Given: (x is number of items) Demand function: d(x) = 768.8 0.3x² Supply function: s(x) = 0.5x² - Find the equilibrium quantity: 859.545 Find the consumers surplus at the equilibrium quantity: X I

Q: 14. Given the graph of g(x), Draw the graph of g-¹(x). Show your strategy for drawing the graph of…

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Q: 5. Let f(x,y) = x² + xy + y² be a function on the domain D = {(x,y) = R²: x¹ + y ≤ 8 and y ≥ 9}. a)…

A: Given fx, y=x2+xy+y2 Domain D=x, y∈R2; x4+y4≤8 and y≥9

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A: The answer is given in step 2.

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: MATH401 Question 3|- functions and numbers A. Prove that cos-¹(-x) = π cos-¹(x) for any real number…

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Q: 3. Find the vertex, focus, and equation of the directrix for the conic given by (x + 1)² = -20(y -…

A: We have to find focus, vertex and equation of directrix.

Q: Evaluate [/FO f(x, y, z) ds. f(x, y, z) = xy Z S: z = x² + y², 9 ≤ x² + y² ≤ 81

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 17 -…

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Q: Use reference angles to evaluate sec (11"). 3 Enter the exact answers. For the number 7, either…

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Q: 1. 2. b. f(-1)= b._lim_f(x) = c. lim f(x)= 3.

A: 1(a). f(-1)= -2 1(b) lim x-> -1- f(x)=  -3.5

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

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Q: aluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

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Q: A college plans to set up an endowment fund that will provide a scholarship of $5,000 at the end of…

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Q: (a) As an iterated integral, with limits of integration A = B = C = D= Suppose f(x, y, z) = E = F=…

A: Let's evaluate triple Integral.

Q: Consider the function f(t) = 5 sec²(t) — 9t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. (2423-4x) dx = [

A: Here we will solve the indefinite integral,

Q: a) 0 1:3 x dx -3√√9-x² V 2

A: The objective is to evaluate the integral.

Q: Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

A: The arc length s of the curve r→t=x(t), y(t), z(t) for a≤t≤b is given by s = ∫abx'(t)2+y'(t)2+z'(t)2…

Q: Find the center and radius of the sphere with equation (x + 2)2 + (y - 3)2 + (z + 6)² = 16 Center:…

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Q: Find the average value of the function over the given Interval. (Round your answer to three decimal…

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Q: Let f(x) = f'(x) = f'(9) = 4log7 (x)

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Q: Let à = (-2, 2, 3) and 6 = (4, - 1,5). Find the projection of b onto a. proj, b =< Check Answer

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Q: Question 2 Compute the following limit. Give your answer as a simplified radical, if necessary. lim…

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Q: m M|L II k=0 CO M« Σ N சிய

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Q: In a cafe, only coffee and tea are offered. The probability of a customer buys a cup of coffee is…

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Q: 3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is…

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Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

A: Let's find volume by using triple integral.

Q: x2-x1/3=0 x1/3(x5/3-1)=0 How do I get to the final simplification from the first equation?

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Q: X A company manufactures mountain bikes. The research department produced the marginal cost function…

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Q: so xe x dx

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Q: 1. Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Using calculus, find the absolute maximum and absolute minimum of the function f(x) = 7x² − 14x + 4…

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Q: (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

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Q: Let à = (-5, 4, Find the projection proja b =< 4) and b = (-4, 0, -1). of b onto a. -

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Q: 8. Evaluate F. dr using Stoke's theorem when F = (2xy — x²)ī — x² − y² )ī and C is the boundary of…

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Q: 3. a. f(-2)= b. f(1) = c. lim f(x) =

A: Note :- This is multiple sub parts questions and according to our company guideline we can do…

Q: 2 8. y' + ²y = -x²y² cos x

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Q: Find two positive numbers with product 625 and whose sum is a minimum. Enter your answers in…

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Q: Basic Level 1. The graph shows the total cost of making compact discs. 250 Namibian Dollars…

A: According to the graph :-cost of 0 compact disc=N$50 thousandscost of 5 thousands compact disc=N$80…

Q: Let v = 17 + 17 and w = 17 + 8j. Find a number c so that w- cv is perpendicular to v. C =

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Q: What form of the particular solution is appropriate for the differential equationy'' - y'=4+4e*.

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Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

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Q: 1. Which of the following functions grows the fastest as x goes to infinity? O 2x О 3x O Ox20 ex

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Q: 2 1 Expand 2y 0.013 2 3. ✓0.0004:

A: Given problem:- Expand 2y210.013y2230.0004

Q: Let f(x) = ln(x² + 2x + 6) f'(x) =

A: We have to find the derivative.

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given: ∫05|10x-5|dx

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Q: Suppose f(x, y, z) = (a) As an iterated integral, 1 x² + y² + z² and W is the bottom half of a…

A: Triple integral