An arch is in the form of a semi-ellipse, with its major axis as the span. If the span is 80 feet and the height is 30 feet write the standard equation.

12th. It's supposed to be pre-calculus, but I question whether it really is. I don't get it either.

To write the standard equation of a semi-ellipse, we need to consider its major axis, minor axis, and center. In this case, the major axis is the span, which is given as 80 feet, and the height is given as 30 feet.

The major axis is twice the length of the semi-major axis, so the semi-major axis is half of the major axis, which in this case is 80/2 = 40 feet. The semi-minor axis is the height of the semi-ellipse, which is 30 feet.

Now, let's consider the center of the semi-ellipse. Since the semi-ellipse is symmetric about its major axis, the center of the semi-ellipse lies on the major axis at the midpoint.

Therefore, the center of the semi-ellipse is at (0, 0) because the major axis is the x-axis in this case.

Now, we can write the standard equation of the semi-ellipse:

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

where (a, b) represents the semi-major and semi-minor axes, respectively.

Plugging in the values we found, the standard equation of the semi-ellipse is:

x^2/40^2 + y^2/30^2 = 1

Hence, the standard equation of the semi-ellipse is x^2/1600 + y^2/900 = 1.