HW08-solutions-1

# HW08-solutions-1 - white(taw933 HW08 ben-zvi(55600 This...

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white (taw933) – HW08 – ben-zvi – (55600) 2 6. r = π 2 Explanation: Diferentiating A = πr 2 , C = 2 implicitly with respect to t we see that dA dt = 2 dr dt , dC dt = 2 π dr dt . Thus the rate oF change, dA/dt , oF area is equal to the rate oF change, dC/dt , oF circum- Ference when dA dt = dC dt , i.e. , when 2 dr dt = 2 π dr dt . This happens when r = 1 . 003 10.0 points Determine the value oF dy/dt at x = 3 when y = x 2 2 x and dx/dt = 3. 1. dy dt v v v x =3 = 16 2. dy dt v v v x =3 = 20 3. dy dt v v v x =3 = 14 4. dy dt v v v x =3 = 18 5. dy dt v v v x =3 = 12 correct Explanation: Diferentiating implicitly with respect to t we see that dy dt = (2 x 2) dx dt = 3 (2 x 2) . At x = 3, thereFore, dy dt = 3(4) = 12 . 004 10.0 points A point is moving on the graph oF xy = 2. When the point is at (3 , 2 3 ), its x -coordinate is increasing at a rate oF 6 units per second. What is the speed oF the y -coordinate at that moment and in which direction is it mov- ing? 1. speed = 10 3 units/sec, increasing y 2. speed = 4 3 units/sec, decreasing y correct 3. speed = 7 3 units/sec, increasing y 4. speed = 7 3 units/sec, decreasing y 5. speed = 4 3 units/sec, decreasing y 6. speed = 10 3 units/sec, increasing y Explanation: Provided x, y n = 0, the equation xy = 2 can be written as y = 2 /x . Diferentiating implicitly with respect to t we thus see that dy dt = 2 x 2 dx dt .
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HW08-solutions-1 - white(taw933 HW08 ben-zvi(55600 This...

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