Vectors ✓ = [3] V and W = [²] Find the area of the quadrilateral with vertices Ō, V, VW, and W.

Q: -1 98 dit 10. (a) Given the following mapping T R³ → R2. Determine whether T is a linear :…

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Q: Let A = {X € R³ : X and (1, 2, 3), (1, 0, 1) are linearly depedent} Show that A is closed in R³.

A: A={X∈R3:X,(1,2,3),(1,0,−1)are linearly dependent} are same as  A=span{(1,2,3),(1,0,−1)}To show that…

Q: Determine the truth value of each statement. The domain of discourse is R. Justify your answer.…

A: Case (i) : Let . If x is positive real numbers , then multiplying it by itself than it will be…

Q: Use the graphs below to evaluate the derivative. (((x)) | x = 5 dx = 80 0 f(x) 80 x 80 0 80 g(x)

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Q: 43-46. Average and marginal profit Let C(x) represent the cost of producing x items and p(x) be the…

A: Since you have posted a multi subparts question according to guidelines I will solve first(a,b,c)…

Q: Use the average daily balance method to compute the finance charge on the credit card for the given…

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Q: Apply the Existence Theorem to justify whether the differential equation y'=sin(x-1)/((x-2)cos(x+3))…

A: We are asked to apply the Existence Theorem to justify whether the differential equation  has a…

Q: Question 4 A salt solution with concentration of 0.09kg of salt per liter of water is added into a…

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Q: 2. Find the solution set of the following equations (3-2x)-¹ (d) x-1 (e) (x-7)x¹ + (x-¹-7)x=0. + x…

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Q: Find the maximum and minimum possible areas bounded by the curve y(x) in the interval 0 ≤ x ≤ 1,…

A: We have to find the minimum  and maximum possible area bounded by the curve  in the interval ,…

Q: Which equation is a quadratic model for the data set? Hint: Use a graphing calculator or a…

A: To find the equation that best models the given data set, we can perform curve fitting.…

Q: Suppose the sequence {sn} is bounded above by M and {sn} converges to M. Prove sup{sn : n € N} = M.

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Q: Consider the following. P(x) = x³ + 3x² - 16x - 48, C = -3 Show that the given value of c is a zero…

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Q: 5. If limn→∞ an 1 (a) limn→∞ bn (b) limn→∞ A and limno bn = B 0, prove B' an = bn B.

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Q: A. Prove that if n is an odd integer, then 7n - 5 is even. Give three different proofs, using direct…

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Q: 2 -+ Suppose T (+) = sin ² (π +_ ) + e + 13 where + = 0 corresponds to mid night, t is measure in…

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Q: Let T(x) = Ax for the given matrix A. Determine if T is one-to-one and if T is onto. 4 30 6 0 1 3 -4…

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Q: Problem 1: (a) Show that Let f(x) = x³ + 5x² - 4x - 20 5 = 5 4 91(x) = x³ + x² 92(x) = √√ (20 +4x −…

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Q: Let T: UV be a linear transformation. Use the rank-nullity theorem t complete the information in the…

A: The rank-nullity theorem says :

Q: Find the inverse of AB if 5 -4 A-¹ and B-1 = = (AB)-¹ = -2 -4 14 -5 2 ]

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Q: Let the temperature of a point in R³ be given by T (x, y, z) = 7x² + 7z². Compute the heat flux…

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Q: The population of a southern city follows the exponential law. Use this information to answer parts…

A: Given exponential function The population get doubled in  month. The current population is We have…

Q: :. Solve the initial value problem y(x)= dx =√3+ sinx (1+y2), with y(0) = 1. Use t as the variable…

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Q: 3. what is the first eigenvector for this?  4. prove that v1, v2 = [-2, 1, 1]^T and v3 = [3, -4,…

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Q: Find a basis for and the dimension of the solution space of the homogeneous system of linear…

A: We need to find the basis and dimension of the solution space.Dimension is the number of elements in…

