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Mathematics
Problem
At what points does the curve
r
(
t
)
=
t
i
+
(
2
t
−
t
2
)
k
\mathbf{r}(t) = t \mathbf{i} + (2t - t^2) \mathbf{k}
r
(
t
)
=
t
i
+
(
2
t
−
t
2
)
k
intersect the paraboloid
z
=
x
2
+
y
2
z = x^2 + y^2
z
=
x
2
+
y
2
?
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