How Do You Model a House Structure Using Mathematical Equations?

[aisha]

Im given a picture of a house, There is a traingular arch on top of the entrance held up by 2 pillars.
point *

l___________l
l___________l
l___________l
10 ft

The distance between the pillars is 10 ft the pillars are 7 ft high and distance from the ground to the triangle arches point is 10ft.

The question said to sketch the pillars and arch on a grid, which I did.

1.)It says for each of the two pillars, determine an equation that models it?
and then state the domain and range of each equation. (I don't even know where to start on this)

2)also determine the function that models the triangular arch. (I have no idea!) state the domain and range

 

[apchemstudent]

Im given a picture of a house, There is a traingular arch on top of the entrance held up by 2 pillars.
point *

l___________l
l___________l
l___________l
10 ft

The distance between the pillars is 10 ft the pillars are 7 ft high and distance from the ground to the triangle arches point is 10ft.

The question said to sketch the pillars and arch on a grid, which I did.

1.)It says for each of the two pillars, determine an equation that models it?
and then state the domain and range of each equation. (I don't even know where to start on this)

2)also determine the function that models the triangular arch. (I have no idea!) state the domain and range

For 1) did you number your coordinates? The domain and range will all be dependent on where you place your pillars. I'm assuming the pillars will just be a line. The domain will be whatever x value the pillar is restricted to. The Range will be the height of the pillar.

For 2) It will be an absolute value equation. It's hard to explain, so it might be easier if you do 1 first.

 

[aisha]

yes i understand that the eqn for the arch will be an absolute value one but what about the pillars? What is the equation for the straight pillars? I don't understand how to do this.

 

[apchemstudent]

yes i understand that the eqn for the arch will be an absolute value one but what about the pillars? What is the equation for the straight pillars? I don't understand how to do this.

It will be a vertical line... x = whatever...

 

[aisha]

It will be a vertical line... x = whatever...

x=0 and x=10? ok I know that much but I am wondering these lines will go on forever how do I make them stop at 7ft?

 

[apchemstudent]

x=0 and x=10? ok I know that much but I am wondering these lines will go on forever how do I make them stop at 7ft?

That's where the range comes in...

 

[aisha]

x=0 y=7 , and x=10 y=7?

When there is range this doesn't look like an equation anymore it looks more like a pair of coordinates.

 

[dextercioby]

x=0 y=7 , and x=10 y=7?
When there is range this doesn't look like an equation anymore it looks more like a pair of coordinates.

They're the coordinates of the pillars' tops.(?,correct English word?? ).However the equation for the pillars are simple:
$$P_{1}:(x=0,0\leq y\leq 7)$$ and $$P_{2}:(x=10,0\leq y\leq 7)$$
Tell us (u didn't make the drawing available) what shape that triangle has.Is it isosceles??If so,the problem to find the equations for its three sides is terribly simple.

Daniel.

PS.For the pillars,u can use the 'closed interval' notation.

 

[aisha]

yes the triangle on top of the pillars is an isosceles triangle

 

[dextercioby]

yes the triangle on top of the pillars is an isosceles triangle

In that case,it's terribly silmple.The base of the triangle is a horizontal bar stretching from 'x=0' to 'x=10' at the height of 'y=7'.It's trivial to write down the equation.Now,in that isosceles triangle on top of the pillars u know the height (the total height of the of the house-the height of the pillars) and the base (formed from 2 sides of 5(m?)on one and on the other side of the height).Use trigonometry to find the angles,and then if you have the equations for the 2 segments are easy to write.

Daniel.

 

[aisha]

ok which angles am I solving for and what do u mean by segments?

 

[dextercioby]

The angles in the isosceles triangle,of course.U only need to know one of them,since 2 are equal and the sum in 180°.U'll be needing the angle between the horizontal pillar and one of the verticals joining at the summit of the arch.
"Segment"??I believe it's the word to describe the line between 2 fixed points...??

Daniel.