Answer:
44
Step-by-step explanation:
The correct answer to your question is k=5 .
We already know that C = 45. All we really need to do is simplify the equation and then solve for x.
45 = x + 0.06x + 0.08x + 0.1x
45 = (1 + 0.06 + 0.08 + 0.1)x
45 = 1.24x
x = 36.2903, which rounds to $36.29 for the haircut.
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
This is all a matter of simple addition. So Bill Peterson's remaining balance would be $1,268.32 or A.