A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min.
(a) How much salt is in the tank after tminutes?(b) How much salt is in the tank after 60 minutes? (Round theanswer to one decimal place.)

(a) After time (t), the amount of salt in the tank is s(t) = 130 − 130e ∧−3t/200 / 3

(b) After 60 minutes, the salt in the tank is s(60) ≈ 25.7153

Step-by-step explanation:

To start with,

Let s(t) = amount of salt in kg of salt at time t.

Then we have:

dt/ds =  (rate of salt into tank) − (rate of salt out of tank)

= (0.05 kg/L · 5 L/min) + (0.04 kg/L · 10 L/min) − ( s kg/ 1000 L x 15 L/min)

= 0.25 kg/min + 0.4 kg/min − 15s / 1000 kg/min

So we get the differential equation

dt/ds = 0.65 − 15s / 1000

= 65 / 100 − 15s / 1000

dt/ds = 130 - 3s / 200

We separate s and t to get

1 / 130 - 3s ds = 1 / 200 dt

Then we Integrate,

Thus we have

∫1 / 130 - 3s ds = ∫1 / 200 dt

- 1/3  · ln |130 − 3s| =1 / 200 t + C1

ln |130 − 3s| = - 3 /200 t + C2

|130 − 3s| = e− ³⁺²⁰⁰ ∧ t+C2

|130 − 3s| = C3e − ∧3t/200

130 − 3s = C4e  ∧−3t/200

−3s = −130 + C4e  ∧−3t/200

s = 130 - C4e ∧−3t/200 / 3

Since we begin with pure water, we have s(0) = 0. Substituting,

0 = 130 − C4e  ∧−3·0/200 / 3

0 = 130 − C4

C4 = 130

So our function is

s(t) = 130 − 130e ∧−3t/200 / 3

After one hour (60 min), we have

s(60) = 130 − 130e ∧−3·60/200 / 3

s(60) ≈ 25.7153

Thus, after one hour there is about 25.72 kg of salt in the tank.

a framing bias

step-by-step explanation:

rodrigo is subject to a framing bias i believe.

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.