Question

The gateway arch in St. Louis was built in 1965. It is the tallest monument in the US. The arch can be modeled with the function y= -0.00635x2+4x where x and y are in feet.
question A: how high above the ground is the tallest point of the arch?
question B: how far apart are the legs of the arch at their bases?
~*show work* especially equations please!

Answer 1

First, do you know about derivatives?

Answer 2

No. I have no idea what I am doing tbh. this is a old assignment that I now realize I need to makeup

Answer 3

Alright. So we can instead use the vertex...

What you have is a quadratic equation...in the form Ax² + bx...

The vertex = -b/2a

so here that would be

\[\large \frac{-4}{2 \times -0.00635 }\]

Solve that and you will have the maximum height...

Answer 4

for part B...this quadratic looks like an upside down parabola...so it will go through the x-axis 2 times....in other words...this equation will = 0 at 2 different points...this is what you want to find...so plug your equation into the quadratic formula and solve for 'x'

\[\large\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Answer 5

Are you sure about those? because i solved the x=-b over 2(a). and got -314.9606299.
and for part B. I just learned that equation today, and this assignment was from a while ago, so I don't think it would pertain to the question?

Answer 6

for the first one...

-b / 2a would be

\[\large \frac{-4}{2 \times -0.00635 }\]
\[\large \frac{-4}{-0.0127 }\]
Which a negative divided by a negative is a positive so this is 314.96

Answer 7

now you would put that number in the original equation for 'x' and solve...this will be your tallest part.

Answer 8

which I did and rounded to -315 which isn't that big of a deal when I'll get close to the answer my teacher wants.

Answer 9

I got y= -4677.8

Answer 10

I don't think thats right

Answer 11

-0.00635(315)^2+4(315) = roughly 630...you need to make sure to use parenthesis or you will get the wring answer

Answer 12

I did.
I hate math so much omg.

Answer 13

y= -1,890.1