de3andenisaco de3andenisaco
  • 24-10-2016
  • Mathematics
contestada

Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5) to the plane x y z = 9.

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skhdg skhdg
  • 24-10-2016
One function you would be trying to minimize is 
f(x, y, z) = d² = (x - 4)² + y² + (z + 5)² 

Your values for x, y, z, and λ would be correct, but 
d² = (20/3 - 4)² + (8/3)² + (-7/3 + 5)² 
d² = (8/3)² + (8/3)² + (8/3)² 
d² = 64/3 
d = 8/sqrt(3) = 8sqrt(3)/3
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