How to Solve for the Width and Domain/Range of a Sloping Roof?

[Nelo]

Homework Statement

Sloping roof : The diagram shows a set of coordinate axes superimposed on the cross section of a sloping roof of height h metres and width w metres. The equation of one half of the cross section is

y=-0.7x + 1.9

a) What is the equation of the other half of the cross section? 0.7x + 1.9
b) What is the height of the roof h? 1.9
c) What is the width of the roof, w, to the nearest tenth of a metre?
d) State the domain/range of the function that models each half of the roof.

How do i do part c and d?

Homework Equations

The Attempt at a Solution

No idea where to even begin

 

[tiny-tim]

Hi Nelo!

For c), what is the value of y at the two ends of the roof? And so what is the value of x ?

For d), just draw a graph, using the answers to a) b) and c).

 

[berkeman]

Homework Statement

Sloping roof : The diagram shows a set of coordinate axes superimposed on the cross section of a sloping roof of height h metres and width w metres. The equation of one half of the cross section is

y=-0.7x + 1.9

a) What is the equation of the other half of the cross section? 0.7x + 1.9
b) What is the height of the roof h? 1.9
c) What is the width of the roof, w, to the nearest tenth of a metre?
d) State the domain/range of the function that models each half of the roof.

How do i do part c and d?

Homework Equations

The Attempt at a Solution

No idea where to even begin

On c) you have two triangles that form the left and right halves of the roof. Use trig to calculate the lengths of the bases of those triangles.

On d), do you know what the domain and range of a function are?

 

[berkeman]

Dang it! TT strikes again!

 

[eumyang]

c) What is the width of the roof, w, to the nearest tenth of a metre?

Find the x-intercepts of both equations. Then find the distance between the x-intercepts.

d) State the domain/range of the function that models each half of the roof.

You should know the domain and range for lines. However, you are only interested in the line segments that form the roof. The x-intercept and the height (y-intercept) should give you a clue.

EDIT: Beaten to it by TWO!

 

[Nelo]

I solved the x intercepts as plusminus 2.714 x.x

 

[Nelo]

The x intercepts are plusminus 2.714, what do you mean find the distance between? like, 2.7 + 2.7 = 5.4 , so the width is 5.4m ?

for domain and range,

I just graph -0.6x + 1.9 (a line with a vertical compression of 0.6?) and reflected?

And the line 0.6x+1.9 being the f(x) and the top being a reflection on x axis?

 

[berkeman]

The x intercepts are plusminus 2.714, what do you mean find the distance between? like, 2.7 + 2.7 = 5.4 , so the width is 5.4m ?

Looks reasonable.

 

[Nelo]

0.7 is 7/10 as a fraction, do i rise 7 run 10? how do i graph that x.x

also, does that mean that one equation taht represents height is this:

y= -0.7x + 1.9

and the other eq, that rep width is this?

y= 0.7x + 2.7 ?

 

[Nelo]

?? anyone?

 

[Strants]

0.7 is 7/10 as a fraction, do i rise 7 run 10? how do i graph that x.x

You have the slope right. As far as graphing goes, just treat it like any other line. Also, keep in mind 3.5/5 = 7/10, so for every five units you travel right, you should travel 3.5 units up.

also, does that mean that one equation taht represents height is this:

y= -0.7x + 1.9

If that was the equation, the roof would be taller than 1.9 m if x was less than zero, correct? The height function should look like the roof itself, so what kind of function 'deflects' like the roof?

and the other eq, that rep width is this?

y= 0.7x + 2.7 ?

x=0 corresponds to the peak of the roof, right? If so, do you think that the width at the peak is 2.7 m?

 

[Nelo]

*sigh* I have no idea, I just need to memorize how to do these by tommorow I usually just follow the script, so far I still don't get what the equations are so i can graph them

 

[berkeman]

*sigh* I have no idea, I just need to memorize how to do these by tommorow I usually just follow the script, so far I still don't get what the equations are so i can graph them

The equations are for two lines, using the form y(x) = mx + b. That looks familiar, right? What is the "m" term? What is the "b" term?

Just plot the two lines that you have specified:

y(x) = -0.7x + 1.9

y(x) = 0.7x + 1.9

Where do these two lines cross? Where do they intersect the y axis? Where do they intersect the x axis?

 

[Nelo]

um, the lines both cross at 1.9 on the y-axis and cross at -2.5 on the x-axis for the positive root... and at 2.5 for the reflected root

 

[Strants]

um, the lines both cross at 1.9 on the y-axis and cross at -2.5 on the x-axis for the positive root... and at 2.5 for the reflected root

For the roof, the lines only make sense between were they intersect each other and where the intersect the x-axis. So, what x values 'make sense' for the lines?

 

[Nelo]

If they only make sense at the value they intersect at, then they are both going to have 1.9 and ones going to be -2.5 and one is going to be 2.5 , right?

 

[Strants]

Not quite, but you have the right idea. The roof starts out at (-2.5, 0) and keeps going up until it hits the point (0, 1.9). So, for the equation that represents the left half of the roof (when it slopes upward), the only valid x values are between the x values of those two points. Does that make sense? (I'm not sure if I did a good job explaining it).

[EDIT] Also, I think it should be -2.7 instead of 2.5, since 1.9/0.7 = 2.7

 

[Nelo]

right... the roof starts and ends... the values between those points are only valid, like the triangle that is formed. how dose that help me though

 

[Strants]

Well, let's keep thinking about the left side of the roof for now. The only valid x are -2.7<=x<=0. That's the domain, since the domain is the only x values a function makes sense on, so to speak. By the same token, the range is the only y values a function makes sense on. Can you see what the range is (what y values make sense for a roof?)

 

[Nelo]

Y values of roof are 0<==y==2

 

[Strants]

Well, actually 1.9 instead of 2, but other than that, yeah, that's right (Don't look off your graph for the exact values; the equations are much more exact). That means that, for the part of the functions y = 0.7x + 1.9 (the left part of the root), the domain is -2.7\le x\le 0 and the range is 0\le y \le 1.9. Can you see how to do it for the right side of the roof, now?

 

[Nelo]

K, well i think i got it.
the two equations are

y(x) = -0.7x + 1.9

y(x) = 0.7x + 1.9


only looking at the triangle/roof it creates you determine the domain/range points... honostly, that wasnt even what i was asking i was just asking if the equations were right that just wasted like 45 minutes of my study time because the rest is simple

thank you though

 

[Strants]

Sorry, I guess I though you were asking something different. . .
And you're welcome, of course.

 

[Nelo]

Id love it if you could help me here though :)

https://www.physicsforums.com/showthread.php?t=515150