Answer:

Step-by-step explanation:
The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.
Volume = 500 gallons
Initial Amount of Salt, A(0)=50 pounds
Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min
=(concentration of salt in inflow)(input rate of brine)

When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.
Concentration c(t) of the salt in the tank at time t
Concentration, 
=(concentration of salt in outflow)(output rate of brine)

Now, the rate of change of the amount of salt in the tank


We solve the resulting differential equation by separation of variables.

Taking the integral of both sides

Recall that when t=0, A(t)=50 (our initial condition)

The answer for t is 46.0416
Answer:
Tn = -4n²+40n+36
Step-by-step explanation:
A general quadratic sequence, Tn = an²+bn+c, where n is the term of the sequence.
So, when n = 1, Tn = 72, which means T1 = a+b+c=72.
when n = 2, Tn = 100, which means T2= 4a+2b+c = 100
when n = 3, Tn = 132, which means T3 = 9a+3b+c = 132.
Now, use a calcaulatot to solve the 3 variable simultaneous equation. According to my calculator, a = -4, b = 40, c = 36.
Hence, you a, b, and c in the Tn equation given above.
Therefore, <em>Tn = -4n²+40n+36</em>
Answer:
x = 20
Step-by-step explanation:
The three angles form a straight line so they add to 180 degrees
x+ 100 +3x = 180
Combine like terms
100+4x= 180
Subtract 100 from each side
100+4x-100= 180-100
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20