A fast-food restaurant has a cost of production C (x) = 13x + 126 and a revenue function R(x) = 6x. When does the company start to turn a profit? Enter the exact answer. If there is no solution, enter NS. If there is an infinite number of solutions, enter IS.

Q: B1(b): Solve the initial value problem : f' (x) = x12 – 4x4 + 12x + 13 and f(0) = 2.

A: The given differential equation is f'x=x12-4x4+12x+13 and the initial condition is f0=2. Solve the…

Q: A manufacturer of lighting fixtures has daily production costs of  C = 800 − 50x + 0.25x2,  where C…

A: For finding minimum of any function take derivative and equate to zero.

Q: A company sells two different types of candles, and their profit function for a week is given by…

A: Consider the provided question, (3)

Q: show that the 2x2-y2=C is a solution to yy'-2x=0.

A:

Q: B1(b): Solve the initial value problem : f'(x) = x° + 12x + 13 and f(0) = 3.

A:

Q: A fast-food restaurant has a cost of production C (x) = 12x + 132 and a revenue function R(x) = 6x.…

A:

Q: Find the general solution for: y'' - 4y' - 5y = -6xe(-x)

A: We need to find the general solution for y'' - 4y' - 5y = -6xe(-x). ---------(1)Idea: First, we will…

Q: 2x1-x-4x₁x₂ = 0 -x + 2x3-4x₁x₂ +10x₁ = 5

A: We need to solve the following system of equations using a numerical method.…

Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Find f by solving the initial-value problem. f'(x) = 7e* – 6x³, ƒ(0) = 5 -

A:

Q: A company can produce a maximum of 1500 widgets in a year. If they sell x wwww m widgets during the…

A: Px=30,000,000-360,000x+750x2-13x3 Differentiating with respect to x, we get…

Q: A fast-food restaurant has a cost of production C(x)=12x+140 and a revenue function R(x)=5x. When…

A: To find the time when company starts to earn profit. Company will earn profit when revenue is more…

Q: A bus service carries 10 000 people daily between Ajax and Union Station. and the company has space…

A:

Q: Solve the initial value problem: f(x)-x7+12x+17 and f(0)=3.

A: We will rearrange and then integrate both sides to find the solution of the given initial value…

Q: Use variation of parameters to find a particular solution of y"- 2y' + y = 14xie Yp(x) =

A: Auxiliary equation for the given equation:

Q: A fast-food restaurant has a cost of production C (r) = 12x + 95 and a revenue function R(r) = 7x.…

A:

Q: Find the particular solution of y''-5y'=x-2 when x=0, y=0, y'=2

A: Given that that a non homogeneous differential equation and we find its solution.   Here i attached…

Q: Find the general solution of tx -3x = t³+2t for t> 0.

A: Given DE is  tx'-3x=t3+2t .......(1) We find the general solution of (1).

Q: A firm can produce 500 units per week. If its total cost function is C = 400 + 1400x dollars and its…

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Q: Find the number of units x that produces a maximum revenue R for R=450x-0.25x^2  A.) The feasible…

A: taking first derivative of equation as 0 to get the maximum revenue

Q: A firm can produce 400 units per week. If its total cost function is C = 700 + 1500x dollars and its…

A: Given  total cost function is C = 700 + 1500x dollars total revenue function  R = 1900x − x2 dollars…

Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

A:

Q: B1(b): Solve the initial value problem : f'(x) = x° + 12x + 14 and f(0) = 2.

A:

Q: Find the general solution to x”-3x’+2x = e^t

A: First we find complementary function then particular integral and then general solution.

Q: Eliminate the arbitrary constants of the general solution: В y = Ax3 + + CVx x2

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Q: Determine the general solution: y' = x - 2y. *

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Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

A: Consider the profit function: Px,y=-x2-y2+4x+10y Given constrains are, x≥0y≥0x+y≥7 Now convert these…

Q: Find the particular solution determined by the initial condition. P(X) = 2x ° = 3x )= -6 2/5 - 3x:…

A: This belong to initial value problem of differential equation.first we solve the differential…

Q: Find the general solution of y'' - 2y' - 8y = 24(x2+1)e4x by using VARIATION OF PARAMETERS

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Q: Find the General and Particular solution of = 3y ; y = 3, when x = 0

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Q: y" - y = x²ex + 5

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Q: Find the particular solution determined by the initial condition. f'(x) = rx) = 2x2/5 - 3x, f(1) =…

A:

Q: A firm produces a product that has the production cost function C(x) = 420x + 14,420 and the revenue…

A:

Q: A small generator burns two types of fuel–low sulfur and high sulfur-to produce electricity. For one…

A: Here we find the minimize cost.

Q: A chemical manufacturer sells sulfuric acid in bulk at a price of $100 per unit. If the daily total…

A: Given:    Cx=100,000+50x+0.003125x2 To solve the amount of sulfuric acid to maximize the profit we…

Q: Max's total profit (in dollars) from manufacturing and selling x units of their model M loudspeaker…

A: Answer

Q: Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

A: Recall: Consider the first differential equation                           dydx +P(x) y =Q(x)…

Q: Solve the problem graphically and calculate the Z value of at the optimal solution (

A:

Q: Find the number of units X that produces a maximum revenue R in the given equation. R= 36x2/3 -2x

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Q: A particular solution of x¨ − 3x˙ + 2x = t2 + 1 is given by

A: given that x''-3x'+2x=t2+1. we need to find the particular solution for the given differential…

Q: -x x²dydx Solve: S. S2 x²+y² 1

A: Solve: ∫01∫x2xx2x2+y2dy dx

Q: c. Solve x2 + 4x-y+3 = 0 and x-y+7 = 0 using any of the two methods.

A:

Q: ufacturer estimates that the cost (C) of production of x units of a certain item is C = 40x −…

A: We have to find the unit  where minimum cost arises

Q: A small generator burns 2 types of fuel: low sulfur and high sulfur to produce electricity. For one…

A: Consider the provided question, Let x be the number of gallons of low sulfur and, y be the number of…

Q: Solve f(x)=2x2+7x-4 and select all of the solutions below. C%3D X=-4

A: Given: f(x)=2x2+7x-4

Q: B1(b): Solve the initial value problem f'(x) = x° + 12x + 14 and f(0) = 2.

A: Solution:Given     f'(x)=x9+12x+14  and f(0)=2Formula:∫xndx=xn+1n+1+C

Q: Find the general solution of (2x –y) = 2y – x

A:

Q: Find the general solution for y' = y – xy³e-2x

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Q: find the solution of y''-2y'=x - e^3x

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.