Step-by-step explanation:
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Xy + 6e^y = 6e
taking first derivative :
<span>xy' + y + 6y(e^y)(y') = 0 </span>
<span>xy" + y' + y' + 6y'(e^y)(y') + 6yy(e^y)y' + 6y(e^y)y" = 0 </span>
<span>Put x = 0,
0 + 6e^y = 6e,
y = 1 </span>
<span>0 + 1 + 6(1)(y')e = 0,
Put y' = 0 </span>
<span>0 + 0 + 0 + 0 + 0 +6 ey" = 0,
y" = 0</span>
Xavier charges the most per hour. I divided each of the allowances earned by the number of hours and his was the most.
Hope this helps;)
Answer:
x(15) = 21 lb
Step-by-step explanation:
Rate of change in volume of salt water solution = rate of volume incoming - rate of volume outgoing
dV/dt = 4 - 2 =2gal/min
So, the equation for volume at cetain time t at given conditions and values becomes,
V(t) = 2t + V
V(t) = 2t + 20 gal-------------------euqation (1)
Rate of change in amount of salt = rate of salt in - rate of salt out
dx/dt = {0.5*4} - {[x(t)/V(t)]*2}
dx/dt = 2-2[(x(t))/(2t+20)]
dx/dt = 2-[(x(t))/(v(t))] lb/min
Now, with integrating factor, we get
exp[∫(1/(1+10))dt)] = t+10
the equation becomes
(t + 10)*x' + x = 2*(t+10)
((t+10)*x') = 2*(t+10)
(t+10)*x = t² + 20t + C
As x(0) = 0,
x(t) = (t²+20t)/(t+10)
x(15) = (15²+20*15)/(15+10)
x(15) = 21 lb
Answer:
36 girls voted for Marisol
Step-by-step explanation: