Answer:
B
Step-by-step explanation:
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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
-9 is the answer. 1/4 of 12 is 3, and their negatives cancel each other. Then you just multiply -3 by 3.
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