1) (a) Circle ONE of the below equations and convert it from either polar to rectangular or rectangular to polar. 4 r = sin(e) - 2x?y = 1

Q: 11 If P(x) 2x* + 6x3 + kx² – 45, find k for which P(-3) = 9.

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Q: Find the particular solution for the following differential equation xy' = y+4x° cos? (2. (2) = 0

A: Given first order differential equation xy'=y+4x5cos2yx with initial condition y2=0 Divide with x on…

Q: Evaluate using geometric series: E 5i(0.5)(-1

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Q: Find the basis of the solution space U of the equation x-y+z-w=0 of the form e_1=(a,1,0,0)…

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Q: 2. Using the given in Example 1, solve using Gauss-Seidel Method.

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Q: In the figure below trapezoid ABCD ~ trapezoid PSRQ. Find the length of AB. A 4y ft (Зу — 5) ft D P…

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Q: b) Consider the following Linear Programming problem: Min z = 2x, – 3x2 Subject to 1 1 z* +2 54 X1 +…

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Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: 1) The multiplicity of the zero -1 of P(x) = -2x(-x – 1)²(x + 1) is: A 2 в 1 D 4 C 3

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Q: Trapezoidal Rule. Use the Trapezoidal rule to approximate the integral 2 ,2 2x dx with n = 4…

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Q: 1. Find the local minima and maxima for f(x, y, z)=x+y+z, subject to the constraints x? –-y² = 1,…

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Q: For the following logarithms, either write the correct value, or explain why the expression does not…

A: Let us determine whether the given logarithmic expressions are correct or not and also determine the…

Q: The differential equation y" – 3/ + y = 0 has y = cje(z/2) sin ( V3z ) + cze(z/2) cos as a two…

A: The solution is given as

Q: Find the optimal solution for the following model graphically Max Z 5X, +2X2 Subject to, X +X2 s 10…

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Q: 5. The half-life period of a certain radioactive isotope is 11 hours. There is a 200 g sample of the…

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Q: of Revolution Centroids of PlaneAreas and Solids of revolution Requirements: a. Graph

A: INTRODUCTION: Calculus provided a method for determining the length of a curve by breaking it down…

Q: Solve the following IVP (without Laplace Transform): d'y , dy - 2y = 6 cos 2t + 2 sin 2t, y (0) =…

A: Solution: Given ivp is

Q: Solve xb =9 mod11

A: Solution:        As 11 is a prime number, by fermat's theorem,        x11-1 = 1 (mod 11)      =>…

Q: siven the power series expression E A_ x(m + 1) A x" n = 1 = 3 1. Force the first power series to…

A: We have to combine two power series which is given in question.

Q: Fatima bought a collector's basketball card in 1990 for $35. The value increases by x % every year.…

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Q: 7. Solve the following congruences, and check your answers: (a) x27 = 3 (mod 110) (b) x7" = 4 (mod…

A: We Know that  Definition of Congruence: If a and b are integers and m is a positive integer, then a…

Q: B. Remainder Theorem and Factor Theorem (Week 2) 1. Using the remainder theorem, find the remainder…

A: Given the functions as (a) 4x3-x2+2x+1÷x-5 let                px=4x3-x2+2x+1 for x=5 p5=453-52+25+1…

Q: Let E be the 3×3 matrix that corresponds to the row operation R3=R3+R1

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Q: 4. Fatima bought a collector's basketball card in 1990 for $35. The value increases by x % every…

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Q: Family of Curves Practice Exercise: Find the differential Equations of the following: 1. Family of…

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Q: Given a polynomial function of degree 6, explain how many minimum or maximum values and how many…

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Q: The point Xg-0 is a singular point to the differential equation csc(x) y" +-y-y-D0. Select one: O…

A: Given differential equation is cscxy''+1xy'−y=0.....1. We have to check whether the point x0=0 is a…

Q: Find the measure of each angle indicated. 6) 52 86 A) 34 C) 35° B) 94 Dy 32°

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Q: The trace of an n × n matrix A = | a;| is the sum of the entries on its main diagonal and is denot…

A: Introduction: Matrix multiplication is divided into two types: Scalar Matrix Multiplication, in…

Q: EThe metabolic rate M of an animal day. This can be approximated by the formula M- 12 of the animal…

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Q: Use the shell method to find the volume of the solid generated by revolving the region x2 and…

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Q: Find all eigenvalues and eigenfunctions of the following e X"+ XX = 0, X (0) = X'(2) = 0.

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Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A O (Ā)ª = Ā - int A |…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find a power series representation for the function. f(x) = x³ tan-1(x³) %3D 8. f(x) = Σ %3D…

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Q: Given: 2a  + 5b + 3c = 2 3a + b - 2c = 3 -a + 2b + c = 1 a. Solve for the system Ax = using Gauss…

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Q: Let r(t) = (V3– t, (el-1) – 1)/(t – 1), lIn(2 – t)). %3D (a) What is the domain of r? (b) Compute…

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Q: 24, , -6 la"b d) Va

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Q: Evaluate the double integral f(r, 0) dA. 3 cos(0) r dr de Sketch the region R. T/2 л/2 2 2 -1 1 -4…

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Q: The matrix -3 - A = has one eigenvalue of multiplicity 2. Find this eigenvalue and the dimension of…

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Q: 2. Let f(z) = cos(rr/4), where r is in radian. Use the huadratic Lagrange interpo based on the…

A: Here given function fx=cosxπ4 and x0=0, x1=1, x2=2, x3=4

Q: Exponential Regression The table below shows the value, V, of an investment (in dollars) after n…

A: Use the calculator to write the exponential regression as follows:

Q: Question 4: Let T be defined as T (v1, v2, v3) = (v1-v2+v3, v2-v3, v1+v2) a) Find the image of (1,…

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Q: PAPER 1 5. FACTORS OF POLY J2009 1

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Q: t solve problem 9

A: Introduction: In vector calculus and differential pure mathematics, the derived function is…

Q: For the following data (10, 20, 30, 52, 64, 67, 98, 100, 200) , the median equal 52 O 67 O 64 O 200…

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Q: 1. Sketch a graph the function Ax) = 3* . Identify the key features. a) domain and range b) any…

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Q: Use the Product Rule or the Quotient Rule to find the derivative of the given function.

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Q: 1. Consider x +y+ z+ 2w + v 3x + 4y + 3z + 3w + 5v W = — 2я — Зу — w - 6у |x, y, z, w E R 2ж + 4у +…

A: we construct a matrix and apply the row operations to get row reduced form from this we can conclude…

Q: 1) (a) Convert the following equations from parametric to rectangular. State the domain and range of…

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Q: Evaluate xy dx + (x+ y)dy along the.curve y = 4x from (- 3,36) to (- 2,16). C xy dx + (x + y)dy =] C…

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