A railroad tunnel is shaped like a semiellipse, as shown below.

A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.

The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.

Radii ok and nl are perpendicular to om because of the radius-tangent theorem. by definition of perpendicular, angles kom and lnm are right angles. this means that triangles kom and lnm are right triangles. angle lmn is common to both right triangles, so by the triangles kom and lnm are similar.

Expresa commuter train leaves downtown sation and travels at a average speed of 55 miles per hour towards the north side sation, which is 50miles away. thirty minutes later, express commuter train #7 leaves north side and travels at a average speed of 35miles per hour towards downtown sation. at the moment the two trains pass each other, how far(in miles) is train #12 from the downtown sation and how long(in minutes) has the #12 train been traveling

What is always true about a positive integer raised to a negative odd power?