assignment #021 021. `query 21 Applied Calculus I 11-27-2007
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13:15:43 **** Query 2.8.4 dy/dt for (3,4) with x'=8; dx/dt for (4,3) with y'=-2 **** What is dy/dt if x=3, y=4 and dx/dt = 8?
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RESPONSE --> f(x)=x^2+y^2=25 dx/dt=8 f'(x)=2xdx/dt+2ydy/dt=0 plug in (3,4) dy/dt=-6 b) (4,3) dy/dt= -2 same deriv, plug in (4,3) dx/dt=1.5 confidence assessment: 3
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13:15:54 At (3,4) you are given dx/dt as x ' = 8. Since 2x dx/dt + 2y dy/dt = 0 we have 2(3) * 8 + 2 * 4 dy/dt = 0 so dy/dt = -48/8 = -6. At (4,3) you are given dy/dt as y' = -2. So you get 2 * 4 dx/dt + 2 * 3 * -2 = 0 so 8 dx/dt - 12 = 0 and therefore 8 dx/dt = 12. Solving for dx/dt we get dx/dt = 12/8 = 3/2. **
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RESPONSE --> yup self critique assessment: 3
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13:17:19 **** Query 2.8.6 roc of volume if r increases at rate 2 in/min, if r= 6 in and if r = 24 in **** What is the rate of volume change if r is increasing at 2 inches / minute?
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RESPONSE --> v=4/3pir^3 v'=4pir^2(dr/dt) dr/dt=2in/min plug in r=6, dr/dt=2 v'(6)=904 in/min v'(24)=14476 in/min confidence assessment: 3
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13:17:36 The shape is a sphere. The volume of a sphere, in terms of its radius, is V = 4/3 `pi r^3. Taking the derivative with respect to t, noting that r is the only variable, we obtain dV/dt = ( 4 `pi r^2) dr/dt You know that r increases at a rate of 2 in / min, which means that dr/dt = 2. Plugging in dr/dt = 2 and r = 6 gives 4 pi (6^2) * 2 = 288 pi = 904 approx. Plugging in dr/dt = 2 and r = 24 gives 4 pi (24^2) * 2 = 4 pi (576)(2) = 4608 pi = 14,476 approx.. **
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RESPONSE --> yup self critique assessment: 3
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