Analytic Geometry Answers

Denote by a, b and c the column vectors a = (1 2 3), b = (-2 1 -3), c = (-2 -1 1) Calculate 2a - 5b, 2a- 5b +c, a'.b,

To find a missing side length set up and solve a ____________________. Put the measurements of the smaller figure on top and the bigger figure on the bottom.

An engineer is working on making a diagram for the cooling tower he was going to construct in the future. Cooling towers can be seen as towers with inward curving sides, or simply, hyperbola looking sides. His daughter asks him how high the center of the hyperbolic sides of tower was y=±(24/7)x+15 and the answers that the asymptotes of the hyperbola are the following, and the area of itsa auxilliary rectangle is 168 squats units. The daughter then find the foci of the hyperbola. At what points on the cartesian plane are these foci found

A big room is constructed so that the ceiling is a dome that is semielliptical in shape. If a person stands at one focus and speaks, the sound that is made bounces off the ceiling and gets reflected to the other focus. Thus, if two people stand at the foci (ignoring their heights), they will be able to hear each other. If the room is 34 m long and 8 m high, how far from the center should each of two people stand if they would like to whisper back and forth and hear each other?