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Question 6Points 3The Gateway Arch in a city has the shape of a catenary (a U-shaped curve similar to aparabola). It can be approximated by the following model, where x and y aremeasured in feet.y=-(3/1000)x + 400)x - 400). How high is the arch?

Question 6Points 3The Gateway Arch in a city has the shape of a catenary a Ushaped curve similar to aparabola It can be approximated by the following model wher class=

Respuesta :

Explanation:

The model is given below as

[tex]=-\frac{3}{1000}(x+400)(x-400)[/tex]

To figure out the value of the height of the we will expand the brackets

[tex]\begin{gathered} -\frac{3}{1000}(x+400)(x-400) \\ =-\frac{3}{1000}(x^2-160000) \end{gathered}[/tex]

With no x-term, the vertex is at x=0

Substitute x=0,to get y

[tex]\begin{gathered} =-\frac{3}{1000}(0-160000) \\ =-\frac{3}{1000}\times-160000 \\ =480feet \end{gathered}[/tex]

Using the graphical method, we will have

Hence,

The final answer is

[tex]\Rightarrow480feet[/tex]

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