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Gennadij [26K]
3 years ago
6

The radius of a sphere decreases at a rate of 6 m/sec. find the rate at which the surface area decreases when the radius is 20 m

. recall that the surface area of a sphere of radius r is given by s = 4πr2
Mathematics
1 answer:
DanielleElmas [232]3 years ago
8 0

The radius of the sphere decreases at the rate of 6 m/ sec

That is, \frac{dr}{dt}=-6

Surface Area of the sphere of radius r is given by S=4\pi r^2

Differentiating with respect to t,

\frac{dS}{dt}=4\pi (2r)\frac{dr}{dt}=8\pi r\frac{dr}{dt}

\frac{dS}{dt}=8\pi (20)^2(-6)=-960\pi \: m^2/sec

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\text{Hey there!}

\mathsf{-40-8b=-6(1+7b)}\\\mathsf{SIMPLIFY\ both\ sides\ of\ your\ equation}\\\mathsf{-40-8b=-6(1+7b)}

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\mathsf{ADD\ by\ 42b\ on\ your\ sides}\\\mathsf{-8b-40+42b=-42b-6+42b}\\\mathsf{SOLVE\ above\ correct\ to\ get\ us\ to\ the\ next\ step!}\\\mathsf{\rightarrow 34b-40=-6}

\mathsf{ADD\ by\ 40\ on\ your\ sides}\\\mathsf{34b-40+40=-6+40}\\\mathsf{Cancel\ out\ -40+40\ because\ that\ gives\ the\ result\ of\ 0}\\\mathsf{-6+40=34}\\\mathsf{\rightarrow New\ equation: 34b = 34}

\mathsf{DIVIDE\ both\ of\ your\ sides\ by\ 34}\\\mathsf{\dfrac{34b}{34}=\dfrac{34}{34}}\\\\\mathsf{Cancel\ out: \dfrac{34b}{34}\ because\ that\ gives\ you\ the\ result\ of\ 1b}\\\\\mathsf{Keep:\dfrac{34}{34}\ because\ it\ solves\ for\ b}\\\\\mathsf{\dfrac{34}{34}=34\div34=1}

\boxed{\boxed{\boxed{\boxed{\mathsf{Thus\ your\ answer\ is:\boxed{\boxed{\mathsf{b=1}}}}}}}}\checkmark

\text{Good luck on your assignment and enjoy your day!}

~\dfrac{\frak{LoveYourselfFirst}}{:)}

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Step-by-step explanation:

Hope this helps. :)

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