contestada

At what points does the helix r(t) = sin(t), cos(t), t intersect the sphere x2 + y2 + z2 = 17? (Round your answers to three decimal places. If an answer does not exist, enter DNE.)

Respuesta :

Answer:

the helix intersects the sphere at t=4 and t=(-4)

Step-by-step explanation:

for the helix r(t) = [ sin(t) , cos(t) ,  t ] then x=sin(t) , y=cos(t) and z=t

thus the helix intersect the sphere  x² + y² + z² = 17 at

x² + y² + z² = 17

[sin(t)]²+[cos(t)]²+ t² = 17

1 + t² = 17

t² = 16

t = ±4

thus the helix intersects the sphere at t=4 and t=(-4)

abidemiokin

The point wher the helix intersect the sphere is at t =  ±4

The coordinate of a helix

Given the coordinate of a helix expressed as;

  • r(t) = [sin(t), cos(t), t]

If these coordinate intersects the sphere  x² + y² + z² = 17

Substitute the coordinate of the helix:

x² + y² + z² = 17

(sint)² + (cost)² + t² = 17

sin²t + cos²t + t² = 17

1 + t² = 17

t² = 17 - 1

t² = 16

t = ±√16

t = ±4

Hence the point wher the helix intersect the sphere is at t =  ±4

Learn more on helix and sphere here: https://brainly.com/question/1767456

Otras preguntas