calculus question.
2014-10-21 7:03 am
Q = 3u^2 + (2u+3v)/(u+v)^2
u=10 v=25
use calculus to estimate the change in v that should be made to offset a decrease of 0.7 unit in u so that Q will be maintained.
回答 (2)
2014-10-26 5:33 am
2014-10-24 3:11 pm
When u = 10 and v = 25, Q = 300 + (20 + 75)/35^2 = 300.078. When u = 10 - 0.7 = 9.3 and Q keeps to 300.078, we get 300.078 = 259.47 + (18.6 + 3v)/(9.3 + v)^2
40.608 = (18.6 + 3v)/(9.3 + v)^2
40.608(86.49 + 18.6v + v^2) = 18.6 + 3v
3512.19 + 755.31v + 40.608v^2 - 18.6 - 3v = 0
2014-10-24 07:14:38 補充：
This reduces to a quadratic equation with unreal root! That means there is no real
value of v to keep Q unchanged.
40.608 = (18.6 + 3v)/(9.3 + v)^2
40.608(86.49 + 18.6v + v^2) = 18.6 + 3v
3512.19 + 755.31v + 40.608v^2 - 18.6 - 3v = 0
2014-10-24 07:14:38 補充：
This reduces to a quadratic equation with unreal root! That means there is no real
value of v to keep Q unchanged.
收錄日期: 2021-04-15 17:00:39
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