● Solution : Question 9: Use Cramer's rule to solve : 6x12x2x3 = 0 3x1 + 3x2 + 2x3 = -1 4x₁x₂ + 3x3 = 1

Q: Use the method of undetermined coefficients to find one solution of y" - 4y + 14y = 80e²t cos(3t) +…

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Q: Electric charge is distributed over the triangular region D shown below so that the charge density…

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Q: Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y² = 5x,…

A: The region in the first quadrant bounded by the given curves is plotted below. See that for the…

Q: Find the eigenvalues of the given matrix. -24 25 -20 21

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Q: Evaluate the integral when I = f(x, y, z) = 2² + 3xy and S is the portion of the plane x + 2y + 2z =…

A: I=∫SfdS where fx,y,z=z2+3xy and S is the portion of the plane x+2y+2z=0 above the unit disk x2+y2≤1

Q: Determine whether the series is convergent or divergent. In n n² O divergent

A: To determine whether the series Σ ln(n)/n^2 is convergent or divergent, we can use the integral…

Q: EVALUATE: A = Ꮭ Ᏻ 7[ Ꮖ cosx + siny dy dx

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Q: [10] (3) EVALUATE: A = = **** sin(y²) dyda HINT: Perform a reversal of integration

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Q: 9.22. Let F be a field, let f(x) = F[x] be a separable polynomial of degree n ≥ 1, and let K/F be a…

A: F is a field, f(x)∈F[x] is a separable polynomial of degree n≥1. K/F is a splitting field for f(x)…

Q: = 11. Evaluate ffs (VXF) dS, where F yi + (x-2x³z)j + xy³k and S is the surface of a sphere x² + y²…

A: To compute the integral we use the stokes Theorem:

Q: You have space in your garden for 60 small flowering bulbs. Crocus bulbs cost $0.25 each and…

A: We have to find number of crocus and daffodil bulbs that can be bought using given data.

Q: = (2xy + z² )i + (x² +z)j + (y + 2xz)k, determine a possible value for .

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Q: Let h(x, y, z) = ln(x² + y² + z²). (a) What is the direction of maximal increase of h at the…

A: Given function:  hx,y,z=lnx2+y2+z2 To find: a) Direction of maximum of h at the 1,1,1. b) The…

Q: 5. Ns 50+ dz dr do.

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Q: Match the graph to its function: a) y=3-5x² b) y=5+3x² c) y = 5-3x² d) y=3+5x²

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Q: 3.1.22 Show that any nontrivial simple graph contains at least two vertices that are not…

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Q: We have said what it means for a formula F to be: (1) a tautology, (2) contradictory. That F is a…

A: We have to find whether given statement is tautology,contradictory or contingent in each part.

Q: An object occupies the volume of the upper hemisphere of x² + y² +2²=4 and has density z at (x, y,…

A: We have to find the center of mass of the upper hemisphere of the x2+y2+z2=4 Density of the…

Q: = a Exercise 7.1.23 Let T: C→C be a linear transforma- tion of the real vector space C and assume…

A: (a) for all z and w in C, there exist real numbers a, b, c and d such that              z = a + ib,…

Q: . Suppose we have a graph with two or more vertices, with no loops (i.e. no edges that have both…

A: A graph with two or more vertices, with no loops and no multiple edges.

Q: Evaluate the triple integral Enter an exact answer. Provide your answer below: z=1 y=zx=-2y-2z+2 Ĵ Ĵ…

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Q: A loan of $15,000 is paid off in 36 payments at the end of each month in the following way: Payments…

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Q: Solve the following set of equations using the Gaussian method. (If there is no solution, enter NO…

A: The given system of linear equations, 111215-351x1x2x3=61514 We have to solve these linear equations…

Q: Draw a Venn diagram that illustrates the relationships among the given sets. S = {Gateway, Dell,…

A: We have to draw Venn diagram using given information.

Q: Which ordered pair is the vertex of y=|x+2|-1 ?

A: Given function is y=|x+2|-1. Using the definition of the modulus function that x=x if x≥0-x if…

Q: onsider the multiplication operator LA: R² R² defined by LA(z) = Az where A = -6 is the standard…

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Q: Find the eigenvalues of the given matrix. Show All Your Steps. 17) -24 25 -20 21 2₁]

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Q: Simplify the Boolean expression. (AC+ BC) + (B+CĀ)=

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Q: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x² + 8 f(x) 1 12

A: We know the formula for the slope of the tangent line y=fx at x=x0is y'=f'x0

Q: Find a basis for the null space of the matrix. Show All Your Steps. 2) [10-7-2] A = 01 7-2 [00 0 0

A: The given matrix is A=10-7-2017-20000. We have to find the basis for the null space of the matrix.

Q: Part 1: The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B- coordinate vector of…

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Q: Determine if the vector u is in the column space of matrix A and whether it is in the null space of…

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Q: Let {u₁(x) = −6, u₂(x) = − 12x, uz (x) = 12x²} be a basis for a subspace of P₂. Use the Gram-…

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Q: Prove, for all sets X and Y, “the inclusion-exclusion principle”, i.e. #(XUY)+#(XnY) = #(X)+#(Y),…

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Q: Let (a) (b) 8 = {positive integers less than 15}; X= {multiples of 2}; Y = {multiples of 3}. Show,…

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Q: A football coach hears that a new exercise program will increase upper-body strength better than…

A: (1). The explanatory variable is the type of program, specifically whether the player undergoes the…

Q: Question 8: Find the characteristic polynomial, eigenval- ues, and ONE eigenvector for the following…

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Q: Define for n ≥ 1, fn(x) = n sin(x² /n²), x = R. Then, limno f₁ fn (x) dx = 0, because fn (x) ⇒ 0…

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Q: Match the parametric equations with the graphs labeled I-VI. Give reasons for your choices. (Do not…

A: There are few parametric equation given with the graph. We have to match the equation with the…

Q: In the given sets: U = {a, b, c, d, e, f, g, h, i} A = {a, c, f, h, i} B = {e, g, h, i} C = {b, f,…

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Q: If the area of shape A is equal to the area of shape B, find the perimeter of the shape below. A) 42…

A: The area of A and B are equal

Q: Question 2 B  What are the features of the funtion f(x)=log_(3)x-1 Full explain this question and…

A: The given function is f(x)=log3x-1. To Explain: the features of this function.

Q: -2 2 2

A: A graph of the function is given, we have to find the equation of the graph.

Q: Sketch a graph of ƒ(t) = et on an arbitraryinterval [a, b]. Use the graph and compare areas of…

A: Graphical representation of three areas:

Q: 5. Shade the given region on the corresponding Venn Diagram. (a) (c) AnB C B (AUBUC) C B A (b) (d)…

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

Q: n as f • 27 (²) 2n n = 1 Evaluate | where f(x) => x" by identifying it as the value of a derivative…

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Q: What is the coefficient of 3 in the expansion of (1 + x) 10₂ 300 78 120. 130 40 30 169

A: Expression : 1+x10

Q: (a) Find all the relative extreme point(s) of g(x) = xe -(R+1)x (b) Use the result of (a) to deduce…

A: (a) The function gx=xe-R+1x is given with the domain x∈ℝ. We will assume R is a constant in the…

Q: 1- Find the solution to the given system that satisfies the given initial condition. -8-1 17 -6…

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Q: Given v = U₁ = 0 V= -8 find the coordinates for v in the subspace W spanned by 1 11 -1 -1 -6 -1 , U2…

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