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Sagot :
Answer:
The diameter decreases at a rate of 0.053 cm/min.
Step-by-step explanation:
Surface area of an snowball
The surface area of an snowball has the following equation:
[tex]S_{a} = \pi d^2[/tex]
In which d is the diameter.
Implicit differentiation:
To solve this question, we differentiate the equation for the surface area implictly, in function of t. So
[tex]\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}[/tex]
Surface area decreases at a rate of 3 cm2/min
This means that [tex]\frac{dS_{a}}{dt} = -3[/tex]
Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.
This is [tex]\frac{dd}{dt}[/tex] when [tex]d = 9[/tex]. So
[tex]\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}[/tex]
[tex]-3 = 2*9\pi\frac{dd}{dt}[/tex]
[tex]\frac{dd}{dt} = -\frac{3}{18\pi}[/tex]
[tex]\frac{dd}{dt} = -0.053[/tex]
The diameter decreases at a rate of 0.053 cm/min.
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