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sbednarek
24.07.2019 •
Mathematics
Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm. (in cm3)
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Ответ:
-1.92 cm³
Step-by-step explanation:
The formula for the volume of a cube in terms of side length is ...
V = s³
Then the first-order approximation of volume for a small change ∆s in side length is ...
V(s +∆s) ≈ V(s) + V'(s)·∆s
and the change in volume is ...
∆V ≈ V(s +∆s) -V(s) = V'(s)·∆s
The derivative V'(s) is ...
V'(s) = 3s²
so the change in volume for s = 8 cm and ∆s = -0.01 cm is ...
∆V ≈ 3s²·∆s = 3(8 cm)²(-0.01 cm) = -1.92 cm³
Ответ:
76 can i have brainliest please i have none
Step-by-step explanation: