The arch of a bridge is a semi ellipse, the span is thirty feet and the top of the arch is ten feet above the major axis. the roadway is horizontal and is two feet above the arch. find the vertical distance from the roadway to the arch at five feet intervals in order to calculate our costs

What is your school SUBJECT? Math? Physics?

It is math, i take a pre-calc/calc class.

sorry!

chanfe

To find the vertical distance from the roadway to the arch at five feet intervals, we need to determine the equation of the semi-ellipse and then substitute different x-values in order to calculate the corresponding y-values.

First, let's consider the equation of an ellipse centered at the origin with an equation of the form:

(x^2 / a^2) + (y^2 / b^2) = 1

Since we are dealing with a semi-ellipse, we can assume that a is the span divided by 2 (half of the span) and b represents the distance from the top of the arch to the major axis.

Given that the span is thirty feet, a = 30/2 = 15 feet.

Also, we know that the top of the arch is ten feet above the major axis, so b = 10 feet.

Thus, the equation of the semi-ellipse can be written as:

(x^2 / 15^2) + (y^2 / 10^2) = 1

Simplifying the equation, we have:

(x^2 / 225) + (y^2 / 100) = 1

Now, we can substitute various x-values at five feet intervals (starting from x = -15 to x = 15) into the equation to calculate the corresponding y-values. This will give us the vertical distance from the roadway to the arch at these points.

For example, when x = -15:

((-15)^2 / 225) + (y^2 / 100) = 1

225/225 + (y^2 / 100) = 1

1 + (y^2 / 100) = 1

(y^2 / 100) = 0

y^2 = 0

y = 0

Hence, at x = -15, the vertical distance from the roadway to the arch is 0 feet.

Similarly, you can substitute x-values of -10, -5, 0, 5, 10, and 15 to calculate the corresponding y-values, giving you the vertical distances at those intervals.

By finding these vertical distances at five feet intervals, you can calculate the costs associated with the construction or maintenance of the arch.