Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into tank A at the rate of 4 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallons per minute, and the solution from tank B is also pumped out of the system at the rate of 4 gallons per minute. The correct differential equations with initial conditions for the amounts, x(t) and y(t), of salt in tanks A and B respectively, at time t are: A) dx/dt=2-x/40+y/5,dy/dt=x/40-y/3,x(0 )=20,y(0)=5
B) dx/dt=2-3x/40+y/15,dy/dt=3x/40-y/5, x(0)=20,y(0)=5
C) dx/dt=4-3x/40+y/15,dy/dt=3x/40-y/5, x(0)=20,y(0)=5
D) dx/dt=4-x/40+y/5,dy/dt=x/40-y/3,x(0 )=20,y(0)=5

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

the answer is 2/54

step-by-step explanation:

first one because it can't have a fraction in it

step-by-step explanation: