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
For this case we have by definition of trigonometric relations of rectangular triangles that, the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. Then according to the figure we have:

We cleared CA:

Answer:
Option A
Answer:
A. 5x^2 − 2x − 24 = 0
Step-by-step explanation:
height = 5b-2
b =x
We can rewrite the height as
h = 5x-2
We know the formula for area of a triangle
A = 1/2 bh
A =1/2 x * (5x-2)
Distributing the x
A= 1/2 (5x^2 - 2x)
We know A =12
12 = 1/2 (5x^2 - 2x)
Multiply each side by 2
12*2 = 2*1/2 (5x^2 - 2x)
24 = 5x^2 - 2x
Subtract 24 from each side
24-24 = 5x^2 - 2x-24
0 = 5x^2 - 2x-24
Answer:
-7
Step-by-step explanation:
-5 + -2 = is the same as -5 - (+2), so the answer is -7