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Chapter 3: Q2 TF. (page 301)

Parametric curves: Imagine the curve traced in the xy-plane by

the coordinates (x, y) = (3z + 1, z2− 4) as z varies, where the

parameter z is a function of time t.

If the parameter z moves at 3 units per second and

z = 0 when t = 0, plot the points (x, y) in the plane

that correspond to t = 0, 1, 2, 3, and 4.

Short Answer

Expert verified

(x,y)=(3z+1,z2-4)

Step by step solution

01

Step 1. Given Information 

(x,y)=(3z+1,z2-4)

02

Step 2. Calculation

Since, dzdt=3

Integrating both sides

z=3t+c,c=integration constant

At t=0,z=0t=0,z=0

Therefore, c=0

Then z=3t

Now for, t=0,z=0

and(x,y)=(1,-4)

Now for, t=1,z=3

and (x,y)=(10,5)

Now for,t=1,z=3

and (x,y)=(19,32)

Now for, t=3,z=9

and (x,y)=(28,77)

Now for, t=4,z=12

and(x,y)=(37,140)

03

Step 3. Graph

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