Match the graph and the parametric equations (labeled I- VI). Give reasons for your choices.&nbsp;x=cos⁡8t&nbsp;,&nbsp;y=sin⁡8t&nbsp;,&nbsp;z=e0.8t,&nbsp;t≥0

Question

Match the graph and the parametric equations (labeled I- VI). Give reasons for your choices.&amp;nbsp;x=cos⁡8t&amp;nbsp;,&amp;nbsp;y=sin⁡8t&amp;nbsp;,&amp;nbsp;z=e0.8t,&amp;nbsp;t≥0

Cherry McCormick · Accepted Answer

Step 1  Elimination. Previously, we learned that the parametric equation x=cos⁡8t and y=sin⁡8t lie on a circle on the xy-plane in R2. In R3, these parametric equations lie on a cylinder pointing to the z-axis. Only IV and VI fits this criterion as they are circular and the circles are oriented along the xy-plane. We have answered VI earlier so this must be IV. Lets

giskacu · Accepted Answer

Step 1&amp;nbsp;Since&amp;nbsp;x(t)=cos⁡8t&amp;nbsp;and&amp;nbsp;y(t)=sin⁡8t&amp;nbsp;we know that the cylinder is where the curve is&amp;nbsp;x2+y2=1&amp;nbsp;(this is because&amp;nbsp;x2+y2=1&amp;nbsp;implies that the projection of the curve on the xy plane is the unit circle).&amp;nbsp;From&amp;nbsp;z=e0.8t&amp;nbsp;we see that z will increase exponentially as t increases, The sole graph with these characteristics isGRAPH IV&amp;nbsp;Answer&amp;nbsp;GRAPH IV

Match the parametric equations with the graph (labeled I- VI). Give reasons for

Answered question

Answer & Explanation

New Questions in Calculus 2