M408D SPRING 2015 HOMEWORK #6 - cheatham (sc36975) HW06 um...

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cheatham (sc36975) – HW06 – um – (53890)1Thisprint-outshouldhave16questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.00110.0 pointsDetermineAso that the curvey= 6x+ 14can be written in parametric form asx(t) =t3,y(t) =At4.1.A= 52.A=43.A= 6correct4.A=55.A= 46.A=6Determine a Cartesian equation for thecurve given in parametric form byx(t) = 3e2t,y(t) = 4et.00210.0 points3.y=12e8/x4.y=12ex/8correct5.y=14ex/26.y=12ex/4Explanation:We have to eliminate the parametertfromthe equations forxandy.Now from theequation forxit follows thatt=14ex/4.But theny=14ex/41/2=12ex/8.00310.0 points
Determine a Cartesian equation for thecurve given in parametric form byx(t) = 4 ln(4t),y(t) =t .1.y=14ex/42.y=14e4/x5.xy2= 366.xy2= 48Explanation:We have to eliminate the parametertfromthe equations forxandy.Now from theequation forxit follows thatet=x31/2,
cheatham (sc36975) – HW06 – um – (53890)2from which in turn it follows thaty= 43x1/2.Consequently,xy2= 48.00410.0 pointsDescribe the motion of a particle with posi-tionP(x, y) whenx= 4 sint ,y= 3 costastvaries in the interval 0t2π.starting at (0,3) and ending at (4,0).Explanation:Sincecos2t+ sin2t= 1for allt, the particle travels along the curvegiven in Cartesian form byx216+y29= 1 ;this is an ellipse centered at the origin.Att= 0, the particle is at (4 sin 0,3 cos 0),i.e.,at the point (0,3) on the ellipse.Now astincreases fromt= 0 tot=π/2,x(t) increasesfromx= 0 tox= 4, whiley(t) decreases fromy= 3 toy= 0 ; in particular, the particlemoves from a point on the positivey-axis toa point on the positivex-axis, so it is movingclockwise.In the same way, we see that astincreasesfromπ/2 toπ, the particle moves to a pointon the negativey-axis, then to a point on thenegativex-axis astincreases fromπto 3π/2,until finally it returns to its starting point onthe positivey-axis astincreases from 3π/2 to2π.Consequently, the particle moves clockwiseonce around the ellipsex200510.0 points
5.Moves once clockwise along the ellipse
6.Moves along the linex3= 1,

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