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The shape of the Gateway Arch in St. Louis,
Missouri resembles a parabola with the
equation h - 0.00635x^2 +4.0005x -0.07875,
where h is the height in feet and z is the
distance from one base in feet,
What is the distance from one base of the arc
to the other? This answer to the nearest foot is equal to u.

The shape of the Gateway Arch in St Louis Missouri resembles a parabola with the equation h 000635x2 40005x 007875 where h is the height in feet and z is the di class=

Respuesta :

Answer:

630 ft

Step-by-step explanation:

The equation of the parabola shaped arc is given as:

[tex]h =-0.00635x^2 +4.0005x -0.07875[/tex]

In a parabola, the line of symmetry divides the parabola into two equal parts.

Therefore, to find the distance from one base of the parabola to the other, we simply multiply the x-value at the line of symmetry by 2.

For a quadratic equation of the form [tex]y=ax^2+bx+c[/tex]:

  • Equation of symmetry: [tex]x=-\dfrac{b}{2a}[/tex]

Therefore, distance from one base of the arc  to the other

[tex]=-\dfrac{b}{2a} X 2\\\\=-\dfrac{b}{a}[/tex]

In our given equation:

[tex]a=-0.00635, b=4.0005\\$Therefore:Distance = $ -\dfrac{4.0005}{-0.00635}\\=630$ ft[/tex]

The distance from one base of the arc  to the other is 630 ft.

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