Answer:
1) The absolute value function equation of the graph is [tex]y = \left | 11.76 \times \left | x - 72.5 \right | - 853 \right |[/tex]
Please see attached graph
2) Yes, It does matter where the building is positioned
3) The domain of the function is 0 < x < 145
The range of the function is 0 < y < 853
4) 4.5 ft from the center
Step-by-step explanation:
The given width = 145 ft
The height = 853 ft
The slope = 853/(145/2) ≈ 11.766
Placing the left base of the pyramid at the origin of the graph with coordinates, (0, 0)
We have;
The y-intercept = 0
The equation becomes;
y = 11.766× x +0
When x > 72.5, we have;
The slope ≈ -11.766
Noting that the slope changes at the center with coordinates x = 72.5, when we multiply the slope by the difference between an x-coordinate value and the midpoint value and subtract that from the height of the building, we get the negative value of the height of the location at that value of x as follows;
[tex]-y_x =11.76 \times \left | x - 72.5 \right | - 853 \right |[/tex]
Therefore, we look for the absolute value of the above expression to get the height of a point, with an horizontal distance of x ft from the left base of the building as follows
[tex]y = \left | 11.76 \times \left | x - 72.5 \right | - 853 \right |[/tex]
The absolute value function equation of the graph is presented as follows;
[tex]y = \left | 11.76 \times \left | x - 72.5 \right | - 853 \right |[/tex]
2) It does matter where the building is positioned because, that determines the relation for the x-value and the center of the building, where the slope changes to negative
3) The domain of the function is 0 < x < 145
The range of the function is 0 < y < 853
4) At 800 ft, we have;
[tex]80 = \left | 11.76 \times \left | x - 72.5 \right | - 853 \right |[/tex]
x = (800 + 853)/11.766 - 72.5 ≈ 68 ft
Therefore, given that the center is at 72.5 ft from the origin, he will be 72.5 - 68 ≈ 4.5 ft from the center
