Atank contains 60 kg of salt and 1000 l of water. pure water enters a tank at the rate 6 l/min. the solution is mixed and drains from the tank at the rate 7 l/min. let y o u be the number of kg of salt in the tank after t minutes. the differential equation for this situation would be:

dy/dt = 7y / (t − 1000)

Step-by-step explanation:

Change in mass of salt = mass of salt going in − mass of salt going out

dy/dt = 0 − (C kg/L × 7 L/min)

where C is the concentration of salt in the tank.

The concentration is mass divided by volume:

C = y / V

The volume in the tank as a function of time is:

V = 1000 + 6t − 7t

V = 1000 − t

Therefore:

C = y / (1000 − t)

Substituting:

dy/dt = -7y / (1000 − t)

dy/dt = 7y / (t − 1000)

If we wanted, we could separate the variables and integrate.  But the problem only asks that we find the differential equation, so here's the answer.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option