suchislifecestlavie suchislifecestlavie

10-11-2021
Mathematics

contestada

Write the equations in cylindrical coordinates.
(a) 6x + 5y + z = 6

(b) −4x^2 − 4y^2 + z^2 = 5

Write the equations in cylindrical coordinates a 6x 5y z 6 b 4x2 4y2 z2 5 class=

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LammettHash LammettHash

10-11-2021

In cylindrical coordinates, we take

x = r cos(t)

y = r sin(t)

z = z

(a) Then

6x + 5y + z = 6

transforms to

6r cos(t) + 5r sin(t) + z = 6

(b) We have

x² + y² = r² (cos²(t) + sin²(t)) = r²

so

-4x² - 4y² + z² = 5

converts to

-4r² + z² = 5

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