(a) Find the arc length parametrization of the line x = − 5 + 3 t , y = 2 t , z = 5 + t that has the same direction as the given line and has reference point − 5 , 0 , 5 . (b) Use the parametric equation in part (a) to find the point on the line that is 10 units from the reference point in the direction of increasing parameter.
(a) Find the arc length parametrization of the line x = − 5 + 3 t , y = 2 t , z = 5 + t that has the same direction as the given line and has reference point − 5 , 0 , 5 . (b) Use the parametric equation in part (a) to find the point on the line that is 10 units from the reference point in the direction of increasing parameter.
(a) Find the arc length parametrization of the line
x
=
−
5
+
3
t
,
y
=
2
t
,
z
=
5
+
t
that has the same direction as the given line and has reference point
−
5
,
0
,
5
.
(b) Use the parametric equation in part (a) to find the point on the line that is 10 units from the reference point in the direction of increasing parameter.
find the parametric equations for the line segment from (-2,5) to (7,-1) your equation for x should not be x=t. define your interval for the parameter t.
Consider the parametric equations for a curve in the xy-plane given by:
x = t^3 - 3t y = t^2 - 2
Find the equation of the tangent line to the curve at the point where t = 2.
Graph the curve with parametric equations
x = sin(t), y = 3 sin(2t), z = sin(3t).
Find the total length of this curve correct to four decimal places.
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