Suppose that x and y vary inversely. Write a function that models each inverse variation. Graph the function and find y when x = 10. x = 1 when y = 11. x = 1 when y = 1 x = 1.2 when y = 3

Q: Consider the following quantities in IR", (a) What will the solution set become (ie, what type of…

A: Solving systems of linear equations is a fundamental topic in linear algebra, with many real-world…

Q: Which of the following is (are) a recursive definition of the sequence {an}, n ≥ 0 if an = 3n+4 ?…

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Q: Recall that the direct sum V₁ V₂ is defined to be the space of pairs of vectors (v₁, v2) such that…

A: note : The subpart (2) & (3) are same questions hence we will only answer the questions (1),…

Q: For the function f(x) = (x² + 2)e¯x the function g(x) is differentiable, and g (x+³) = f-¹(x), and…

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Q: Find y as a function of t if y(0) = 8, y'(0) = 3. y = 64y" + 304y +361y = 0,

A: The given differential equation is 64y''+304y'+361y=0. The initial conditions are y0=8 and y'0=3. To…

Q: A straight line is drawn through the point P(2,3) and is inclined at an angle of 30\power{∘} with…

A: Here,(x1,y1)=(2,3),θ=30°.the equation of the line is x-2cos 30°=y-3sin 30°or  x-23/2=y-31/2or…

Q: The object shown in the figure is axially symmetric and its curved surface is described in…

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Q: Let T be a linear transformation represented by T = -5 -5 - 4 1 5 -5 - Check ALL vectors which are…

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Q: Find the equation of the line passing through the point 4(2, 3) and maki an angle of 45° with the…

A: The equation of a line passing through A and making an angle of 45\degree with the x-axis isx-2cos…

Q: Solve the following differential equation by using integrating factors. xy=9y-8x²

A: xy' =9y-8x2A first order linear ODE has the form of y'x+pxy=qxRewrite in the form of a first order…

Q: Find the slope-intercept form of the equation of the line that passes through (−3,9) and is…

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Q: Sue earns £8.30 per hour for a 35 hour week and time and a half after that. How much would she earn…

A: Given Data: Let us consider the given Sue earns £8.30 per hour for a 35 hour week and time and a…

Q: 2. (a) Let V be an n-dimensional vector space, and let {₁,...,Vn} be a basis for V. Show that if T:…

A: Given V is n- dimensional vector space and v1,…,vn is a basis for V.

Q: EX 4A The table is given 1 -2 1 -1 2 2 2 -4 -3 Find the reduced scalar form of matrix A and then…

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Q: 3. Give the lattice of subgroups of Z₂ X Z₁.

A: Sol:- The group Z2 × Z4 is the direct product of two cyclic groups of order 2 and 4, respectively.…

Q: Let y = 6 3 d= 1= -1 4 -4 -5 -3 1 10 Compute the distance d from y to the subspace of Rª spanned by…

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Q: Let R be any ring. If f(X) = ao + α₁X + a₂X² + . = ao + a₁X + a₂X² + ... + a₂X¹ € R[X], define the…

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Q: an n=1 3n2 – 4sini - 4n4 + 1

A: Series is ∑n=1∞3n2-4sinn4n4+1≡∑an.     By limit comparision test if ∑an and ∑bn are  series of…

Q: Express the following function in terms of the unit step function: 0 2. 0, f(1) = %3D 1,

A: Introduction : Another name for Unit Step Function is Heaviside. Function is a function that can be…

Q: Suppose there is a homomorphism Φ from G onto Z2 ⨁ Z2. Provethat G is the union of three proper…

A: Proof: 1. Since Φ is a homomorphism from G onto Z2 ⨁ Z2, we have that Φ(G) = Z2 ⨁ Z2. Let e denote…

Q: 7.10 Suppose that a line 1 contains a point D that is in the inside of a triangle ABC. Then show…

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Q: Q) Find the relation error use the Simpson's rule to approximate the definite integral. Use n=4,5xdx…

A: Given: In this question, the given details are, To find the relation error use the Simpson's 1/3…

Q: Consider the statement For all n E N, 1+3+5++ (2n-1) = n². (the left hand side is the sum of the…

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Q: Consider the differential equation d xcos(y)+(x+2)sin(y) = 0. First, show this equation is not…

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Q: Show that the matrix TR2 is the inverse matrix of (R-1)²T-1.

