2. Find the centroid of the area in the first quadrant under the curve y = 4 – x2. Answer:

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Q: 2) Using Rational Root Theorem and Descartes' Rule of signs. Find all roots of f(x)=D3x° + 2x² - 12x…

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Q: Exercise 1.4 Let E be a nonempty subset of an ordered set; suppose a is a lower bound of E, and 3 is…

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Q: HW.2 Find ylo.u), y (4.8) , y (19) ,y(2.1) for the hllowing data in the below table 2 4 5 6 1 -2…

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Q: Logical Equivalence 1. Show that p J (q V r) and (p l q) V (p l r) are logically equivalent using a…

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Q: 4 a Evaluate In 3. b On the axes below, sketch the graph of y = Inx -3 2 3 -2 -3 The graph y = In x…

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Q: 10s s² +16 1.) 4.) 1 1 2.) [s°] 5.) s3 +5s 4 1 48 5 3.) 6.) s² +4s+6 2

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Q: Do the following: (a) The analytical solution to this problem is given by this equation: T(x, t) =…

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Q: Find the best least squares fit by a line to the points (-2, 1), (2,–3), (0,0), (-4,7).

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Q: Let V and W be vector spaces over the field F and let T be a linear transformation from V into W. If…

A: We have to show that inverse of invertible linear transformation is linear transformation.

Q: LDE with Constant Coefficients dªy dx4 + 2y = e-* + xe-* dx dx2

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Q: e of $14,000 roughly 20 years after it was purchased. If we assume that the value of the tractor…

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Q: 2. If the product of matrices cos² 0 cos e sin 0 A = cos O sin 0 sin² 0 cos² cos o sin sin? ó B =…

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Q: y - 2 -1, 3 z - 1 2. Suppose the symmetric equations of lines l1 and l2 are 2 2 - y = z and a = 2…

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Q: 1.37] Consider the following problem: Мaximize subject to 3x1 -X1 -2x1 + 6x2 + 2x2 < 2 + X1 X1, 2x2…

A: 1st we will draw graphs for constraints and then use corner points method to find optimal solution…

Q: Consider the group D4 = (a, b) = {e = (1), a, a², a³, b, ab, a²b, a³b} %3D %3D where a = (1 2 3 4)…

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Q: 3 If X 1 - the value'of X" is 1 3n - 4n (a) 2 + n 5-n (b) - n | 3" (- 4)" (c) (d) None of these 1"…

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Q: theorem/ Letxis Hilbert Sface and T, SEBCK),26F then D Pracf %3D 3.

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Q: Compute the left regular representation of the group G = {e, a, b} given by the group table below by…

A: Inverse element : Suppose G is a group and a∈G then their exit an inverse element b(let) such that…

Q: 6. (a) Express the function f(x) = x in on [0, T] as a Fourier cosine series S(x). What is S(-1)?

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Q: Find the equation and sketch the graph of the surface generated by S revolved about the y-axis.

A: We are asked to find the equation of the surface generated  by the surface S revolved about the…

Q: Consider the group D4 = (a, b) = {e = (1), a, a², a³, b, ab, a²b, a³b} where a = (1 2 3 4) and b =…

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Q: d'y dy Consider the second-order equation +p + qy = 0, where p and q are positive. dt 5. %3D dt2 (a)…

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Q: Part 1 Use differentiation and/or integration to express the following function as a power series…

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Q: Question 3. Prove the vectors m = (0,5) and n = (-2,1) span the vector space R?, or find a vector…

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Q: 15. y = sec'x, y 8 cos x, -T/3 < x< T/3

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Q: August eats a mix of Food X and Food Y for lunch. The amount of protein, calories,and sodium per…

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Q: Problem Four: In a dental clinic with one dentist, the average number of patients from time to time…

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Q: 6) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Review Exercises for Chapter 2, #…

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Q: s-3 F(s) = The inverse Laplace Transform of is O f() = sin 3t- 3 cos 3t O f() = \3 sin 3t-3 cos 3t O…

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Q: Let V and W be vector spaces over the field F and let T be a linear transformation from V into W.…

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Q: • Consider the fiunction g defined by glx, y)> cos (7x y)+ logs (x-y) la) determine dydx

A: The function in the form z=g(x,y) is called a multivariable function. The output of the function…

Q: how that , Oi – y)² = , &i – y)? + E, Vi - ŷa %3D1 =D1

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Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y = eV guaranteed by…

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Q: Given an 8-inch wafer costing $2200 each, with Y, 80%, Y = 98% and die area of 4 x 4 mm², estimate…

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Q: ) Compute the following integrals (i) I = f 8(9– 10.22 + x*) cos(Tx) dx. (ii) I2 = S 6(a(1- a²)) x…

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Q: +)Use the improved Method Salvelue:. -C1ゃ)りy ッh=oて

A: Solve the differential equation using improved Euler's method

Q: Find the particular solution to the equation - 5t ]n t y'' + 10y' + 25y = e Yp(t) =

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Q: 3. The general form of a linear, homogeneous, second-order equation with constant coefficients is dy…

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Q: Consider the group D4

A: Given: Group D4=a,b=e=1,a,a2,a3,b,ab,a2b,a3b and a=1 2 3 4, b= 2, 4 To find : The value of…

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Q: Find the volume of the solid generated when the plane region bounded by: y = ex and the x-axis is…

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Q: Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES: y co) = し h=o.2…

A: Given the ODE y'+5x4y2=0 and  y0=1⇒x0=0, y0=1   Step size h=0.2 Solve using Euler's Method at a…

Q: Solve using a. Gaussian elimination and b. Gauss Jordan elimination methods 2x1 + 6x2 + x3 = 7 X1 +…

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Q: is a function of x and y, z arddns (r and asc, 24evinx Solve for dz and dz

A: We will use chain rule of partial derivative and also for implicit function