Please explain

Q: Prove that the function ƒ : R – {5} —> R - {3} defined by f(x) = 3x +1 x-5 is a bijection.

A: Consider the function  defined by .To prove that f is a bijection, we have to prove that f is both…

Q: Adrian buys a used car for $4500. The car depreciates at a rate of 16% per year. How long will it…

A: The depreciated cost after n years is given bywhere

Q: Let -∞<a<b<∞, f is a bounded function from [a, b] into R, a: [a,b] → R is increasing. Choose all the…

A: The conditions under which f&amp;#x2208;R(&amp;#x3B1;)" data-mce-style="display: inline-block;…

Q: Suppose three tests are administered to a random sample of college students. Let X₁, ..., Xy be…

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Q: Given f(x)=x^4-2x^3+28x^2-4x+52, and that 1+5i is a zero of f(x). Find all the zeros.

A: Given f(x)=x^4-2x^3+28x^2-4x+52, and that 1+5i is a zero of f(x).Find all the zeros.

Q: Let V be a vector space, v, u € V, and let T₁: V → V and T₂: V → V be linear transformations such…

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Q: Find a matrix X such that AX=B 0 6 A = [²2 -B = [1 2 ] 91 L7 8. 4

A: Given that we have to find a matrix  .Obviously order of the matrix  is .Let Now so  ,

Q: If T: R³ R³ is a linear transformation such that then T ([;)) *(CD) - [E] *(Q)-E]· · (C)-E] T T 3 2…

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Q: 2. Determine whether or not the set is an ideal in the ring M2×2(R). J-{(8₂9) | PCR} = ER

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Q: -3 5 6 6 6 5 6 38 41 53 Define the linear transformation T: R³ → R¹ by T(T) = A. Find a vector whose…

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Q: Calculate the property tax rate required to meet the budgetary demands of the community. Note: When…

A: We need to find given data.

Q: The average energy E (in kcal) needed for a lizard to walk or run a distance of 1 km has been…

A: Consider the given average energy.

Q: Let -2 3 -3 3 -4 -2 -3 -4 6 -16 1 15 Define the linear transformation T: R³ → R¹ by T(T) = Añ. Find…

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Q: advertising.

A: a) As the amount spent on advertising increases the total revenue will initially increase at a…

Q: 19. For the matrix A = 4) 6 -6 -4 find a general formula for A".

A: The matrixThe characteristic equation|A−λI|=0λ2−(6−4)λ+(−24+24)=0λ2−2λ=0λ(λ−2)=0The Eigenvaluesλ=0,2

Q: Find eigenvalues and eigenvectors for the matrix he smaller eigenvalue he larger eigenvalue has an…

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Q: I draw this on paper

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Q: The linear tranformation L defined by L(p(x)) = -2p' +9p" maps P4 into P3. (a) Find the matrix…

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Q: Find the eigenvalues and eigenvectors of the matrix 5 0 0 -8 -3 0 -3 -3 0 From smallest to largest,…

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Q: The EECS department has 80 professors. They need to choose a EECS1028 redesign team of 4 members and…

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Q: Formulate but do not solve the following exercise as a linear programming problem. TMA manufactures…

A: Let the number of televisions shipped to City A from the location I be x and to City B be y.As the…

Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that are…

Q: The function y₁(x) = x is a solution of the equation (x² +1)y" − 2xy' + 2y = 0. Use Abel's formula…

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Q: 7. 8. Another way of writing 5 = log41024 is a) 54 = 1024 Evaluate log525². a) 25 b) 1024 = 45 b) 4…

A: logbx = y is equivalent to by = x ,where x &gt; 0 ,y &gt; 0 ,b &gt; 0 ,b ≠ 1.logaa = 1 for a&gt;…

Q: every group of order 720 has a subgroup of order 12. disprove by providing counterexample

A: The statement  provided is incorrect. Not every group of order 720 necessarily has a subgroup of…

Q: 6 2 3 26 32 38 X

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Q: 11) The graph of the first derivative, f', of a function f is shown. (Assume the function is defined…

A: Consider the graph of the function , where the function defined for .We know that a differentiable…

Q: A = A basis for the image of A is طانت سته -3 12 4 -1 1 -3 -2 -3 3 5 Find a basis for the image of A…

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Q: Let f(x) = x³ + x² - 4x − 4, g(x) = x¹ + 3x³ + 5x² +9x + 6 and consider the ideal I = (f(x), g(x))…

A: Let ,  and consider the ideal  generated by f and g in the rings  and .Since these are both…

Q: 11 To compare intensities of earthquakes use the formula log₁0 = R₁ - R₂ where I, is the intensity…

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Q: The income distribution for a certain country is represented by the Lorenz curve with the equation…

A: It is given that the income distribution for a certain country is represented by the Lorenzcurve…

Q: ven par Compute the derivative dy/dx as a function of t. Answer: A x = 3tt³, y=9-4t

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Q: Find the matrix A of the linear transformation T(f(t)) = 9f '(t) + 5f(t) from P2 to P2 with respect…

A: The linear transformation defined by .We have to find the matrix .

Q: Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D²: P4 P2…

A: D2: P2 to P2   is a linear transformationD2(x)

Q: True or False? Please justify your answer! (a) (b) If v is an eigenvector of both A and B, then it…

A: We know that a non zero vector v is an eigenvector of a matrix A, if there exists a scalar λ such…

Q: solve and convert this equation into ppm y=21.242x+0.0173

A: We have given equation,

Q: 3. Diagonalize the following matrix. Use this diagonalization to compute A¹⁰ 1 А A = [¹₁2] 2.

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Q: Evaluate the line integral Jox² xz+yz ds where C is represented by r(t) = (t - 1,1-t, 1-t) with 0 ≤…

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Q: Evaluate the triple integral JJS S - 8x² - -8y² dv where S is the solid that lies in the half space…

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Q: Let V be a vector space, v, u € V, and let T₁ : V → V and T2 : V → V be linear transformations such…

A: Here we can use the composition of function formula to find the required values.

Q: Find Sdr where C is a circle of radius 3 in the plane x+y+ z = 5, centered at (2,1,2) and oriented…

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Q: Construct a sequence having {2,7,17,27,63} as its set of accumulation points.

A: We  have  to  construct a  sequence  having  as  its  set  of accumulation points.Note  that : if a…

Q: [PERT] start 9 O 30 months, 20 months O 32 months, 20 months O 33 months, 17 months 00 O 30 months,…

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Q: Let u (x,y) = e ² cosy + x² - y² 2 u is harmonic Find all v (xay) such that u(xsy)tiv (xsy) is…

A: Given that  and  is harmonic.The aim is to find the function  such that is analytic on .

Q: The matrix The eigenvalue X₁ is A has two real eigenvalues, one of multiplicity 1 and one of…

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Q: 9. 10. Evaluate log₂ (1³. a)-12 c) 6 b) 8 The equation of the vertical asymptote for the function y…

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Q: Determine whether the given matrix A is diagonalizable. [1 A = 2 12 -2 0 -3 0 -2 -1

A: An n × n matrix with n distinct eigenvalues is diagonalizable..

Q: f(x) = 1 on [1,00)

A: Let I be an interval and a function  is said the be uniformly continuous on I if corresponding to…

Q: 6. Consider the matrices A= = 2 6 -15 1 1 12 -5; B -6 = 5 -7 3 6 -9 4 (1) Compute the characteristic…

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Q: Find and describe the region inscribed by the lines (x-axis), (y = -x+2) and (x = 2y-4) under the…

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