1. n Express the number (12.34)5 in base 10 as m where m, n are positive integers such that m, n do not have common divisor larger than 1, that is, gcd(m, n) = 1.

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A: Part (a):We are asked to determine what the zeros of f(x) become in the combined function…

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Q: 10. Define a relation p on S = {1, 2, 3, 4, 5, 6} by p = {(1, 1), (1,2), (2, 1), (2, 2), (3, 3), (3,…

A: We can find the equivalence classes [1], [2], [3], [4], [5], [6] by determining which elements are…

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Q: Note for the student: For the SVD, eigenvalue decompositions, and matrix approximations, you may use…

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Q: Let x be any set then the indiscrete topolagy ■ is coarser that any topology I defined on x- 5 Let x…

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A: Step 1: Identify the logarithmic rules that apply to the problemn logb x = logb (xn) blogb(k) = k…

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A: Step 1: Givenlog2​P=x and log2​Q=y Step 2:log2​(PQ)=log2​P+log2​Qlog2​(PQ)=x+y Step…

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Q: Z2 are fixed. 8. Determine how the line x = 1 maps into the w-plane under the mapping w = f(z) =…

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A: Given that  log5​(x)=y , we can solve the following expressions: A.  log5​(x2)Using the logarithmic…

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A: Total Present ValueNow, we sum up all the present…

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Q: Problem 1. For the graph in Figure 1. Find an edge cut with 4 edges. Problem 2. Use edge cuts to…

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A: Part a) Find the stationary point(s) of f(x). Step 1: Differentiate f(x)We need to find the…

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Q: Solve for the flow rate along each street. 90 85 Z y V X W 90 06 95 If the road whose flow is z is…

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Q: Solve 2y"-y'-10y= 0, y(0) = −8, y'(0) = 2.5 y(t) =

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Q: (1) Two cables AB and AC are attached to the tower. If the tension in cable AB is T₁ = 8 kN and the…

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Q: 4.8 Let S and T be nonempty subsets of R with the following property: st for all se S and tЄ T. S…

A: Part (a):  We are given that ( S ) and ( T ) are nonempty subsets of  R  (the real numbers), and…

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A: Step 1: Verify if the zero vector is in the seta3=b3 holds for the zero vector:03=030^3 =…

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Q: 2. Find all values of k = R (if any) such that k 個 {1}· [4]} s k is a basis of R².

A: Step 1: Basis: A basis for a vector space is a set of linearly independent vectors that spans the…

Q: 2. Solve the following PDE using Laplace transform: ux + 2xut = 2x, u(x, 0) = 1, u(0,t) = = 1.

A: Given PDE: ux + 2xut = 2x Initial Condition: u(x, 0) = 1 Boundary Condition: u(0, t) = 1 Applying…

Q: (2) A person exerts a force P = 6 lb to open the door as shown. The applied force P lies in the…

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Q: *Exercise 35: Ja Show that Fab (N) (detits A· odj (A) = adj (A). A = A = det (A) IA Lo out (4) (2)…

A: Proof: To prove: A⋅adj(A)=adj(A)⋅A=det(A)⋅IA​ adj(A)=(Cij​)Twhere Cij​ is the cofactor of the…

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Q: (7) Determine the required horizontal force P that the worker must exert on the rope to position the…

A: Mass of crate, m = 50 kg. Thus, weight, W = mg = 50 × 9.81 = 490.5 N. g -acceleration due to gravity…

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A: The formula for compound interest is given by:FV=PV⁢(1+rn)⁢(n⁢t)where:FV is the future valuePV is…

Q: Linear AlgebraShow calculations

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Q: 4. Recall that the principal branch of the inverse tangent function was defined on the complex plane…

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Q: 3. For each of the following sentences, indicate whether or not it is a logical truth, and whether…

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A: Equal size of sliced cake: It is possible to cut the square cake to 9 slices, for instance by making…