y" + 4y = 8 +34 cos x ; y(0) = 3;y'(0) = 2

Q: The total cost (in dollars) of producing a product is given by C(x): = 200x + 0.1x² + 1100 where x…

A: The answer provided below has been developed in a clear step by step manner.

Q: sin(x) = x x3 a) Evaluate the limit of the function your reasoning. b) Find any points on the curve…

A: For limit we will going to use power series of sinx  for tangent we will use slope of tangent

Q: Let A, B and C be sets, and let g: A → B and f: B → C be functions. Prove: (i) If f, g are…

A: (i) Let, f : B → C and g: A → B are injective.      Now, f ◦ g is a function from A to C.…

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Q: hi can solve for Cartesian coordinates (Do not solve the integrations)

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Q: olve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Minimize z = x +…

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Q: A system of coupled ODES, where x = x(t), are expressed in the matrix form 7 x' = (-10 3³4)x where x…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Let G be the region bounded above by the sphere x² + y² + z² = a² and below by the cone ==√√²+² √x²…

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x² + y² + x²y + 9, D =…

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Q: Well, we know that: ae0.3196 = MC(0.319) = 222.23, and aeb = MC(1) = 247.33. So, an exponential…

A: The given conditions are: ae0.319b=MC0.319=222.23 and aeb=MC(1)=247.33. To Find: Exponential model…

Q: The matrix below is in echelon form. xy 1 10 00 00 Write the corresponding linear system. equation 1…

A: Answer given below.

Q: Find the length (magnitude) of a function gradient z(x, y) = √√2+ sin(x²)- y² at the point P(√7, 1).…

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Q: [S S Use Stokes' Theorem to evaluate curl F. dS where F = (x + y)i + (y − x + 3) j + e^²+y−² k and S…

A: Surface integral

Q: 6. 3%) Find the (₁1-1)) (20%) Consider the linear transformation T: RR represented by T(x)= Ax. Find…

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Q: What is the distance of the point (7, 2, 8) to the line through the points (-3, 0, 1) and (1,-4,-1)?…

A: We know,             Equation of the straight line passing through the points (x1, y1, z1) and (x2,…

Q: Let f (t) be the population (in thousands of people) of Math City, as a function the time t (in…

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Q: (a) Find the slope of the curve y=x²-3x-2 at the point P(2.-4) by finding the limiting value of the…

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Q: Graph the solution set. -x+3y < 6

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Q: Using the appropriate substitution, what is the homogeneous form of the given ODE. (x - 2y + 4)dx +…

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Q: U(X) = 2 = + x² + + ( Ult) d U(x)=2x Proof By adomain direct

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Q: Let A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by: xRy ⇔ |x| = |y|,…

A: It is given that S=PA, where A is a set and PA denotes the power set of A. The relation is defined…

Q: Prove directly from the definitions that if g : ℝ → [1, ∞) is a function so that lim x → c g ( x ) =…

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Q: 3. Let f A → X be a function such that A CX. Show that if A is compact, then the range of f defined…

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Q: Let (a) Show that f(x) is differentiable and that the derivative f(x) is continuous.

A: The given series is fx=∑k=1∞sinkxk3. To Show: fx is differentiable and f'x is continuous.

Q: If r = (x, y, z), prove that V (²) Sim

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Q: Q2. Find L{f(t)} if a. f(t)=e" sin 5t b. f(t)=t² cost

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Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A: The given sequence, an=ln 3-ln 2+ln 4-ln 3+ln 5-ln 4+.....+ln n-1-ln n-2+ln n-ln n-1 We have to…

Q: ²5° c) Evaluate x² (1 + x³)³ dx

A: We solve given integral by method of substitution.  To make integral easier,  we substitute some…

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Q: Find P(27 < X < 32) if X is normally distributed with mean 24 and standard deviation 5.

A: The answer provided below has been developed in a clear step by step manner.

Q: Find the directional derivative of the function z(x, y) = e³tan(y) + (x + 1)²sin(2y) at the point…

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Q: The average profit of a company (in millions per month) from 2001 to 2015 can be modeled by the…

A: The average profit of a company from 2001-2015 is modeled by y=4.51.2x+1.05 where x is the number of…

Q: Prove the correctness of kruskal Algorithm.

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Q: A rectangle has its base on the x-axis and its upper vertices on the parabola, y = 27 - x². Find the…

A: A rectangle has its base on the x-axis and its upper two vertices on the parabola, y=27-x2 We have…

Q: Graph the solution set. x ≥ 6 O ● No Solution Help -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 A 10 9 8 7 6 5 4…

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Q: 3. Construct a convergent sequence (n) and a bounded sequence (yn)-1 such that both (n + yn)n-1 and…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: i. Show that if y(t) is a real function satisfying y = y, then cn = Cn for all integers n, where the…

A: For i) take conjugate both sides.For ii) multiply e^{-imωt} and then integrate .

Q: Consider the triangle in R" whose vertices are the origin, the point all of whose coordinates equal…

A: Given a triangle in ℝn whose vertices are the origin, the point with all coordinates equal 1 except…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Prove that if x is any non-empty set then the function d (x,y)…

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Q: The flow diagram below indicates the traffic flow in and out of three intersections during rush…

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Q: 5. Prove that if S and I are countably infinite sets (meaning |S| = |N| = |T|) then SUT is also…

A: Due to Bartleby answering guidelines I have solved only question no 5.

Q: f(x) = ₁ ; a X x-[ax] [3,4) ( D=? (domain)

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Q: A maple leaf is caught between a car's windshield and the windshield wiper. The windshield wiper is…

A: Given that the windshield wiper is 50 cm in length and sweeps through an angle of 143°. The leaf…

Q: 1. Consider the function f: R → R defined by f(x) = x sin(¹). A. For every x in R, the following…

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Q: Given: D is the midpoint of AC, ED FD and LEDA LFDC. Prove: ZA ZC. Note: quadrilateral properties…

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Q: Let X(t) be a zero-mean WSS Gaussian random process with Rx(t) = e¯¹². Suppose that X(t) is input to…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Find the exact value of each expression. (a) sin(40°) cos(20°) + cos(40°) sin(20°) (b) sin(75°) (c)…

A: Using formula, sinAcosB+cosAsinB=sinA+B in part (a) ,we have (a)-:…

Q: 2. Consider the function g(x) = x cot (3x). 3x A. Function g can be rewritten as · cos(3x) (33).…

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Q: Solve the equations, giving your answers in exact logarithmic form each time (a) sinh x = =coshx;…

A: We solve the following equations.

Q: Given the function y=ex+2x+1. Find the derivative of the inverse function at x=0.

A: The given function y=ex+2x+1. We have to find the value of the derivative of the inverse function at…