Answer:
A) 630 feet
B) 630 feet
C) Domain: [0,630] and Range: [0,630]
Step-by-step explanation:
The gateway arc in St. Louis was built in 1965. It is the tallest monument in the united states.
The modeled of arc, [tex]y=-0.00635x^2+4x[/tex]
where x and y are in feet
Part A) The given model is parabolic curve. The highest point at vertex of parabolic curve.
The x-coordinate of maximum height, [tex]x=-\dfrac{b}{2a}[/tex]
where, a is coefficient of x² and b is coefficient of x
a = -0.00635
b = 4
[tex]x=-\dfrac{4}{2\times -0.00635}[/tex]
[tex]x=314.96[/tex]
Put x = 314.96 into model to get the value of y
[tex]y_{max}=-0.00635(314.96)^2+4(314.96)[/tex]
[tex]y_{max}=629.92\approx 630\text{ feet}[/tex]
Hence, the tallest point of the arch at 630 feet above ground.
Part B) The distance between the legs of arch is difference of zeros of equation.
[tex]-0.00635x^2+4x=0[/tex]
[tex]x=0\text{ and }629.92\approx 630[/tex]
Hence, the legs of the arch 630 feet apart to each other.
Part C)
Domain: It is input value of x where function is defined.
Range: It is output value of function for all defined value of x.
For this model, It is a function of arch. So, y value can't be negative.
Therefore,
Domain: [0,630]
Range: [0,630]
