sachinpokharel99 sachinpokharel99

09-03-2022
Mathematics

contestada

If x2 + y2 + z2 = 9, dx dt = 3, and dy dt = 9, find dz dt?

Respuesta :

zsm2800 zsm2800

14-03-2022

Answer:

dz/dt = -(3x + 9y)/z

Step-by-step explanation:

x² + y² + z² = 9

2x dx/dt + 2y dy/dt + 2z dz/dt = 0

x dx/dt + y dy/dt + z dz/dt = 0

x * 3 + y * 9 + z dz/dt = 0

so

dz/dt = -(3x + 9y)/z

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