A swimming pool contains 2 gallons of water at time t = 0. Water is added to the pool using a hose at a constant rate of 3 gallons per minute. Find the function W(1), the amount of water in the pool as function of time. OW(t) = –3t +2 %3D OW(1) = 2t + 3 %3D OW(t) = 3t + 2 %3D None of the options displayed. OW(t) = 21 - 3 OW(t) = -2t + 3 O W(t) = 3t – 2 %3D OW(1) = -2t – 3 OWO : -31

Q: Given: (x is number of items) Demand function: d(x) = 768.8 0.3x² Supply function: s(x) = 0.5x² -…

A: Given: (x is number of items) Demand function: d(x) = 768.8 - 0.3x² Supply function: s(x) = 0.5x²

Q: p=250-x/50 C(x)=20,000+40x Find the marginal revenue function in terms of x R'(x)=?

A:

Q: Find the profit function Pix) for a corporation for the years 2004-2012 given the revenue function…

A:

Q: The demand function for a product under pure competition is p = (64 - 4x)1/2  and the supply…

A:

Q: A company is planning to manufacture snowboards. The fixed costs are $100 per day and total costs…

A: Given: A company is planning to manufacture snowboards. The fixed costs are $100 per day and total…

Q: The demand and supply functions for a product are modeled by Demand: p = −0.2x + 8 and Supply: p =…

A: The given demand function is p=-0.2x+8 and supply function is p=0.1x+2, where x is the number of…

Q: A​ T-shirt manufacturer is planning to expand its workforce. It estimates that the number of​…

A: A function T(x) is givenT(x)=-0.25x4+x3,       0≤x≤3

Q: The demand for a certain commodity is D(x)  =  1000e−.02x units per month when the market price is…

A: The given function is D(x)=1000e-.02x, where D(x) represents the demand for a certain commodity and…

Q: Given a total-revenue function R(x) = 800/x - 0.2x and a total-cost function C(x) = 1600 (x +5)+…

A: Total-revenue function R(x)= 800x2-0.2x Total-cost function C(x)= 1600(x2+5)13+500 Profit function…

Q: Given: (x is number of items) Demand function: d(x) = 961 –- 0.6x? Supply function: s(x) = 0.4x²…

A:

Q: The demand for a particular item is given by the function D(a) 1, 300- 3x2 Find the consumer's…

A:

Q: The supply function of a form is given as p=x^2+4x+5. Find the Producer’s Surplus given that the…

A:

Q: A company produces chocolate Easter bunnies at a cost per unit of 0.50 + 0.005x dollars, where x is…

A: Given that the cost of producing 1 unit= 0.50+0.005x  So the cost of producing x units=…

Q: Assuming that the company sells all that it produces, what is the profit function? P(x)=Px=   .…

A:

Q: The demand for a particular item is given by the function D(x) = 1, 500 – 3x² . Find the consur the…

A: The consumer's surplus: - The term "consumer surplus" refers to the monetary value of a person's…

Q: After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream…

A:

Q: The estimated monthly profit realizable by abc corporation for manufacturing and selling x units of…

A: From the given profit function:   px=-4x2+24000x-100,000 dollars   Now differentiate the function…

Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by g = (95 -…

A: Given,  q=95-2p2 Recall: Revenue=p*q

Q: The reproduction function for a sardine is  f(p) = −0.0004p2 + 4p,  where p and  f(p)  are in…

A: fp=-0.0004p2+4p The population giving maximum sustainable yield if found by maximizing the function,…

Q: The number of deaths N per week has been observed to be linearly related to the average…

A: Given :          The number of deaths N per week has been observed to be linearly related to the…

Q: Your Cabaret nightspot "Jazz on Jupiter" has become an expensive proposition: You are paying monthly…

A: Given, monthly cost = $40,000 Cabaret artist charges $2700 per performance. Jazz ensemble charges…

Q: The demand function for a certain model of a ten-speed bicycle is given by p= D(x) = -0.001a2 + 250…

A:

Q: Consider the following total revenue function for a hammer. R = 20x – 0.01x² (a) The sale of how…

A: The revenue function of the hammer is R = 20x-0.01x2.

