P3 have the inner product given by evaluation -3,-1, 1,3 produce an orthogonal busis for P2 by applying Gram-schmidt process to the polynomials 1, t, t²

Q: of Calculate the following divison (6x4y3) (4x45) (12x4) (x²y) and write your final answer in the…

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Q: Find the volumes of the solids generated by revolving the shaded regions in Exercises about the…

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Q: A number of particular articles has been classified according to their weights. After drying for two…

A: Given data Class 1st weighing 2nd weighing 0-5 a x 5-10 b y 10-15 11 40 15-20 52 50…

Q: Given: U= {x|x is the set of positive integer} A = {x|x > 19} B = {x | x is divisible by 5} Choices:…

A: Here we use basic set theory

Q: J What region in R³ is represented by the inequalities 3. 3 3 +852²+3x+3+ y²-2y + 5+ 3²-4²+4≤ ³+10?…

A: To find the volume if the region use the formula of volume of the sphere .

Q: transformation

A: We find required standard matrix A for T.

Q: The altitude of the equilateral triangle ARMS is SA = 27. Find the exact length of M.S. S M 27 A R

A: For an equilateral triangle, h=32a. Here, h is the length of the altitude and a is the length of the…

Q: Q.7 (a) Find the Fourier series corresponding to the function f(x) = (1-x², 1 (-2,-2 ≤x≤0 0<x<2

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Q: A car accessory is sold for $41.33. The store's markup based on cost is 46%. (a) What is the cost of…

A: The markup is calculated by subtracting the cost price from the selling price.   The markup based on…

Q: (b) Let f and g be contraction functions with common domain R. Prove that (i) The composite function…

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Q: With the use of: local linear approximation Estimate: In (V0.99)

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Q: Question #3 3. a matrix and a scalar A are given. Show that A is an eigenvalue of the matrix and…

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Q: Consider the region R below bounded by the curves C₁ x - 4y = 4, C₂ : y =√x - 1, and C: x + 2y = 4.…

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Q: 6. Show that when 0 <|z − 1| < 2, (z-1)(z-3) Complex Analysis -3 (2-1)" 2n+2 R=0 2(z − 1)²

A: We prove this by using Laurent Series Expansion.

Q: The value of the integral Im(iz)dz, where C: z = 2, counterclockwise, is

A: Given integral is ∮CImizdz, where C:z=2 counterclockwise. We have to evaluate the given integral.…

Q: Find the inverse of the following matrix 2 3 0 1 4 6 ol

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Q: 42.Suppose the prefix form of an expression is + c-d*fg. What is its postfix form? A. cd+fg*- C.…

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Q: 2 cos²xsinx V2+cosx S- dx

A: It is known that ddxsinx=cosx. It is known that: ∫xndx=xn+1n+1+C.

Q: For items 53-55. Refer to the graph below: B E F H 53. Using Kruskal's Algorithm, the last edge to…

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Q: The sum of the squares of two nonnegative numbers is to be 4. How should they be chosen so that the…

A: Given that the sum of the squares of two nonnegative numbers is to be 4. Let the number be x and y…

Q: Prove the following equalities using equivalence laws: a. (r^s) A (rVs)=r b. r→(st)=(rA¬s) → t (pq)…

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Q: Question 5 Use variation of parameters to solve the differential equation x²y" + y = x. [Leave ₁ and…

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Q: 2. Refer to the figure below. Point O is a center of the circle, and BC is a segment. Solve for the…

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Q: 17. Given the following degree of the vertices of an undirected graph H = (4,1,5,3,4,3), we can…

A: For the given degree of the vertex of an undirected graph which of the following is correct :-

Q: 16. Which of the following statements is/are true? I. The order of directed graph G is always half…

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Q: volume of the solid obtained by rotating the region bounded by y=x^2, y=3x about the line x = 3…

A: In this question, the concept of the volume of revolution about the line is applied. Given,…

Q: III. Let R be the region below enclosed by the curves 2 x = y + 2y, x + 5y = 0, and x = 5. Set up…

A: Suppose a region is enclosed by two curves x=fy and x=gy. To calculate the volume of the region…

Q: 1.2 The relationship between the displacement, s, velocity, v, and acceleration, a, of a piston is…

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Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x,y) =…

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Q: f(x) X- COS(X) 1 + x 2 By using newton rafson find the solve.de ToL = 0.0005 1 X₂=1

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: VI. Determine the instantaneous rate of change of the function 2 f(x) = ² Love √x sin (³) dt 1+√t 10…

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Q: 15.Consider the group (A, *) where *is defined by the table below A B C D ABA D C BA в с D C D C A B…

A: Here we use cayley table to find this.

Q: tebooks are sold. age cost per notebook at a minimum?

A: The given information are  1. inverse demand function P=70-0.25x 2. cost function C= 0.5x2+10x+800

Q: Back Substitution Solve the following system by back substitution 1. x₁ - 2x₂ + x3 = -1 1 x₂-3x3=5…

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Q: 4. A binary operation a*b = 1/(ab) defined on positive Rational Numbers (Q+) is just a groupoid a…

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Q: 30. The region in the first octant bounded by the coordinate planes and the surface z = 4 - x² - y

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Q: (a) Solve the differential equation ' + y + y = 0. (b) Use the method of undetermined coefficients…

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Q: 23. Which of the following is/are true among the Graphs A, B, and C? A Only Graph B is a subgraph of…

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Q: VII. Given a region R enclosed by the curves πχ y = 1 + sin 4 as shown below. (2,4) (2, 2) (-2,0) Y…

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Q: out the ar and y axes shown in the figure and the z' and y' axes with origin at the centroid. y =…

A: find area of curve

Q: III. Let R be the region below enclosed by the curves 2 x = y + 2y, x + 5y = 0, and x = 5. Set up…

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Q: 6. Let U = {2,4,5,6,8,9,10} Y = {yly = 0.5U} Enumerate: a.) P(X U (YOZ)) X = {x | x² 13x + 42 = 0} Z…

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Q: VII. Given a region R enclosed by the curves πχ y = 1 + sin as shown below. (-2,0) Y R (2,4) (2, 2)…

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Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis, and…

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Q: I. Evaluate the following limits. sinh r x² 1. lim r→0 sinhr — –r

A: Given that limx→∞sinhx2-x2sinhx-x

Q: draw the solid x² + y² +Z²- √3x² +31² 2:

A: Any point in the three dimension can be represented by the point: x, y, z. Use a graphing utility to…

Q: egion R enclosed by the curves y = 1 + sin (77), below. y=4- (x - 2)² 4 and x =

A: This is the problem of Arc length calculation.

Q: Question 8 Use the method of separation of variables to solve the boundary value problem ?u ди - :0,…

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Q: 4.x₁-x₂2x3=3 - x₁ + 2x₂ + 3x₂=1 X 2x₁2x₂2x₂=-2 3

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Q: 0.The inverse of the elements of A = {0,1,2} under a*b = (a+b) modulo 3 are A. 0' = 0, 1' = 1, 2' =…

A: The given set A under * is the set ℤ3A=0,1,2a*b=a+b modulo 3Consider the table, Eg:…