The marginal cost of manufacturing a certain product is dC/dX = 17 + 0.005x .  If the cost of producing 100 units is R2000, the cost of producing 400 units is R

Q: 4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (b) Show that k-1 (k+1) n n+1 for every n ≥ 1.

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Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

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Q: (c) Find the slope of the objective function. Slope = (d) What are the values of x and y that give…

A: given objective function fx,y=30x+42y (c) slope of the objective function it is known that function…

Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 cos 0 E³r = g(0) = 1/2 500 € C D: r = 3 the…

A: (1)C : r =f(θ) =3-3cosθ,E : r =g(θ) = 32secθSo,C0 : r =f(θ) + g(θ) =3-3cosθ +32secθ⇒r =3-3cosθ…

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: We can solve this using given information

Q: Resume 1.pdf Use Venn Diagram to find answer to this question. In a party we have these people: 35…

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Q: The principle of Analytic a region in C and f in

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Q: (a) Solve the first order linear ordinary differential equation dy x sin x- + (sin x + x cos x) y =…

A: The solution is given as

Q: ) Using each graph of y = f(x), sketch th [(x) and g(x).

A: (a) Given,

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

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Q: 4). Use rules of replacement to prove the following: a). (p^~q) (p^q) = p b). (pvq) →→ r = (p → r) ^…

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Q: Let S be the surface with equation (z −4)² = 4x² + 4y². 1. Find an equation of each trace of S on…

A: we will find equations of traces and then find type of surface represented by comparing with…

Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

A: given total cost C=500e3x8 and production function x=5t6+1

Q: 2. y" - 6y +9y = 2 sin 3x; y(0) = 1, y'(0) = 1

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Q: 14. Write the given system of differential equation as a matrix equation X' = AX. dx = 2x + 3y, dt…

A: System of differential equations: A finite set of differential equations with one independent…

Q: A company determines that its total cost, in thousands of 3x rands, for producing x items is C =…

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Q: QUESTION 3 Consider the following payoff Table Decision Alternative D1 The State of Nature. 0.84…

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Q: The general solution for the linear homogeneous system depends only on the free variables and there…

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y² - 3x² and…

A: Using trigonometric substitution

Q: Every Möbius transformation w

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Q: X Question 3 of 11 > Find the minimum and maximum values of the function f(x, y, z) = 5x + 2y + 2z…

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Q: 3. The population of Nigeria can be approximated by the function P(1)=130.5-(1.024)' where r is the…

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Q: EV and V' be vector spaces over a field I xists a unique linear transformation, t: V at

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: find the volume of the solid generated by revolving the area bounded by the given curves about the…

Q: Determine the equivalent effective rate of a money compounded continuously at r=5%.

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Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy…

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Q: Find the 4-point Discrete Fourier Transform (DFT) of the sequence x(n) = {1,3,3,4}.

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: Find the Laplace transform, F(s), of the convolution cos(7t) * 8(t - 3) F(s) =

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Q: 1). Which of the following are propositions? Give the truth value of each proposition. a). It is an…

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Q: In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

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Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

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Q: (5² 41² Use t^p (t) = (-1)^ J" (fisi)

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Q: For each problem below, use algebra to answer the questions. You may find it helpful to draw and…

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Q: 8). Prove the validity of the arguments using the method of conditional proof. a). p → q (qvr) → s…

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Q: State the final value theorem and state a practical application where it is of use. Verify the…

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Q: ds π Find a particular solution of = 10csc² 2t determined by s= 2 when t = dt 3

A: I have to find a particular solution to the differential equation                             ds/dt…

Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂:r = 2-2 sin (in red) and let R be the…

A: Given,C1 : r =3C2 : r =2-2sinθand r > 0 , θ∈[ 0, 2π )

Q: Let S be the surface with equation 4y² + 4z²x² - 16 = 0. 1. Find an equation of the trace of S on…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If R(0) = (-1,4,-5),…

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Q: Let C be a curve with the parametric equation in the given. a. Set-up the integral that will give…

A: Set-up the integral that will give the length of C and Determine (algebraically) if C is concave or…

Q: A projectile is fired vertically upward with an initial velocity of 210 m/sec from a point 2 m above…

A: According to the given question we have the following figure.

Q: Q3: Use finite difference method to solve Laplace equation in the red (hand written plzzz) domain…

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Q: Use Eular diagram to determine whether the argument is valid or invalid. State the interpretation of…

A: Argument Some women are mothers. All mothers love children. Therefore, some women love children

Q: rector spaces over a field I and t: V--V' be a linear transformation and to be the dual map of t,…

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Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

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Q: The gradient of the tangent to the curve (image attached)   at  x = 2  is  4. The value of  a  is…

A: The gradient or the slope of the tangent to the curve: y=fx at x=a is f'a.  It is known that…

Q: Find the volume of the solid generated by the region bounded by x² + y = 6, y = x, y = -2 and x = -2…

A: Here we see for a small depth then extend it to all the region.