Mathematics: Let S be the sphere of radius 1 centered at (1, 4, 7). Find the distance from S to the plane x + y + z = 0. (HINT: Use Lagrange multipliers to find the distance from the plane to the center of the sphere.) Incorrect: Your answer is incorrect.

Let S be the sphere of radius 1 centered at (1,

mrush1122

21.01.2022

5.93 unit distance

Step-by-step explanation:

First we would need to calculate the distance between the sphere center and the plane x + y + z = 0

$d = \frac{|Ax + By + Cz|}{\sqrt{A^2 + B^2 + C^2}}$

where A = 1, B = 1, C = 1 are the coefficients of the plane x + y + z = 0

and x = 1, y = 4, z = 7 are the coordinates of the center of the sphere

$d = \frac{|1*1 + 4*1 + 7*1|}{\sqrt{1^2 + 1^2 + 1^2}} = \frac{12}{\sqrt{3}} = 6.93$

Since the sphere has a radius of 1, then the distance from the plane to the surface of sphere would then be:

6.93 - 1 = 5.93

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