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August 24, 2016
Posted by **abby** on Friday, April 16, 2010 at 6:43pm.

(Round your answers to three decimal places. Enter your answers from smallest to largest z-value.)

- Calculus -
**MathMate**, Friday, April 16, 2010 at 7:31pmThe sphere, S, is given by:

S(x,y,z): x²+y²+z²-26=0

The helix, r, is given by:

r(x,y,z): sin(t),cos(t),t

which means that the helix is constrained to the cylinder of unit radius, C: C(x,y): x²+y²=1

Thus, the solution for the intersections is given by the solution of

S(sin(t), cos(t), t)=0

from which it can be deduced by inspection that t=5 gives an exact solution, since

(sin²(5)+cos²(5)) + 5²

=(1) + 25

=26

Similarly, t=-5 is a solution.