why is that line segment used for f', couldn't the other line y=3x+1 be used?

Q: (12) (a) Prove that if x € Z and r² is even, then x is even. (b) State and prove an analogous…

A: We prove following statements by using contrapositive method.

Q: find general solutions  (x^(2) + 1) dy -xydx = 0   b) dv/dx - v = 3e^(x)

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Q: Sketch or graph the given function, which is assumed to be zero outside the given interval.…

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Q: Scenario 1: Start working with a $10,000 bonus and then have your boss pay you 10,000 for 3 full…

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Q: 2) Let m be an integer. One of the following is true: a) m² <2m - 1. b) If m is even, then m³ is…

A: To choose correct statement form given question

Q: Show that Q(√2, √3) = Q(√2 + √3).

A: We have to prove that Q(√2, √3) = Q(√2 + √3).

Q: How many free indices does this expression have? A B + ε v B ij jk ijl j lk A B 1 0 C 3 D) 2

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Q: Conjecture a general formula for the cofactor expansion along the 3rd row of a 3 x 3 matrix. Test…

A: First I have written the general formula for cofactor of 3×3 matrix along 3rd row, then used that to…

Q: (x-2) dx + 4 (x + y - 1) dy = 0 a.) (x + 2y) In (x-2y) c = -2 (y-1) b.) (x + 2y) In (x-2y) c = 2 (y…

A: Given x-2dx+4x+y-1dy=0. This can be written as: 4x+y-1dy=2-xdx⇒dydx=2-x4x+y-1…

Q: (14) Let E denote the set of even integers, O denote the set of odd integers, and x, y € Z be any…

A: I have given the answer in the next step. Hope you understand that

Q: 1. Evaluate the following integrals. esin z (b) fo fo U DO y dy dx

A: Value of the double integration

Q: Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 0.4 [100…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: The following table gives the monthly premiums for an insurance policy on people of various ages. a.…

A: Given data is as follows Age (x) Monthly premium ($) (y) 35 120 40 151 45 219 50 334…

Q: Compute D,x= DEX D'S Dex5 Do you recognize a pattern? Compute De (2x+3x²+4² +5³ +17² −15r=z D²…

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Q: Exercise. Solve the system by Gauss (Unique solution) 2x + 5y + 4z = 4 x + 4y + 3z = 1 x - 3y - 2z =…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: T: R³ R³ be the linear transformation that projects u onto v=(2,-1,1). Find T(x, y, z) Find A, the…

A: Linear transformation and associated matrix

Q: Prove that the zero transformation and the identity transformation are linear transformations. (a)…

A: Given information Let V and W be a vector spaces, let v and w be vectors in V and W.

Q: 2. Let a be a real number, and consider the function h: (-∞, a) U (a, ∞) → R defined by h(x): A. The…

A: We will use the results from the part A and part B.

Q: Find the x-values of the inflection points of f(x) = 4x4 + 54x³ - 42x2 + 6. (Give your answers as a…

A: The inflection points are the points on the graph where the second derivative is equal to zero or…

Q: Find the coordinate vector [x] of x relative to the given basis B = {b₁,b2, b3}. b₁ 11 1 -1, b₂ = -4…

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Q: a) 1) The statement (p^q) vr⇒-pvr is not a tautology. A counter-example is p: T; q: F; r: T. p: T;…

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Q: nt) Consider the discrete-time dynamical system x1+1 = 4x,(1-x₂). If x₁ = ₁, X1+1 = Is x = an…

A: see my solution below

Q: • Let A be an n x n positive definite and symmetric matrix, and X an n × n invertible matrix. Show…

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Q: Graph the linear equation. y=-3X¯ x-5

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Q: Let y(t) be the solution to y = 4te satisfying y(0) = 2. 0.2 to approximate y(0.2), y(0.4), ...,…

A: The step by step solution by using Euler method is given as follows.

Q: Locate the centroid x and y of the area. У T 4 m y = 4 16x² - 8 m- X

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Q: Proving Sequents Using only the Primitive Rules of Proof, prove each of the following sequents.…

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Q: For the equation ax^2 + bxy + cy^2 = 0, let A = [a b/2 b/2 c] (A is a 2x2 matrix) Show that if…

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Q: Determine whether the argument given below is valid or invalid. If I am going to run the marathon,…

A: The logical symbol "∨" is used to denote "OR". The logical symbol "∧" is used to denote "AND". The…

Q: Let D, be the linear transformation from C'[a, b] into C[a, b] from this example. Determine whether…

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Q: . Maximum profit occurs at those x-values for which R'(x) = C'(x) and R"(x) < C"(x), where R(x) is…

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Q: 3) (A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned…

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Q: Solve the recurrence relation subject to the initial conditions. 3. A(1) = 7, A(2) = 18, and A(n) =…

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Q: 4.2 Find the solution subject to the following boundary and initial conditions of the heat equation,…

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Q: Solve the given system of differential equations by systematic elimination. (D² - 1)x (D1)x+ (x(t),…

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Q: Write the equations of two lines such that the system of equations has a solution at point A and so…

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Q: Let x 2 be any real number. We have π (t) t 0(x) = n(x) log x T(x) = - 2² I 0(x) + log x Ta -dt 0…

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Q: Solve f(x) = x3- 2x - 5 using secant method correct up to 3 decimal places. You may also use excel…

A: Let  fx=x3-2x-5 f0=-5&lt;0f1=-6&lt;0f2=-1&lt;0f3=16&gt;0 Since  f(2)&lt;0 and f(3)&gt;0 ( opposite…

Q: 2. Solve the initial value problem. Leave the function in implicit form: - y² yx + 3x² ›Y(1) = −2 dy…

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Q: 1.) Given the equation below, solve it using the following: a.) Method of Undetermined Coefficients…

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Q: 3. Evaluate the following integrals. •√a-r² (b) f ₁-² ¹-² dzdydx fo

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Q: 340°= Hide answer choices A (В B (c) D 17 9 17 9r 17 radians 9r 17

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Q: Let f be a function that maps X into y. Let {Gx|x€ A3 be an indexed family of subsets of Y. Show f"…

A: We use set theory to prove.

Q: 3. Define ln(x) = f₁du. Fix x € (-1, 1). Use u-substitution to prove that Cx x [+1=² - In (1+²) -dt…

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Q: Define F : R → R and G : R → Z by the following formulas: F(x) = (x^2)/3 and G(x) = ⌊x⌋ for every x…

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Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

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Q: Jess bought a car worth $22,348. Her car lost 11 % its worth per year for 6 years. Create the…

A: The exponential depreciation is represented using the equation: f(t)=a1-rt, where a is the initial…

Q: Determine the intervals on which the function is (a) increasing; (b) decreasing; (c) constant. I (a)…

A: The open interval is represented using: (   ) and the closed interval is represented using:     . A…

Q: Exercise III.2. Graph the following sets S in R² and determine which are convex: (i) B = : { ( ₁ ) :…

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Q: 1. Find the critical points and determine their nature for the system x = 2y + xy, y=x+y. Hence…

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