Can you help me match the graphs 13 is graph iv 15 is graph

Can you help me match the graphs?

#13 is graph iv

#15 is graph I

#17 is graph iii

IV a Screen Shot 2016-11-22 at 10,49,55 PM Search 13-18 Match the equations with the graphs labeled I-VI give reasons for your answers. Determine which families curves have u constant and which have v constant. 13. r(u, v) ucos wi u sin v j v k 15. r (u, v) (u 16. x (I u)(3 cos e) cos 4mu, y (1 u003 cos v) sin 4mu u) sin v 17. x cos u cos\', y sin u cos v, z Sin v 18 x sin u, y cos u sin v, sin v

Solution

13) r(u,v)=ucosvi+usinvj+vk

The parametric equations are

x=ucosv

y=usinv

z=v

Looking at the grid curve first by fixing v, x and y parametrize a straight line in the plane z=v intersecting the z-axis.

If u is held constant, the projection onto the x-y plane is circular with z=v takes helix shape for each grid with spiralling ramp surface.

hence the graph is iv..

15) r(u,v)=(u³-u)i+v²j+u²k

graph is i

17) x=cos³ucos³v

y=sin³ucos³v

z=sin³v

If v is constant the z=sin³v is constant. therefore the corresponding grid curves lie in the horizontal plane. But the curves for this surface are neither circles nor straight lines. The vertical grid curves corresponds to u=u_o held constant then

x=cos³u_ocos³v

y=sin³u_ocos³v

Therefore the grid curve lies in the vertical plane y=(tan³u_o)x through the z-axis.

Henc the graph is iii.