Suppose that the price p​ (in dollars) and the weekly sales x​ (in thousands of​ units) of a certain commodity satisfy the demand equation 4p3x2=33,600 Determine the rate at which sales are changing at a time when x=40​, p=20​, and the price is falling at the rate of $.10 per week. the rate at which sales are chanigng is_______ thousand units per week.

Q: A manufacture has been selling 1900 television sets a week at $360 each. A market survey indicates…

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Q: A phone company charges $0.39 per minute for the first 10 minutes of a long-distance phone call and…

A: NOTE: Refresh your page if you can't see any equations. . A phone company charges $0.39 per minute…

Q: Suppose that for a certain product, during a certain month, the price-demand equation is x = 2500 –…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: The number of units of an item per month for which there is a demand is related to the unit price by…

A: Given demand function px=50.1x2+4, 0≤x≤20 where p(x) is unit price (in dollars)  and x is number of…

Q: For a consumer with a demand function q 10 - 2p2, find the answers to the following. a. Consumer…

A: * SOLUTION :-

Q: The demand function for a tablet is given by the model p = 200 - 16x2 where p is measured in dollars…

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Q: A company is increasing the production of a product at the rate of 20 units per week. The demand and…

A: The revenue function R(x) is given by, R(x)=x×p(x)R(x)=x60-0.03xR(x)=60x-0.03x2

Q: The price-demand equation and the cost function for the production of table saws are given,…

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Q: Find the consumers' surplus at a price level of p= $150 for the price-demand equation below. p= D(x)…

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Q: A manufacture has been selling 1200 television sets a week at $540 each. A market survey indicates…

A:

Q: The demand function for a tablet is given by the model p = 200-16x2  where p is measured in dollars…

A: Our objective is to Derive the number of tablets that the company could sell to make the same amount…

Q: Suppose that the price p​ (in dollars) and the weekly sales x​ (in thousands of​ units) of a certain…

A:

Q: Find the consumers' surplus at a price level of p = $150 for the price-demand equation below. p=…

A:

Q: Suppose the demand for a certain item is given by D(p)=-2p2-5p+900, where p represents the price of…

A:

Q: The price-demand equation and the cost function for the production of table saws are given,…

A:

Q: A company produces computers. The demand equation for this computer is given by p(q) = -5q+6000. the…

A: Given the demand functionp(q)=-5q+6000where q represents the number of units:total Revenue…

Q: A manufacture has been selling 1600 television sets a week at $450 each. A market survey indicates…

A: x= number of TV y=price two points are the slope of the line is given by

Q: Suppose that x thousand units of a commodity can be sold weekly when the price is p dollars per unit…

A: So this is related rates. We already have an equation relating the desire quantities to the known…

Q: Use the demand function x- 275 (1- 3p/5p+1)  to find the rate of change in a demand x for price p=$4

A: Consider the demand function x

Q: Consider the demand equation where x represents the quantity demanded in units of a thousand and p…

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Q: A company is increasing the production of a product at the rate of 20 units per week. The demand and…

A: We have given, The demand function p = 60 − 0.02x and the cost function C = 5000 + 40x − 0.04x2.

Q: suppose that the price p(in dollars) and the weekly sales x (in thousands of dollars) of a certain…

A: Given query is to find rate of change of sales.

Q: Assume that the demand equation for tuna in a small coastal town is given by 80 p = q0.5 where p is…

A: The given data is: p=80q0.5  1. To find the marginal revenue function in terms of q

Q: A manufacture has been selling 1900 television sets a week at $450 each. A market survey indicates…

A:

Q: In this problem, p is in dollars and x is the number of units. Find the producer's surplus at market…

A: Demand function is:  p=100-x2 Supply function is: p=x2+6x+44

Q: The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p =…

A: Given, Demand equation p=-15x+200 To find the cost C as a function of the price p: Solve the demand…

Q: The price p,in dollars,of a certain commodity and the quantity x sold obey the demand equation p =…

A: Consider the provided equations,

Q: |A manufacture has been selling 1400 television sets a week at $480 each. A market survey indicates…

A: Solve the problem as solved below and then find the answer.

Q: The demand function for a product is modeled by p= 56e-0.000012q where p is the price per unit (in…

A: We have p=56e−0.000012qRevenue function Rq=qpRq=56qe−0.000012qDifferentiate w.r.t…

Q: The price p, in dollars, of a certain product and the quantity x sold obey the demand equationp = -…

A: Given price function - P = -x4+100Let's solve for x - x4 = 100-Px = 4100-Px = 400-4P…

Q: Find the consumers' surplus at a price level of p = $150 for the price-demand equation below.…

A: Given p=400-0.02x

Q: It is known that the demand function for a good is shown by the equation P = - 5Q + 110 and the…

A: Given that, the demand function is px=-5Q+110 and the production cost is Cx=100+10Q+5Q2. Obtain the…

Q: The demand function for a product is modeled by p = 54e −0.00002x, where p is the price per unit (in…

A: Given that the demand function is p=54e-0.00002x where p is the price per unit and x is number of…

Q: Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750 ml size is…

A: First solve the given demand function in terms of p :

Q: express the price p in terms of the demand x, and find the domain of this function  x=4,000- 40p

A: Given an equation in terms of x,

Q: A company produces computers. The demand equation for this computer is given by p(q) = - 5q + 6500.…

A:

Q: A manufacture has been selling 1250 television sets a week at $480 each. A market survey indicates…

A:

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

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Q: 3. Suppose that the price p​ (in dollars) and the weekly sales x​ (in thousands of​ units) of a…

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Q: -; A price p (in dollars) and demand x for a product are related by 2x2 – 12xp + 50p² = 6400. If the…

A: Here I am attaching image so that you understand each and every step.

Q: The monthly demand for a certain brand of perfume is given by the demand equation p = 100e−0.0001x +…

A: p=100e-0.0001x+75 a). Differentiating with respect to x, we get…

Q: A manufacture has been selling 1100 television sets a week at $420 each. A market survey indicates…

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Q: A company is increasing the production of a product at the rate of 25 units per week. The demand and…

A:

Q: A manufacture has been selling 1500 television sets a week at $540 each. A market survey indicates…

A:

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

A:

Q: If the demand function for math anxiety pills is p = D(x) = -5x + 59 and the corresponding supply…

A: solve the following

Q: A manufacture has been selling 1600 television sets a week at $540 each. A market survey indicates…

A: (a) Here x is the number of television sets sold per week and p(x) is the corresponding price in…

Q: A company produces computers. The demand equation for this computer is given by p(g) = - 5q + 6500.…

A:

Q: Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain…

A: Given demand equation, 4p³+x²= 4100 x=10 p=10 dp/dt=- $ .20/week Differentiating w.r.t to t we have,…

Q: Suppose that for a certain product, during a certain month, the price-demand equation is x = 2500 –…

A: Since you have asked the last 3 questions, we are answering the parts e, f, and g. Given, The…

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.