Answer:
a) 
b) 
Step-by-step explanation:
By definition, we have that the change rate of salt in the tank is
, where
is the rate of salt entering and
is the rate of salt going outside.
Then we have,
, and

So we obtain.
, then
, and using the integrating factor
, therefore
, we get
, after integrating both sides
, therefore
, to find
we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions
, so 

Finally we can write an expression for the amount of salt in the tank at any time t, it is 
b) The tank will overflow due Rin>Rout, at a rate of
, due we have 500 L to overflow
, so we can evualuate the expression of a)
, is the salt concentration when the tank overflows
Part A: first multiply 2 by x and -3, then combine the like terms, after that add 6 from both sides, then subtract 6x from both side, the answer is -5.
4x + 2(x-3) = 4x + 2x - 11
4x +2x -6 = 4x + 2x - 11
6x -6 = 6x - 11
6x = 6x -11 +6
6x = 6x -5
6x-6x= -5
0 = -5
part B) add the like terms
Answer:
To do this, you need to multiply out the expressions. This is a bit tedious, but remember like FOIL for binomials, for these trinomials you must multiply each term. If you need a step-by-step, I'd be happy to provide it. Let me know.
Once you have simplified the expression, you get
-x-9/2x-4
But, the problem stipulates that a must equal 1. We can equivalently factor out the negative sign and put it on the denominator with no change to write
x+9/-(2x-4) = x+9/-2x+4
So, seeing where each coefficient corresponds between the two expressions, you get a = 1, b = 9, c = –2, and d = 4.
Answer:
A) 12x-36=360 (equation to find x)
B) X=33
C) 71 for 3x-28 and 109 fo 3x+10
Step-by-step explanation:
So first we know tha there are vertical angles present (the opposite side of an angle directly)
And we also know the two sides since the two angle measures are just two different sides
If you add up all the 4 angle syou’ll get 360
So initially
3x-28+3x-28+3x+10+3x+10=360
Combine and get 12x-36=360
Now solve for X
Answer:
y = -3.75
Step-by-step explanation:
1 - 0.5 = 2(y+4)
0.5 = 2(y+4)
0.5 = 2(0.25)
0.25 - 4 = -3.75 = y