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alina1380 [7]
3 years ago
5

Let 3z=(2w-5)^3. If dw/dt =1/3, find dz/dt when z=9

Mathematics
1 answer:
jekas [21]3 years ago
5 0

3<em>z</em> = (2<em>w</em> - 5)³

When <em>z</em> = 9, we have

27 = (2<em>w</em> - 5)³   →   3 = 2<em>w</em> - 5   →   <em>w</em> = 4

Differentiate both sides with respect to <em>t</em> :

3 d<em>z</em>/d<em>t</em> = 3 (2<em>w</em> - 5)² d<em>w</em>/d<em>t</em>

d<em>z</em>/d<em>t</em> = (2<em>w</em> - 5)² d<em>w</em>/d<em>t</em>

Plug in everything you know and solve for d<em>z</em>/d<em>t</em> :

d<em>z</em>/d<em>t</em> = 3² • (1/3)

d<em>z</em>/d<em>t</em> = 3

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<h3>Solving system of equations</h3>

Given the following system of equation expressed as:

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