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Charra [1.4K]
3 years ago
13

x}^{2} = 0" alt="5 {x}^3 - 20 {x}^{2} = 0" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
adell [148]3 years ago
7 0

5x^{2}  \times (x - 4) = 0 \\ x^{2} \times (x - 4) = 0 \\  {x}^{2} = 0 \: x = 0 \\ x - 4 = 0 \: x = 4
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The surface area of a sphere is decreasing at the constant rate of 3π sq. cm/sec . At what rate is the volume of the sphere decr
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Whooh



SA=4pir²
take derivitive
dSA/dt=8pir dr/dt

and do the volume as well
V=(4/3)pir³
dV/dt=4pir² dr/dt

we need to solve for dV/dt
to do taht we need dr/dt
so

dSA/dt=8pir dr/dt
given dSA/dt=3pi cm/sec
r=2
3pi=8pi2 dr/dt
3=16 dr/dt
3/16=dr/dt

now do the volume
dV/dt=4pir² dr/dt
r=2
dr/dt=3/16
dV/dt=4pi2² (3/16)
dV/dt=16pi(3/16)
dV/dt=3pi

nice
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