A rope is placed diagonally across two corners of the trampoline. What is the area of both triangles? What is the area of one triangle? Explain how you know.

Q: In this question let W := Mat(n, R) denote the vector space of real n x n matrices with n ≥ 2, and…

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Q: Solve the given system of differential equations by systematic elimination. (D² + 2)x - (x(t), y(t))…

A: The given system of differential equations, D2+2x-2y=0-2x+D2+5y=0 Using the elimination method to…

Q: 12. Write the equation of an exponential equation whose base function is y=2* and has been reflected…

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Q: Find the root by using Newton-Raphson method and use initial value Xo 1.7500. where f(x) = 1/x -0.16

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Q: 6. (a) Let f : [0, 1] → IR be a continuous function. Prove that k−1 k και η - Σ'() = lim Σ'()=…

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Q: Problem 4: Determine the Fourier series for the periodic function of period 2. defined by: f(1) = 2…

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Q: 1. a. 37 b. 38 For the given triangle, use one of the reciprocal ratios to determine to the nearest…

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Q: Prove: if Σ1 fn is convergent on D, then limn→∞ fn(x) = 0 for each x = D. n=1

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Q: If   C(t)=53.2te−0.21t measures the​ concentration, in ngml​, of a drug in a​ person's system t…

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Q: Consider the following graph. • V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,…

A: Solution:

Q: Obtain the particular solution satisfying the initial conditions indicated. 3. (y² + xy)dx-x²dy = 0;…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: Given , v1 , v2 , v3 is an orthogonal set of vectors in ℝ5 .  And  'w' be a vector in span(v1,v2,v3)…

Q: Suppose that Shaquille O'Neal's cumulative free throw percentage, one month into the NBA season, is…

A: Given: Shaquille O'Neal's cumulative free throw percentage, one month into the NBA season, is below…

Q: How many vectors are there in the basis of Col A: Nul A:

A: We have the matrix A and we need to find the number of vectors in basis of col(A) and Nul (A)

Q: Apply the nearest neighbor algorithm to the graph above starting at vertex A. Give your answer as a…

A: The nearest neighbor algorithm to the graph starting at vertex A:                       .

Q: What is the equation of the asymptote for the function f(x) = 0.5(4*-2). + 3? C. x=3 d. y = 4 4. a.…

A: The given problem is to find the equation of asymptote for the given function f(x). Given function…

Q: There is a [Emerald Jade] Mazu altar 8m*6m, the elevation of the completed RC surface (cm) is as…

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Q: Could you please put final answer if its true or false the statement thank you

A: ∀xFx→∃yGy, Fa     ∴∃xGx

Q: X1 0 e) Fill in the following table: Basic Solutions 20 $1 15 $2 4 Intersection Point (from part c)…

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Q: Obtain the general solution of the following differential equations 4. x(x² + y²)² (ydx − xdy) +…

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Q: (Proof by cases: (p₁ V P2 V (Pn →q)) Prove or disprove. V Pn) → q = (P₁ → q)^(p2 →q)^^...^ "The 4th…

A: Let x be any integer.  We need to prov        x4 does not leave remainder 2 when divided by 3.…

Q: In Exercises 17-26, use a Venn diagram like the one in Figure 2.15 to shade in the region…

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Q: Let (,) be an inner product on a vector space V over the field of complex numbers C. Using the…

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Q: Find the equations for W by writing the plane W in R³ as null(A) for a matrix A: 1 W = span 3 1 3 2…

A: Given: W=span13132 , 1131-1 To Find: Equation for W by writing the plane W in R5 as null(A) for a…

Q: Let R be an integral domain and let a, b, c € R. Suppose that ab = ac with a 40. Prove that b = c._

A: Since, the image contains two different problems, according to the guidelines, I am solving the…

Q: factor x as a product of three linear polynomials in Z/30Z[x] by using Chinese remainder theorem

A: Ans- To factor x as a product of three linear polynomials in Z/30Z[x], we first need to factor 30…

Q: G is a graph with adjacency matrix A. We know the following about the matrix A: • The 2nd row of A…

A: The graph G has adjacency matrix A.  Now, by one theorem, we know,          Number of routes that…

Q: Consider the sequence defined recursively by a₁ = -2, a₂ = 2, an+1=-3an-1-4a. We can use matrix…

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Q: Find the third degree Taylor polynomial of f(x, y, z) = xy2z³ at (1, 0, -1). ciuth degree Taylor…

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Q: 2) At an agricultural show, 10 Shetland sheep were ranked by a qualified judge and by a trainee…

A: Entry A B C D E F G H I J Qualified Judge (x) 1 2 3 4 5 6 7 8 9 10 Trainee (y) 1 2 5 6 7 8 10 4…

Q: The compound amount, or future value, Sonia needs in 9 years is $14,000. Her investment will earn 6%…

A: The compound amount, or future value, Sonia needs in 9 years is $14,000. Her investment will earn 6%…

Q: What are the A Courd Vector for [+], [10]. [^] How do A Coords and B-Coords Compare ?

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Q: Exercises I. Let Go be the graph of Fig 1:29. (a). Find G-U where U = {2,0 %zilveszte (b). Find G-F…

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Q: Consider the following equations. f(x) = √x + 6 g(x) = x + 6 Sketch the region bounded by the graphs…

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Q: A tank containing 10 kg of salt dissolved in 1000 L of water has two salt solutions pumped in. The…

A: Given:  The initial salt in the tank is 10 kg. The rate of the first salt (0.2kg/L) is 20L/min. The…

Q: Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix…

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Q: Sketching orthogonal projections Find projvu and scalvu by inspection without using formulas.

A: The given graph is shown: To find: projvu and scalvu by inspection without using formulas

Q: Let V be an inner product space over R. Define a function d: V x V → R by d(u, v) = ||uv|| where u,…

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Q: Find Vf(a), given the following data. 91 Calculate 91, 92 and 93 such that Vf(a) = 92 93. 91 92 93 =…

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Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: The general solution of the following homogenous equation y" - 3y' - 4y = 0 is O y=c_1 e^(x)+c_2…

A: Here we have to find the general solution of the given equation:    y"-3y'- 4y=0

Q: The following differential equation y" - ty' - 2y = sint is a linear equation with independent…

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Q: Find the eigenvalues of A, given that A = and its eigenvectors are v₁ = 1 -0-0-0 A = 2 and v3 = 2 -1…

A: Given: It is given that A=136-84-24-3-1. The eigenvectors of the matrix A are given by v1=-1-11,…

Q: 12. Write an equation to represent the sinusoidal function in the following graph: 0 60 120 ANAA -1…

A: Write the equation of the given sinusoidal function in the following graph .

Q: 14. Suppose we have a diamond-shaped geometric figure defined by the following vertices. ·1. V₁2…

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Q: Consider the set S = 0 3 1 10 8 11 21 27 2 2 0 3 4 CR4 It can easily be seen that S does not form a…

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Q: Use the chain rule to find dw dt dw dt w = xey/z, x = t², y = 6-t, z = 4 + 5t ||

A: I have explained everything with in the solution. Please go through that.

Q: (21) Let A, B and C be sets. (a) Prove that (AUB) × C = (A × C) U (B × C). (b) Prove that C × (An B)…

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Q: 2. Describe the complete solution (all possible solutions) of the linear system Ax = b, where 1 -10…

A: Here we solve the linear system Ax=b.

Q: A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost…

A: The joint cost function is C(x,y)=3x2+10xy+7y2+3900 (A)  When X=190 units, Y=110 units The total…