A 50-gallon barrel is filled completely with pure water and then salt water with a concentration of 0.3 lb/gal is pumped into the barrel. The resulting mixture overflows at the same rate. The amount of salt in the barrel is modeled by Q(t)= 15(1-e-0.04t) where t is measured in minutes and Q(t) is measured in pounds.

Q: The volume of a right circular cylinder varies jointly as the height and the square of radius of the…

A: Given that:  Volume(V)=58096.28 cubic yards,r=29yards,h=22yardsand the right circular cylinder. A…

Q: A 500 gallon oil spill undergoes a cleanup process. The company hired to clean the spill can remove…

A: It is given that 15% of the spilled oil gets cleaned and initially there are 500 gallon of oil is…

Q: The water depth in a harbor is 18.5 m at high tide and 9.5 m at low tide and one tidal cycle is…

A:

Q: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the…

A: The objective is to find the rate at which base of the triangle is changing when altitude is 10…

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A: given: dA = 5 cm2/min dh = 1 cm/min A = 86 cm2 h = 11 cm   Equation for area of a triangle: A = .5 b…

Q: y=x2e1/x.

A:

Q: The following equation represents the relationship between hours of TV watched per day (x) and the…

A: From the given information, ŷ = -0.776X+ 36.841 Here, X: hours of TV watched per day Y: number of…

Q: Find the maximum area of a rectangle in the first quadrant with one corner at the origin, an…

A: To Find the maximum area of a rectangle in the first quadrant with one corner at the origin, an…

Q: A bacteria culture starts with 300 bacteria and grows at a rate proportional to its size. After 5…

A: " Since you have posted a question with multiple subpart, we will solve first three subpart for you.…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.