Show that the projection into the xy-plane of the curve of intersection of the parabolic cylinder z=1−5y2 and the paraboloid z=x2+y2 is an ellipse. (a) Find a vector-parametric equation r⃗ 1(t)=⟨x(t),y(t),z(t)⟩ for the ellipse in the xy-plane.

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. the mean arrival rate is 10 passengers per minutes. compute the following probabilities. p(x = 4) p(x > 11)

Polygons efgh and e′f′g′h′ are shown on the coordinate grid: what set of transformations is performed on efgh to form e′f′g′h′? a. a translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin b. a translation 1 unit to the right followed by a 90-degree counterclockwise rotation about the origin c. a 90-degree clockwise rotation about the origin followed by a translation 2 units to the right d. a 90-degree clockwise rotation about the origin followed by a translation 2 units to the left

Which equation represents the partial sum of the geometric series?