- #1
kochibacha
- 14
- 0
i want to find V(t)
At first i found this problem was very simple but when i try to write differential equations i ended up with these
V' = kA that's for sure
then i confined the problem only to spherical shape and no other shapes of raindrops involved
as i can't express A in term of V alone( surface area of sphere = 4∏r2, volume of sphere is 4/3∏r3 ) then i have to
use chain rule, dV/dt= dVdrdrdt substitute dV/dt from
V'=k4∏r2
i get
4∏r2r'= K4∏r2
r'=k
r = kt+c
r3 = (kt+c)3
4∏r3/3 = (kt+c)34∏/r=V(t)
im i correct? the answer to this problem is V'=kV2/3 I am not sure how they transform Area to variable V alone
At first i found this problem was very simple but when i try to write differential equations i ended up with these
V' = kA that's for sure
then i confined the problem only to spherical shape and no other shapes of raindrops involved
as i can't express A in term of V alone( surface area of sphere = 4∏r2, volume of sphere is 4/3∏r3 ) then i have to
use chain rule, dV/dt= dVdrdrdt substitute dV/dt from
V'=k4∏r2
i get
4∏r2r'= K4∏r2
r'=k
r = kt+c
r3 = (kt+c)3
4∏r3/3 = (kt+c)34∏/r=V(t)
im i correct? the answer to this problem is V'=kV2/3 I am not sure how they transform Area to variable V alone
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