Q: Let: Equation 1: Runs created 0.5 + 0.10(Wickets)+ 0.15(Wides) M Equation 2: Wins = 6 + 0.3(Runs…

A: Given that:Equation 1: Runs created (Wickets) (Wides) Equation 2: Wins (Runs created per game) (Runs…

Q: The range of a linear transformation is a subspace of the codomain. The null space of an m x n…

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Q: Q: find the solution of This system of ordinary differential equations by numerical Euler's method…

A: As per the question, we address a system of linear nonhomogeneous differential equations using…

Q: 6. Let A be a 5 x 4 matrix and B be a 4 x 3 matrix. (a) What is the domain of the transformation…

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Q: (a) Let a and b be integers. Show that (3a + 2b)2 + (2a − 3b)2 = (3a − 2b)2 + (2a + 3b)2= 13(a2 +…

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Q: Give examples of two sets A and B such that An P(A) = B and P(A) ≤ AUB.

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Q: For solving the solution of, x – e¯x = 0, in [0, 1], the fixed point method gives, P₂ = e¯ P-¹, for…

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Q: Analysis of multiple variable functions (#differentiation) Let f (x, y) = 1+z²y² (a) Find the first…

A: As per our company guidelines, we are supposed to answer only the first three parts of the question.…

Q: . Sketch the following subsets of R2 and decide whether they are of type 1 (only), type 2 (only),…

A: Type 1 : A Type 1 region lies between two vertical lines and the graphs of two functions of x.Type 2…

Q: Problem 2 (Contour integrals) (a) Evaluate the integral S where y is the regular polygon obtained by…

A: Let us solve the above problem using Cauchy's integral formula and Cauchy's theorem

Q: 3. Find the base of a rectangle of height 7 m and whose area is three times the length of its…

A: Given height of rectangle =h=7mlet base =b mso area =base X height=perimeterGiven area=three times…

Q: Problems 8-9, make a scatter plot of the data. Write the equation of a trend line by estimating the…

A: Scatter plot of data using Python

Q: Show that if a, b, c ER then: (a) a−b=-(b-a). (b) (a + b)(ab) - a(a - b) + b(b-a) = 0. (c) a b=0⇒a=0…

A: To prove Hence proved.

Q: (2k+1)! > 10¹

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Q: explain why x=sin^-1(-0.4) is not a solution to the equation sin(x)=-0.4 on the interval (0,2π).

A: We are asked to explain why is not a solution to the equation on the interval .

Q: Verify that Euler's Theorem holds in Zm, m = 6,9, for all elements a for which gcd(a,m) = 1. Also…

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Q: Show that the wave functions for a particle in a one-dimensional box are orthogonal using B=…

A: We are asked to show that the wave functions for a particle in a one-dimensional box are orthogonal.…

Q: 5. Show that: b>0 and a <0 such that a² = b⇒a= -√b. 6. Prove that there are real numbers a and b,…

A: We are given that b&gt;0 and a&lt;0Now, let a2 = b    Taking square root on both sides, we get,…

Q: If then A-¹ = Given 6 = E 1 3 solve Ax = b. 0 x = A = 3 3 -1 -9 5 -8 5 3 -2

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Q: #1 Let (123) (45). Fill out the following table: TH 7 simplified (as disjoint cycles): The order of…

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Q: to,' i.e. Let X be the space of integers and let R be relation 'less than or equal x Ry if x ≤ y…

A: The given relation is .

Q: Use the Laplace transform to solve A thin 10 rod of length L with insulated lateral surface is held…

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Q: solve xy′ = y ln(y/x)

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Q: Does the limit   limx→0+ sin(1/x) exist? Justify your answer.

A: The given problem is to find whether the limit exists or not.Given limit,limx→0+sin(1x)

Q: Let {an}_1 be a bounded sequence in R and ƒ : R → R be a continuous and increasing function. Prove…

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