Initially, a large tank with a capacity of 100 gallons contains 50 gallons of pure water. A salt solution with concentration of 0.1 lb/gal flows into the tank at a rate of 2 gal/min. The mixture is well stirred and flows out of the tank at the rate of 4 gal/min. Find the initial-value problem that describes the amount of salt in the tank until the tank is empty.

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.

-4, -2, 1, 4

step-by-step explanation:

domain = x values

range = y values

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west