The tank shown in the figure was filled with 100 liters of substance A in a concentration of 10g / L. Material A is fed into the tank at a flow rate of 5L / min in 1g / L variation. At the exit of the tank, there is an outlet flow at a rate of 5L / minute and the tank is continuously mixed. In the tank, substance A is converted into substance B. Derive the equation that ties the concentration of substance B in the tank to time. ( Reaction constant = 0.1)

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

A:

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

A:

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: Consider a tank with volume 100 liters containing a salt solution. Suppose a solution with 2…

A:

Q: Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. If…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Consider a reservoir with a volume of 8 billion cubic feet (ft^3) and an initial pollutant…

A:

Q: Initially 35 grams of radioactive substance was present. After 5 hours the mass had decreased by 11…

A: Given:- Initially 35 grams of radioactive substance was present. After 5 hours the mass had…

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A:

Q: The acceleration of a Maserati is proportional to the difference between 250 km/h and the velocity…

A:

Q: Find the work done by the gas with an initial volume of 3 cubic feet and a pressure of 1000 pounds…

A:

Q: snowball melts so that its surface area decreases ata rate of 1cm^2/min, find the rate at which the…

A: Given query is to find the rate of chnage of diameter.

Q: A spherical drop of liquid evaporates at a rate proportional to its surface area. If a given drop…

A:

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

Q: 7) The rate of water flowing in a tank is given by: R(t) = 0.5t* + 20t Gallons/minutes. How much…

A:

Q: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

A: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

Q: 7. A 6ft tall human is walking away from a 20ft lamppost. Given that the length of the shadow of the…

A: Let the distance of the person from the bottom of the light post be x. Let the length of the shadow…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P C where C is a…

A:

Q: A metallic ball with a diameter of 12 cm is covered with a layer of ice, so if the ice begins to…

A:

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is present.…

A:

Q: The height of a triangle is increasing at a rate of 4 cm/s while the area of the triangle is…

A: Let the height, base and area of a triangle be 'h', 'b' and 'A' Given, dhdt=4 cm/sdAdt=56 cm2/s

Q: The lower base of a trapezoid is 8 m. If its height is increasing at the rate of 0.5m/sec while its…

A:

Q: In the electric currect​ flow, it is found that the resistance​ (measured in the units called​ ohms)…

A: Resistance R ∝ 1/D2 R = k/ D2; where k is the proportionality constant. A wire 0.01 inches in…

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

A:

Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: After 2 days, 10g of radioactive chemical is present. Three days later, 5g is present. How much of…

A: Given:      After  2 days, 10g of radioactive chemical is present. Three days later5 g chemical is…

Q: The length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

Q: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

A: Pressure and Volume are related by equation At a instant

Q: snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate (in cm/min)…

A: Given query is to find the rate at which diameter of snowball is decreasing.

Q: The volume (v) of a sphere varies directly with the cube of its radius (r). If k is the constant of…

A:

Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

A:

Q: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

Q: If the base h of a triangle is increasing at a rate of 3 inches per minute while its height h is…

A: Area of a triangle of base b and height h is given as, A=12bh The derivative of area with respect to…

Q: A snowball melts in such a way that the rate of change in its volume is proportional to its surface…

A:

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

A:

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

A:

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: A body weighing 64 Ib is dropped from a height of 100 ft with an initial velocity of 10 ft/sec.…

A:

Q: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

A: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

Q: The radius of an air bubble is increasing at the rate of 1/2 cm/s.At what rate is the volume of the…

A:

Q: Assign variables and restate the following problem in terms of known and unknown derivatives (but do…

A:

Q: A tank contains 2000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

A:

Q: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

A: Given: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

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.