Given: (x is number of items) Demand function: d(x) = 841 -0.4x² Supply function: s(x) = 0.6x² Find the equilibrium quantity: Find the producers surplus at the equilibrium quantity:

Q: Set-up the integral using horizontal element for the volume of the solid obtained by rotating the…

A: fristly given curve are simplyfy and diagram curve then use for shell method

Q: Find the lengths of the curves in Exercises 1-2. If you have a grapher, you may want to graph these…

A: Concept:  For y = f(x) in the Cartesian coordinates defined on interval a,b  The curve length is…

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Q: Find the cost function for the marginal cost function. C'(x) = 0.03 0.05x 0.05x, fixed cost is $9 e…

A: Given query is to find the cost function.

Q: Find sin 0 and cos 0 if tan 0 sin = 3/5 sin = -3/5 sin = 4/5 sin = -4/5 cos = 3/5 cos = -3/5 cos =…

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Q: Set-up the integral using vertical element for the volume of the solid obtained by rotating the…

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Q: Consider the function. f(x) = x-1 x + 8 Step 2 of 2: Determine the open intervals on which the…

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Q: 3 s cos³x + 8sin x cos²x 20652x basin ²x dx;cosx 0

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Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

A: we know the work needed to stretch the spring W=12kx2 where x is the elongation. x=xf-xi=45-30=15…

Q: Find parametric equations for the sphere centered at the origin and with radius 8. Use the…

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Q: A helicopter takes off at an initial (ground) velocity of 175 km/h toward the west, climbing at an…

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Q: Consider the ODE: (2x siny)dx + (x2² cosy + cosy)dy = 0 a. Solve the ODE by separation of variables…

A: We have to solve ODE by seperation of variable

Q: Find the area under the given curve over the indicated interval. y=x²; [0,5] The area under the…

A: Given: Now, we need to find the area under the given curve.          Area = ∫05x2dx          =x3305…

Q: Trig Identities Practice Use fundamental identities to simplify the expression. Basic Trigonometric…

A: 1) csc(theta)/sin(theta) 2)cot(theta)tan(theta)+sin2(theta) /cos2(theta)…

Q: -7x Find an equation of the line tangent to the graph of G(x) = e The equation of the line is y=. at…

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Q: Use the graph of f, shown on the right, to find the given limit. When necessary, state that the…

A: The graph of the function is To evaluate: The value of limx→4fx

Q: A particle moves along a straight line with equation of motion s = f(t), where s is measured in…

A: Here to find the velocity and speed we have to derivate the function s=f(t).

Q: f(x) = x³, Y Find the volume of the solid obtained by rotating the region A about the x-axis. A B

A: The region A is bounded by y=1 and y=x3 from x=0 to x=1

Q: 1. 3x, If R is the region in the first quadrant bounded by x-axis, 3x + y = 6 and y = evaluate ff 3y…

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a vertical element, the total…

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Q: Use the graph to find the following limits and function value for each value of a. i) lim f(x) ii)…

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Q: T T Set-up the integral using horizontal element for the area of the plane region, 0≤x≤ bounded by…

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Q: Evaluate the given integrals. Please Show the complete solution. Then identify the u, du, and other…

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Q: dx Using Rationalizing Substitution ·S =ff(v)dy, find fry)dy x√√x-1 O In(y) + C O2ln(y) + C O…

A: To find out the integration.

Q: Evaluate using the method of trig substitution 6. S dx √16-x²

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Q: IF y = u+ + 3u2 & u = 3x Find dy dX

A: If y=f(u) and u=g(x),thendydx=dydu.dudx dundu=n.un-1

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: Given:-f(x)=3+3x-3x2 ; 0, 3f'(x)=3-6xfor critical pointsf'(x)=03-6x=06x=3x=36=12second derivative…

Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

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Q: A spherical tank of diameter 6 m is full of water. Set-up the integral for the work done in pumping…

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Q: In Exercises 4-7, consider harmonic oscillators with mass m, spring constant k, and damping…

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Q: TT ind the area of the plane region, 0≤x≤. ≤ bounded by y=sin X₁ X=- 2 O1s.u. 1.111 s.u. S.U. 2 О…

A: We have to find out the area

Q: 1. f(x, y) = 4x² + 2y² + 5 subject to the constraint x² + y² - 2y = 0

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Q: 4) x² (1-8)² + 100 25 =1

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Q: Using Rationalizing Substitution a=4, b = 9 a = 8,b=27 a=64, b= 729 a=2, b=3 729 S 64 dx √x - √√x =…

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Q: Evaluate the given integrals. Please Show the complete solution. Then identify the u, du, and other…

A: hhh

Q: Find the average value of the function f(x)=x²-9 on [0,9]. The average value of the function…

A: Use the average value formula for finding the value

Q: the graph shown, identify a) the point(s) of inflection and the intervals where the function is…

A: Given query is to find the point of inflection and  interval where concave up and adown.

Q: -9.763332111 is O True false a Whole number.

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Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: What is the area of the region between y=x²-2x-3 and the x-axis from x=0 to x=4? H

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Q: evaluate the integral using methods of trig integrals S cos³ x dx

A: Solution is here

Q: Assume the annual rate of change in the national debt of a country (in billions of dollars per year)…

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Q: 2 f(x) = √2x + x².

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Q: - f (x)) then, the Fourier transform of fex- called Fourier sine transform and denoted Fs { fcx)},…

A: answer is in next step

Q: y"" + 4y = 0 when x = 0, y = 0, y = 0, y″ = 1|

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Q: 1. Find of the trigonometric function: dx y=−10x + 3 cosx

A: Derivative of Cosx is -Sinx

Q: w Dy ),-0 7 By b. Əw əz C. aw əz

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Q: Set-up the integral using horizontal element for the volume of the solid obtained by rotating the…

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Q: .729 dx "J64 √X-3√x" √ or(v)dy, and f(x). find = Using Rationalizing Substitution © 6y+6+ 6 y-1 6y²…

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Q: A particular computing company finds that its weekly profit, in dollars, from the production and…

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