Put the equation that is in general form: y = x² + 12x + 32 into standard form: y = (x - h)² + k: Answer: y =

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A: Note; since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 3. Evaluate [[[ 20 av G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Solution :

Q: 3. Let f: AB and g: BC be invertible functions. Prove that (gof): A+C is invertible and (gof)-¹=f-¹…

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Q: 1. Solve the difference x²-2x-8 < 0.

A: Solution of the difference equation

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Q: The following are the coordinates of a triangle: A(4, 4, -3), B(2, 4, 4), and C(-2, 4, 0), find area…

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Q: 1. Given cot 0= -√√3, how many possible measures of angle are in the domain -27 ≤ 0≤2n.

A: Given that cotθ=−3

Q: Complete the table. y + 1 = -X -2 0 1 Alu y 00000 (x, y)

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Q: Find a general solution to the differential equation. y' + 2y = 2 tan 2t - 3t 21-11e³1

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Q: {₁,...,} is linearly independent if and only if {₁,...,} is an orthogonal set. True False

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Q: 5. Solve the following differential equation using the Method of Variation of Parameters -2x y" + 3y…

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Q: TRUE or FALSE 1. The set R³, with the vector addition operation defined by (a1, a2, as) (b₁,b2, bz)…

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Q: let P: XY be a function prove that Phas an inverse if and only if fis abijection.

A: Let us define a bijective functions. We know that , a function f : X → Y is bijective if it is both…

Q: In each of Problems 13 through 20, verify that each given function is a solution of the differential…

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Q: The average score of Lovely in her 6 math quizzes is 19.If she will not include her lowest score,…

A: Average: It is defined as the ratio of the sum of numbers of the given data set to the total number…

Q: Q2/ Find the slope of the tangent to the curve at x = 8 y = 3x5 + 2√x + 4 + 4 + + 2³√√x+¹2+√5 3x²…

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Q: What is the order of the unique Lagrange inter- polating polynomial that passes through n + 1 data…

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Q: Fit the following data using Lagrange Interpolating Polynomial X 1.5 5 -4 10 f(x) -4 25 -10 7.5

A: Lagrange's interpolation formula for 4 points can be defined as :…

Q: 2. Given a non-linear equation (e^-x) - x =0. Use fixed point iteration method to find the root of…

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Q: [4] Let f(x) = = {₁2 of f. (b) (c) (d) Sketch the odd periodic extension of f. 1 (e) Find the…

A: The given problem is to find the Fourier sine series of given periodic function with given period.

Q: 1. Find the product of the following decimal numbers. 1.) 4.54 x 0.16 = N 4.) 0.38 x 7.11 = N 2.)…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the system of linear equations below: 5x-4y+2z=21 -x-5y+6z=-24 -x-4y+5z=-21 a.      Solve…

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Q: Iff is Riemannintegrable fuction, then prove the following Ⓒlft is Riemannintegrable (2) • fis…

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Q: Low-Order Polynomial Model Problem Given the set of data points below 6 7 Xi 0 1 2 3 4 5 Yi 23 48 73…

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Q: Suppose that at each birth, having a girl is not as likely as having a boy. The probability…

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Q: 3.7 2 Find the values of the numbers a and b such that the change of variables u = x + ay, v = x +…

A: Given: u = x + ay v = x + by

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

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Q: Find the least-squares solution to the equation 1 0 2 x = 1 2.1. Suppose = (x₁, x₂), then X1 x2

A: For a system AX=b least square solution is : x→=(ATA)-1ATb

Q: H.W: Solve the differential equation y'-(1+x)(1+ y²) = 0

A: To solve the below differential equation. y'-1+x1+y2=0

Q: Solve the initial value problem. Express y explicitly in terms of t. dy t = dt y (1 + f²) y(1) = -2

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Q: Suppose that at each birth, having a girl is not as likely as having a boy. The probability…

A: To find the expected number of boys in a 3-child family.

Q: Find a general solution to the differential equation. y'"' + 2y = 2 tan 2t 3t -1/1e³t 4

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Q: Use variation of parameters to find a general solution to the differential equation given that the…

A: We are given a second order linear differential equation with variable coefficient and two linearly…

Q: Determine the classification of error when the errors are derived from a computing machine.…

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Q: The number of salespeople assigned to work during a shift is apportioned based on the average number…

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Q: O d) the height of corn in a field and the amount of precipitation during the growing season

A: Follow the answer.

Q: y=etan 3x

A: We find the derivative of y=etan(3x).

Q: Let t, ao,..., an-1 be real numbers. As usual, let Id, denote the n x n identity matrix. By using…

A: The answer is given with explanation in the Step-2 Box. Please check it.

Q: 10+1 + 10 + 1 is divisible by 3 for n E N.

A: To prove the given statement we will use the method of mathematical induction in which first we…

Q: 9 The outward flux of the vector field F(x, y, z) = (+0 the boundary of the region E = {(x, y, z) =…

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Q: Show that the given conditional statement (p ^q) v(p ^r) → (q vr) is a tautology using truth table.

A: We know that ,  Conditional Statement are those Statement where a hypothesis is followed by a…

Q: a) Suppose A, B and C are sets. What do you need to show to prove the following using the definition…

A: Definition : A⊂B iff (x∈A⇒x∈B)WLOG : Without Loss Of Generality.

Q: Find the general solution to the differential equation (7x+5y)dx + (5x - 8y³)dy = 0

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Q: Use the separation of variables method to find the solution of IBVP du du at ax² 0≤x≤4, 120 Subject…

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Q: a -> Show that the given conditional statement (p ^ q) v (p^r) (qvr) is a tautology showing the…

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Q: .. Solve the following differential equation using the indicated method. (c) y" + 3y' + 2y = 3e-2x +…

A: We now solve the equation y"+3y'+2y=3e^(-2x)+x by the mathod of variation of parameters.

Q: Let C be the space curve represented by represented by & (+) = [(4-2+, 36-2, 61) a.) Reparametrize R…

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Q: Determine if there are any inflexions on the graph given by y=2x4-3x³+ x²+6. Proof they are points…

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Q: See Handout 14. Let f(x) be a function of period 2 , where f(x) = 4x for 0<x< π and f(x)=0 for…

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