Let a, b ∊ R, and suppose that for every ɛ>0 we have a≤b + ɛ. Show that a≤b.

Q: a. Given that v1 = eigenvalues. A₁ = X2 = [] and 72 = 4 are eigenvectors of the matrix -17 12 -18]…

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Q: Suppose you have a value (g = 23) in the field F79. Is g a primitive root (do not compute all powers…

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Q: Don has two pairs of shoes, six pairs of pants, and six shirts. If all items are compatible, how…

A: Given that Don has two pairs of shoes, six pairs of pants, and six shirts. If all items are…

Q: What is the Laplace transform of sint cost? 1 OF +4 O O O 1 s+2 1 2t+2 1 2s+4

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Q: 3. Consider each function f : DR below, where D is its (natural/largest possible) domain. In each…

A: The given function is  and D is its domain.(i) The given values are  , to determine whether the…

Q: A couple received a $133,000 inheritance the year they turned 51 and invested it in a fund that…

A: Given thatA couple received a $133,000 inheritance the year they turned 51 and invested it in a fund…

Q: a. Zadia placed $800 in a savings account which pays 6% interest compounded annually. At the end of…

A: Zadia invested  in a savings account which pays  interest compounded annually.The aim is to find the…

Q: Laplace transform of t² sin2t. [12s²-16] [2323 .(s²+4)². 35²-4 [(s²+4)³. [12s²-16 .(s²+4)6 O [12…

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Q: S Exercise 6.1.13: Find the inverse Laplace transform of (s²+s+2)(s+4)*

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Q: 1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n) = 5n+20 n³ - 10 n² + 10

A: To show that: P(n)=O(n4)We will use the definition of big oh notation to show this, we will find a…

Q: assume a beetle has a normal life span of 3 years. allowing us to categorize the beetles based on…

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Q: Find the partition numbers of  f '(x).  (Enter your answers as a comma-separated list.)

A: .

Q: Use the bar graph from the World View "Comparative Output (GDP)" to answer two questions. 20.6 0.01…

A: Using a bar graph we have to calculate the percentage for given 2 conditions a. and b.

Q: Jump to level 1 Find the Frobenius distance between the given matrices. 市 品品 语言 品品 A= d(A, B) = Ex:…

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Q: ) A) Show that the set of all odd integers is countable, by producing a 1-1 unction F From J onto…

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Q: Ex:2-31 Find all the root of the function: f(x) = x+r³-39x² +31x + 70. Anster: -7, -1, 2; and 5.

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Q: Problem #4: Suppose that a matrix A has characteristic polynomial p() = 24 - 32³ +62² 15. Consider…

A: (i). Given characteristic polynomial is p(λ)=λ4−3λ3+6λ2−15.If λ=2 is an eigenvalue of A then…

Q: Find the approximations Tn. Mn, and S, for n = 6 and 12. Then compute the corresponding errors ET,…

A: Thus, the integral value is 36.Let us assume..

Q: How does per capita GDP in the following countries "stack up" against America's (in percentage…

A: To compare per capita GDP in different countries to that of the United States in percentage terms,…

Q: Let A, B,C M.(R) be three square invertible matrices with real coefficients. Solve the following…

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Q: Let u4 be a linear combination of {u₁, U₂, U3}. Select the best statement. OA. We only know that…

A: In linear algebra if set A .

Q: Consider the pattern. use it to solve for 123456789 x 7200 123456789 x 9 = 1111111101 123456789 x…

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Q: Prove that if R is an equivalence relation on a set A, then the inverse relation R−1 is an…

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Q: The number of elements in a finite field of characteristic p is of the form p\power{n}, where n…

A: We have to prove given statement , which is that "The number of elements in a finite field of…

Q: If f is a bijection of A onto B, show that f-1 is a bijection of B onto A.

A: Since  is a bijection from  onto , the inverse  is a bijection from .

Q: 3. Evaluate : Z 5+2 5+3 L' £^ ( (3 + 25 +2) (65² + 25 +5)

A: We have to evaluate

Q: (c) Prove that there are infinitely many prime numbers.

A: Assume there are finitely many prime numbers. Then, we can say that there are n prime numbers, and…

Q: The bar graph below shows the scores that Gabrielle earned on her recent midterm grade report. 100…

A: Given bar graph isThis bar graph shows the scores that Gabrielle earned on her recent midterm grade…

Q: 1. Consider the matrices 0 4₁-(13), 1 3)₁ 4₂2 - ( -8 -2) ₁4₁ = (3-2). 0 1 3 -5 -4 A₁-(3) -4 0 and A4…

A: We have to match the given matrix with the function represented in the graph

Q: 8. Determine the equation of the quadratic function with the zeros 3+√5 and 3-√√5 containing the…

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Q: rectangular domain R = [0, 3] × [0, 2]. Partition the domain into 6 squares of equal size and…

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Q: 6. Explain why a quadratic function needs to be in vertex form in order to determine the inverse.

A: A quadratic function is given.To Explain:Why does a quadratic function need to be in vertex form in…

Q: Solve the heat equation k a²u 0x² u(x, t) = = u(0, t) = 0, u(L, t) = 0, 0 0 (see (1) in Section…

A: Let u(x,t)=X(x)T(t)From the conditions:u(0,t)=X(0)T(t)=0u(L,t)=X(L)T(t)=0⇒ X(0)=X(L)=0From the…

Q: Find the nullity(A) and a basis for the null space of the given matrix. (If an basis for the null…

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Q: Compute the indicated 3 x 3 determinant. ab 0 0 a b a 0 b

A: The given problem is to find the determinant of the given 3*3 matrix.

Q: . Find the general solution of dy d.x = 2 y + 1 x+y-2 2

A: Given differential equation isdy/dx = 2 ((y+1)/(x+y-2))2

Q: Solve the following linear programming problem by applying the simplex method to the dual problem.…

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Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. F(s) = 12 = s² +9 Your answer…

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Q: 7. Determine the values of k for which the following quadratic equations x²+kx+9=0 with have: a. One…

A: Given quadratic equation: We have to determine the values of  for which the given quadratic equation…

Q: 6. LADW #2.2.1bf, page 46 (you only need to do (b) and (f)) - Note that you need to solve the system…

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Q: Help with the following question. please write the solution on a paper because math problems don’t…

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Q: 6. An object is moving along a horizontal line modelling the position function s(t) = t²-10t; 0 ≤ t…

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Q: 1 Find the inverse of the matrix, if it exists. Use the algorithm for finding A by row reducing [A…

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Q: Write five other iterated integral that are equal to the integral off f(x, y, z) dx dz dy

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Q: When yeasts dissolve with sugar in warm water they activate: the yeast fungi me- tabolize the sugar…

A: Given differential equation ( in billion)The yeast get doubled in  hour

Q: 25.000 0.02 (1+ 1 + . 0.02 48 12 0.02 46-1 12

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Q: ove the following corollary of the projection theorem: Given a linear variety VC R* associated with…

A: Projection Theorem: Given a Hilbert space H and a closed subspace M of H, for any x in H, there…

Q: 5" n→∞ 72n+1 lim,

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Q: 1. Every convergent sequence is bounded. 2. If (s) is a convergent sequence with lims, = s and (t)…

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Q: 4. Let (X, d) be a metric space and d' be a metric on X that is equivalent to d. Let and be the…

A: Let us prove above result