WEBVTT
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We're talking about a spherical balloon and so we have
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the the volume are the radius and tea time,
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and we want to look at the different expressions of
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rates. So if you see DVD are, think
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about what V means and what are means. V
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means volume are means radius, so this would be
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the rate of change of the volume with respect to
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the radius. However, if you have DVD t
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think about what V means and what team means,
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that would be the rate of change of the volume
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with respect to time. Okay. Now, for
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the second part of the problem, the rate of
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change of the volume with respect to time could be
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expressed as the rate of change of the Radius DVD
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R times, the rate of change of the radius
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with respect to time DRD t. Now let's find
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ER DVD are remember, the volume of a sphere
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is 4/3 pi r cubed. So if we want
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to find the derivative of that with respect to our
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, we can leave the constant 4/3 pi and use
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the power rule, bring down the three and raised
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the art of the second and when we simplify that
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we have four pi r squared So we substitute that
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in for DVD are and we have four pi r
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squared times drd t and that's DBT.