A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the first model made, and let y represent the number (in millions) of the second model made. The company's revenue can be modeled by the equation R(x, y) = 80x + 170y 2.x? – 3y? – xy - - Find the marginal revenue equations, R and R.,. Then find the production levels that will maximize revenue.

Q: Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the…

A: Let Q(x,y,z) be the point closest to the point P. Let D be the distance between these two points.…

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Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: A bicycle dealer has found that if 10-speed bicycles are sold for æ dollars apiece and the price of…

A: The solution is given below:

Q: . Suppose that your best friend has calculated the partial derivatives of a given function f(x,y)…

A: Please see the below picture for detailed solution for detailed solution.

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: The Critical Point of y = xe-*

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Q: A division of Ditton Industries manufactures a deluxe toaster oven. The daily marginal profit…

A: (a) Consider the marginal function as p'x=-0.0003x2+0.02x+24. The total profit realizable from the…

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Q: Find the critical point of f (x, y) = 3x² + xy - 5x + y°, and determine its nature.

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Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

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Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

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Q: If the national consumption function is given by C(y) = 6(y + 6)/2 + 0.4y + 1 %3D where is the…

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Q: Find the relative maximum and minimum values. f(x,y) = 3x² – 4y?

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Q: Find the critical point of the function: f(x, y) = 4x2 + 2y2 − xy + x

A: we have given a function f(x, y)  We have to find the critical point

Q: the demand function for a particular beverage is given by D(q)=(3000)/((3q+2)^(2)) and if the supply…

A:

Q: Find the​ consumers' surplus if the demand function for a particular beverage is given by…

A: We are given the demand function for a particular beverage as: D(q) = p=30003q+72 The equilibrium…

Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: Find the orthogonal trajectories of the family of curves x²- y2=C² A) x- y=C (B xy3=C xy=C D…

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Q: f(x,y) = 100x062y0 38. Find the marginal productivity of labor and capital.

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Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: Express y = 3x2 – 8x - 1 in the form y = 3(x – p)² + q, where p and q are constants and hence find…

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Q: Use the method of variation of parameters to find a particular solution of the DE…

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Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: The demand and supply functions for three (03) goods are given as follows: Dx = 100-3Px+Py+3Pz Dy…

A: The equilibrium point is the point where demand function is equal to the  supply function. Thus,…

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x² 5x…

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Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: As a result of urbanization, the temperatures in Paris have increased. In 1891 the average daily…

A: Average temperature is calculated by the total sum of temperatures divided by number of observations

Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: The weekly demand function for butter in the Toronto- Canada is Qd = 20000 - 500Px + 25M + 250Py,…

A: Given that - The weekly demand function for butter in the Toronto- Canada is Qd = 20000 - 500Px +…

Q: A manutacturer has determined that fhe marginal profit from theiprdoction and Sale of X ice cream…

A: Profit can be easily found out by putting x = 48 in profit function 360 -6x . Profit = 360 - 6 × 48…

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: Gator Tee Shirtz has determined that its productivity is given by the equation f(x, y) = 36x 4, when…

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Q: Assume that the demand curve is P = f(Q) = 60 − 0.2Q and the supply curve is P=g(Q) = 30 + 0.3Q.…

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Q: The time (in hours) that a branch of Amalgamated Entities needs to spend to meet the quota set by…

A: T(x, y)=x4+16y4-32xy+43Tx =4x3+0-32y(1)+0Tx=4x3-32yTxx =12x2-0Txx =12 x2Ty…

Q: 2. Determine the critical points of the function: R(y) : y2 – 6y -

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Q: Find the four second partial derivatives. z = 6x2 + y5 a2z дхду дудх ду?

A: We will find all the asked second order partial derivatives as following.

Q: Find the critical point of the function f(x,y) = 7x²y² + 4y² + 4x².

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Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: C(x) = 1500 + 13x – 0.1x2 + 0.0005x3. - %3D Find the marginal inal cost finctien?

A: Given query is to find the marginal cost function.

Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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Q: determine the coefficients of the equation y=ax^3+bx^2+cx+d so that will have a slope of 9 at…

A: The equation y=ax3+bx2+cx+d so that will have a slope of 9 at (-1,-4),a critical point at x=2, and a…

Q: Find the relative maximum and minimum values. f(x,y) = x² +y2 +4x- 12y

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Q: Find the critical point of the function f(r, y) = – 4+ 8z + 7z - 5y + 6y

A: Find the critical point (x,y)

Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

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Q: (b) Form the partial equation by eliminating function f from z = f(x?

A:

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.