Q: George and Sandra both decide to open small cafes in town, on the same block: "George's Gourmet Tea"…

A:

Q: 10. A building materials company sells gravel. Suppose that C(x) = 0.5x² +3x %3D represents its…

A:

Q: The reproduction function for a sardine is  f(p) = −0.0004p2 + 2p,  where p and  f(p)  are in…

A: Please see the explanation below

Q: Consider the following total revenue function for a hammer. R = 36x – 0.01x² (a) The sale of how…

A:

Q: 4. The function f(x) = x³ – 6x² + 9x – 4 has a relative maximum at (A) x = 0 (B) x = 1 (C) x = 2 (D)…

A: Let f(x) = x3 - 6x2 + 9x - 4 Suppose the function has critical point at x = c then If f'(x) > 0…

Q: A​ T-shirt manufacturer is planning to expand its workforce. It estimates that the number of​…

A: The number of​ T-shirts produced by hiring x new workers is given by Tx=-0.5x4+2x3…

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

A:

Q: The supply for a particular item is given by the function S(x) 15 + 5x . Find the producer's surplus…

A:

Q: Consider the following total revenue function for a hammer. R = 60x − 0.01x2 (a) The sale of how…

A: a) Consider the given revenue function:

Q: Please

A: The given function is

Q: Given: (x is number of items) Demand function: d(x) = 809.2 – 0.3x? Supply function: s(x) = 0.4x²…

A: As given above: Demand function is:  dx=809.2-0.3x2 Supply function is: sx=0.4x2 Now for equilibrium…

Q: For some positive constant , a patient's temperature change, T , due to a dose, D , of a drug is…

A: Given: For some positive constant c and D=Drug Dose  T=Patient's temperature change T=C2-D3D2

Q: The Holling type I function is described by g(x) = ax, where x is the amount of prey available and a…

A: Given The Holling type I function is  g(x) = ax The Holling type II function is  f(x) = bxn+x

Q: 22 + 0.49x² . Find the producer's surplus if th The supply for a particular item is given by the…

A:

Q: In a town of 50,000 people, there were initially 80 cases of a particularly virulent strain of…

A:

Q: George and Sandra both decide to open small cafes in town, on the same block: "George's Gourmet Tea"…

A: Let xt represents the daily profit (scales to have an appropriate unit, like hundreds of dollars) at…

Q: Consider the following total revenue function for a hammer. R = 28x − 0.01x2 (a) The sale of how…

A: The given revenue function is Rx=28x-0.01x2. (a) It is known that the maximum value occurs at the…

Q: Consider the following total revenue function for a hammer. R = 44x – 0.01x²2 (a) The sale of how…

A: We have given the total revenue function for a hammer.              R = 44x - 0.01x2  We have to…

Q: The reproduction function for a sardine is  f(p) = −0.0005p2 + 4p,  where p and  f(p)  are in…

A:

Q: 100e0.1z thousands of Over the next 5 years, a company projects its continuous flow of revenue to be…

A: To find the expected profit of the company

Q: Consider the following total revenue function for a hammer. R = 32x – 0.01x² (a) The sale of how…

A: a) R= 32x-0.01x^2 Differentiate with respect to x dR/dx = 32 -0.02x dR/dx=0 => x= 1600

Q: A baseball team plays in a stadium that holds 68000 spectators. With the ticket price at $8 the…

A: a) Given:         Let x be the average attendance               y be the price    The two points are…

Q: The demand for a particular item is given by the function D(x)=1500-3X^2. find the consumers surplus…

A: Given equilibrium price = 300 and demand function.

Q: 7000 Find the consumers' surplus if the demand function for a particular beverage is given by D(q) =…

A: Here we have to find the consumer's surplus if the demand function for a particular beverage is…

Q: The reproduction function for king salmon in a sea is f(p) = − 1/8 p2 + 8.5p, where p and f(p) are…

A: The reproduction function for king salmon in a sea is

Q: have

A: Please refer to the image below

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.