When x gets large, you can ignore everything except the highest-degree terms of the numerator and denominator. Effectively, you want the value of
-2x/x
= -2
The horizontal asymptote is -2.
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:
1546 in
Step-by-step explanation:
Answer:
59 plain donuts
Step-by-step explanation:
17 chocolate+23 maple=40 in total
89-40=59
59 plain donuts
You can notice the sequence:
5*2=10
3*3=9
following the same sequence:
2*6=12
therefore, the missing number is 12
(2,6,12)
