Q5: Euler totient function of n (we use the Greek symbol phi to denote Euler totient function) is the number of positive integers that are between 1 and n-1, inclusive, and are relatively prime to n. What is the Euler totient function of 108?

Q: Use the given information to find the left and right-hand Riemann sums for the following function.…

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Q: k kjer 1 1+ sin² r -dx

A: Given : 11+sin2x. To find:Convergence and  ∫-π2π211+sin2xdx.

Q: If u = 2 + i and v = 2 - 2i, then what would be the result of the following combinations in the form…

A: We know that complex numbers are of the form z=a+bi where a is real part and b is imaginary part.…

Q: Find the volume of the ellipso it x² + y² + 7x² = 49₁

A: The equation of the ellipsoid is        x2+y2+7z2=49          divide…

Q: 1. Show the function T : R² → R³ given by T(x – y, 3x + 2y, 0) is linear.

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Q: 4y"+y=2sec X 2

A: To find the value of y for the given x and the differential equation 4y''+y=2sec(x2) Given that…

Q: Determine whether the sequence converges or diverges. If it converges, find the lin DIVERGES.) 500-n

A: Introduction: A series is considered to be convergent if the partial sums tend to a particular…

Q: Find a basis of the subspace of R4 that consists of all vectors perpendicular to both Basis: 0 -3 9…

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Q: What is the value of f 4xy² dx + (4x²y + 2)dy when C is the part of the circle x² + y² traveling…

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Q: Find (as a unit vector with negative first term) an eigenvector of the matrix corresponding to the…

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Q: et A, B, and X be sets. Prove that if ACB, then AnxCBnx.

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Q: Suppose the first and last columns of a 3 by 5 matrix are the same (not zero). Then __ is a free…

A: Given : A matrix of size 3×5 where first and last column are same. Then _?__ is a free variable.…

Q: The tangent plane to a surface S at a point (a, b, c) is given by the equation a cos(√a² +6²) b…

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Q: Find vectors x and y with llxlls = 1 and llyllm = 1 such that llAll1 = llAxlls and llAll∞ = llAyllm…

A: The given matrix, A=4-2-10-123-30 We have to find the vectors x and y with xs=1 and ym=1 such that…

Q: Which of the following graphs are bipartite? H OA H OC X X S A G T

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Q: a. Supply the missing values in the sequence. 3. 11, 18, 27, 38, 51, 66, 83, 102, 123, b. Given the…

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Q: dy dx -2 y(0)=3 solve the initial value problem given above. y(x)=? OA) 2x+3 OB) x+2 OC) 2 OD) x+1…

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Q: We always want to express step functions in terms of the unit step function Hide answer choices A)…

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Q: Evaluate the surface integral. (x² + y² + z²) dS, S is the part of the cylinder x² + y² = 16 between…

A: Given: x2+y2=16 ,          :  plane z=0 and z=5 To find: ∬Sx2+y2+z2dS.

Q: 2. Find and express the solution of the initial value problem in terms of a convolution integral…

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Q: Find all possible congruence classes x mod 6 such that 2x + 3 = −1 (mod 6).

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Q: Let 18 -3 3 3 [0] ý 3 6 –6 -3 -12 73 Use the Gram-Schmidt process to determine an orthonormal basis…

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Q: A factory contributes £1 million into a small city. It is estimated that 75% of that money is…

A: Total contribution of factory into a small city is  £1million, Money is re-spent back into the…

Q: Find the solution of the initial value problem y" + y = 8(t− n) +8(t−2π), y(0) = 0, y'(0) = 0.

A: The initial value problem is given by:  y''+y=δ(t-π)+δ(t-2π) With, y(0)=0, y'(0)=0 We have to solve…

Q: Let T: R² → R² be a reflection in the x-axis. Find the image of each vector. (a) (2,7) (b) (6, -8)…

A: T: R2 - >  R2 is a inear map which is basically reflection in the x Axis. Therefore for any point…

Q: Let u, v, w be vectors in a vector space V. Which of the following properties need not be true?…

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Q: . Use the power series method to solve (x-3)y""+2x²y"−4xy' y (0)= -2, and y" (0)= 7, Find at least…

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Q: What is the value of f 4xy²dx + (4x²y + 2)dy when C is the part of the circle x² + y² = 1 from the…

A: Here, we will use the Green's theorem. According to Green's theorem: ∫CMdx+Ndy=∬(∂N∂x-∂M∂y)dxdy

Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: Please write it in a function to represent your talyor series.

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Q: I find the 1 f (t) = co + C₁ Sing least squares. best to the fit line or function of the form points…

A: x y x2 xy 0 2 0 0 1 2 1 2 1 6 1 6 ∑x=2 ∑y=10 ∑x2=2 ∑xy=8

Q: math induction

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Q: 5. A field-hockey ball must stay below waist height, approximately 1 m, when shot; otherwise, it is…

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Q: 8. (p f(A) ≤ f(B), then ACB. Let f: XY. Prove that for all A, B C X, if f is one-to-one and

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Q: 0" − 0 = xẻ st

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Q: In the 75th Congress (1937−1939) there were in the Senate 75 Democrats, 17 Republicans, and 4…

A: In the 75th Congress 1937-1939 there were in the Senate 75 Democrats, 17 Republicans, and 4 members…

Q: 2. Use implicit differentiation to find az/ax and az/ay for yz + xlny = z² 3. Use the first…

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Q: 1 1. Let A = (1, -2,4) and B be a nonzero vector parallel to 0, 3 2 2 such that AB = 14. a. Find the…

A: The given vectors are A→=1,-2,4 and B→ is a nonzero vector parallel to 0,12,-32 such that A→·B→=14 .…

Q: A sample of a radioactive substance has an initial mass of 761.7 mg. This substance follows a…

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Q: Given f(x)= x)==-3x+5 Find f¹(3). Write your answer as a whole number or as a fraction. f¹(3)=

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Q: 3 Prove that bim li a) b) lin (√√m² + +1 M-) D (√√√²+1 -√₂)=0 nti M-) D 2 ·m) = a -

A: By rationalisation

Q: Calculate the housing expense ratio and the total obligation ratio (in %) for the following mortgage…

A: Given: The monthly gross income is $2,600. The monthly PITI expense is $633. The other monthly…

Q: Let Anxn be upper triangular. Prove by induction that |A| = []”—1 ªii

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Q: +∞ (-2)(x+5)n-1 n² Determine the radius and interval of convergence of the power series > n-1

A: Given a power series ∑n=1∞-2nx+5n-1n2. To find the radius and interval of the convergence of given…

Q: The velocity vector, v(t) of a particle in motion is given by v(t)=t√r² +4i+e²j+z Find: (i) (ii)…

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Q: Consider the definite integral n lim n→∞ Olim Which of the following expressions represents the…

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Q: 1. Find the first four nonzero terms in the MacLaurin series for the function f(x) = e-² DA. 1 + x²…

A: We use MacLaurin Series of ex and substitute x=(-x2) in MacLaurin series of ex.

Q: The surface area of your surface is

A: Introduction: Calculating a parametrized surface's surface area is quite similar to calculating a…

Q: Please explain what it means to: Rewrite a number to a different base Add two or three numbers to a…

A: 1)Answer    Explanation:-i) Rewriting a number to a different base means Converting the number from…

Q: (a) Show that power series representations are unique. In other words, suppose that for all x € (-R,…

A: As per the guidelines I have solved first question. Power series representation are unique.