Answer:
x(t) = 581.66 lb
Step-by-step explanation:
From the given information:
Consider the salt quantity in the tank at time t be x(t) lb.
∴ the rate of change of salt content in the tank is 
where:
the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons
=21 lb/s
rate of outflow = salt conc. in the tank × flow rate
= x/250 × 9
= 9x/250 lb/s
∴
This is a 1st order linear differentiation,
The integrating factor if 
∴
at t = (0) and x(0) = 100 lb
Hence;
∴
after time t = 1 minute i.e 60 s
x(t) = 581.66 lb
Answer:
x=24
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
4x-2 + 3x+14= 180
Combine like terms
7x +12 =180
Subtract 12 from each side
7x+12-12 = 180-12
7x = 168
Divide each side by 7
7x/7 = 168/7
x =24
Answer:
c = 8
Step-by-step explanation:
Use synthetic division here; it's the fastest approach.
Given that (x + 2) is a factor, take -2 and use this as the divisor in synthetic division:
-2 4 c 1 2
-8 (-2c+ 16) (4c-34)
---------------------------------------------
4 (c - 8) (-2c + 17) 4c - 32
The remainder, 4c - 32, must equal zero if (x + 2) is a factor.
Then 4c - 32 = 0, and c = 8