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Q: (b) f: M₂x2 → R¹ given by a+b+c+d a+b+c +) a+b a (a b) (c) f: M2x2 → P3 given by a b с →c+ (d+c)x+…

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Q: (9) Convert each English sentence to a symbolic statement or vice versa. (a) Every nonzero real…

A: a) - Every Nonzero real number has a multiplicative inverse.  b) Every real number has Additive…

Q: The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus…

A: Given that                        Lower limit of range H = 710 220-a ------------- (1)…

Q: An investor is setting up a fund which requires 11 years of contributions. The investor pays £200…

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Q: [10] (2) GIVEN: The three points in R³: B C FIND: a) the measure of ZABC, A = (-1,2,0) (1,0,1)…

A: Given 3 points are  A = -1, 2, 0  ,  B = 1, 0, 1  ,   C = 0, 1, -2             BA→ = OA→ -  OB→…

Q: Transform all Elements of the equation (t) into the Basis B and check their validity in the the new…

A: As per the question, we are given a system of linear equations in the standard basis and asked to…

Q: 3. Prove from first principles that the following sequences converge. (Hint: your first job is to…

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Q: Given α = 0.01, x²=X0.005 = 49.645, s² = 213.16, and n = 28 compute the lower bound for a 99%…

A: Given that α=0.01,χα22=χ0.0052=49.645, si2=231.16 and n=28.We have to compute the lower bound for a…

Q: cy(1) = 4, y'′(1) = −2. y = x²y" +7xy +9y = xº,

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Q: [10] (4) GIVEN: The plane, 2 CR³, 2: 2x + 3y + z = 5 and the point, P = R³, P = (1,3,2) FIND: The…

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Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: The figure shows the graphs of three functions. One is the position function (s) of a car, one is…

A: Graph of the three functions are given, we have to find the graph of position, velocity and…

Q: i) sin² x = -(1−cos 2x) (I used this to no- ii) cos²x == (1 + cos2x) - 2 1 iii) sin a sinb= 2…

A: Euler's formula is  e-ix = cos x - i sin x        From this we…

Q: determine how many Jordan canonical forms are with the given eigenvalues(not counting rearrangements…

A: To Find: All possible Jordan canonical forms of a 3x3 matrix with eigenvalues λ=1,1,1.

Q: a) let-1 ≤x≤ 1. Show that b) Using part (a), find En-1/ 1)", cos(x) c) Find The type of singularity…

A: (a)  Let  fx = x2  x ∈ -1, 1          Since fx = x2 is an even function so the Fourier series of fx…

Q: Find all positive integer solutions for x and y 1 1 ।४ + y 1 5

A: Sol:- To solve the equation 1/x + 1/y = 1/5 for positive integers x and y, we can start by…

Q: 8. Let S = (12345), T = (13)(45) in S5. Describe the group generated by S and T?

A: Sol:- The group generated by S and T is the group {S, T} = ⟨S, T⟩. We first observe that S and T…

Q: 7. Solve the following problem by using Solver in your spreadsheet: Steelco manufactures three types…

A: Given: In this question, the given details are, Solve the following problem by using Solver in your…

Q: 7. Nila drew a 15-sided convex polygon. One of the interior angles measures 155 degrees. Is it a…

A: Sol:- No, the polygon is not regular. To see why, let's use the formula for the measure of each…

Q: Question 5 Solve the exact differential equation (-5 sin(x) -y sin(x) + 3 cos(x))dx + (cos(x))dy = 0…

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Q: (1 point) If E[X] = 5 and Var(X) = 1, then - E[(1 +5X)2] = and Var(1 + 2X) = I

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Q: 5n 4n - 3 Let an = This sequence converges to L = 5. (a) Find the smallest N EN such that |an − L|…

A: Given the sequence an=5n4n-3 which converges to L=54. We have to answer the given questions.…

Q: Let p be a prime and k a positive integer such that ak mod p = a mod p for all integers a. Prove…

A: Given: p is a prime and k is a positive integer such that ak mod p =a mod p for all integers a. To…

Q: Show that y = 2e cos x e sin x is a solution to y" + 2y' + 2y = 0.

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Q: 11. Prove that the set of all 2 × 2 matrices with entries from R and de- terminant +1 is a group…

A: To show that the set of all 2×2 matrices with entries from R and determinant +1 is a group under…