θ=0) at zero speed. Use g=10 m/s2. (See figure) (a) What is the magnitude of the force (in … 
algebra
a hemisphere dome on top of a silo has a diameter of 40 feet, find the volume of the dome r=6cm v=4/3 times 3.14 times radius6cubed 
Geometry
A glass dome covers a pool making an indoor Waterpark. If the height of the dome is 30 feet then what is the surface area of the glass dome?