2. A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate of 0.5 L/min. The mixture is kept homogeneous by stirring and the solution is being pumped out at twice the rate of input. Find the function of salt in the container at any given time. When will the salt in the container be half its original amount?

Q: (3) The demand function for a tablet is given by the model p= 200–16r where p is measured in dollars…

A:

Q: (3) The demand function for a tablet is given by the model p= 200-16x where p is measured in dollars…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 4. Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in…

A: It is given that annual cost is C'x=x2+65x and annual savings is S'x=212-x2. (a) Suppose P'(x) is…

Q: A tank contains initially 400 liters of brine holding 100 kg of salt in solution. Water containing…

A:

Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

A:

Q: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

Q: uppose the marginal prosperity to consume is (dC)/(dy)=0.04+(\ln (y+1))/(y+1)(in billions of…

A:

Q: If the marginal revenue (in dollars per unit) for a month is given by MR = 0.3x + 450, what is the…

A:

Q: At what rate in cubic centimeters per minute is the volume increasing at this instant?

A:

Q: 1. The cost (in pesos) of producing x corkboards is given by x2 + 20x + 500, while the price (in…

A: Since you are asking multiple questions. We are answering only the first question as per our…

Q: 2. A tank initially contains 1000 gallons of fresh water. Brine containing 3 lbs/gallon of salt…

A: The time taken for the quantity of salt to reach 100 lbs is 16.80555 minutes

Q: Suppose the Marginal product of labor in the economy is given by MPN= .002(16,000-N), while the…

A: a. The market-clearing wage rate equates the demand and supply of labour Solve for w first Therefore…

Q: A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500…

A: Given, Demand function is, q=360-pp=360-q Now, the Revenue function is, Rq=pq=360-qq=360q-q2…

Q: A 50 – gallon tank of pure water has a brine mixture with concentration of 2 pounds per gallon…

A: Form the first order differential equation then find its solution to get amount of salt at any time…

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

A:

Q: The population of a bacteria culture grows at a rate of P = 100(2)n, where P is the population and n…

A:

Q: 2. Suppose that the marginal revenue for a company manufacturing coffee machines is given by…

A: Given expression for marginal revenue of the company is: Q=100-0.5x where, Q is the marginal revenue…

Q: 9. The rate at which the value, V, of a painting changest years after it is completed is given by…

A: Image is attached.

Q: Tank A initially holds 100 gallons of brine that contains 150 pounds af salt, and tank B holds 100…

A: Tank A initially holds 100 gallons of brine that contains 150 pounds of salt.Tank B holds 100…

Q: Suppose a company wants to introduce a new machine that will produce a marginal annual savings in…

A:

Q: Suppose that an lowa class battleship has mass around 52,000 metric tons (52,000,000 kg) and a…

A: Assume that the ship loses power when it is moving at a m speed of 8 m/s. a. We have to find about…

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

A:

Q: Suppose that the direct demand and direct supply functions are x = √200 - p and x = √p - 38,…

A:

Q: 4. Suppose the produetivity of a country can be approximated by: Y(L, K) = 10L0 K®9 where L is units…

A: Topic - derivative Marginal productivity Of anything is the change in output when one unit of that…

Q: Suppose that the marginal propensity to consume is dC = 0.04 + dy In(y + 1) y + 1 (in trillions of…

A:

Q: 1) The revenue for a product is R(x) = -0.004x² + 21x ost is C(x) = 0.02x + 38, for x units produced…

A: According to our company policy we can answer only first question and rest can be reposted

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

Q: Suppose we have a tank that contain 10 litres of water and 50 g of salt. The salt solution is…

A: given , tank that contain 10liters of water and 50 gram of salt .  so , initial concentration =>…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Percentage : Percentage of the item is 100th part of the number.  It is denoted by x% or written as…

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

A:

Q: 11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f = 0(g) and g…

A:

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

A:

Q: Suppose that an lowa class battleship has mass around 54,000 metric tons (54,000,000 kg) and a…

A:

Q: 1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at…

A: Given that, a tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: A bacteria culture starts with a population of 1000 bacteria, and after 2 hours, the population grew…

A: Solution and Explanation is given below

Q: (3) The demand function for a tablet is given by the model p= 200–16x where p is measured in dollars…

A:

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

A:

Q: Suppose the sales of potato chips generates a profit at the rate P′(t)  =  10t ln(7t) dollars per…

A:

Q: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

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

A: Given that When air expands adiabatically (without gaining or losing heat), its pressure and volume…

Q: 23. Suppose that total national consumption is given by a C(x)=200–0.6x–0.05x0“, where x is the…

A:

Q: 1. There are 64.000 subscribers to an online fashion magazine. Due to competition from a new…

A:

Q: Two substances, A and B, are being converted into a single compound C. In the laboratory it has been…

A:

Q: (3) The demand function for a tablet is given by the model p 200 – 16x where p is measured in…

A:

Q: A 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at…

A: A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture…

Q: For the production function given by x-2 Hab - Aa² - Bb², ow that the marginal rate of technical…

A: The marginal rate of technical substitution (MRTS) shows the rate at which  one input can be…

Q: The population of Normal, Illinois grows proportionally to its population at time t. At an initial…

A: Given, dPdt=kP Where P is the population and k is the proportionality constant.

Q: Tank A contains 407 litres of brine holding 181 N of dissolved salt, and tank B contains 407 litres…

A:

Q: Suppose the average daily metabolic rate for certain types of animals can be expressed as a function…

A: