Q2) Use the factor Theorem to factor the following polynomial: 2x³ + 3x²-17x - 30

Q: Give an example of how the following equations can be used in everyday life, perform a graphical…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 3. Let p and k be natural numbers, with k ‡ 1, k ‡ p, and k | p. Show that p is not prime.

A: Given, p and k are natural numbers where k ≠ 1 and k ≠ p also k | p. Now, k | p so, p = ka ---(a),…

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Q: Find the maximum and minimum of f(x, y, z) = 2x + y - z subject to the constraints 2x + z = 2/ √5…

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Q: Evaluate the triple integral JIJ f(x, y, z) dV over the solid E. f(x, y, z)=√x² + e√x² + y², E =…

A: fx,y,z=ex2+y2E=x,y,z|1≤x2+y2≤16,y≤0, x≤3y, 2≤z≤3

Q: Find all values of x so that the triangle with vertices A-(x, -5, -2), B-(2,-8,-4), and C-(4, -9,-5)…

A: The  area of a triangle with vertices  A(x,-5,-2)  , B2,-8,-4 , C(4,-9,-5) is  '1' .  (.). Area of…

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Q: K Use the given conditions to write an equation for the line in point-slope form and in…

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Q: Consider the Secant Method applied to minimising f(x) = x² + x³ in |x| < 1. We know the minimiser is…

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Q: Find all values of k so that k+4 2 9 k+1 is invertible. 12 To enter your answer, first select…

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Q: Use cylindrical coordinates to calculate Jw J(x, y, z) dv for f(x, y, z) = x, (Use symbolic notation…

A: To evaluate ∫∫∫Wfx,y,zdV, Where fx,y,z=x  &amp; W is the region bounded by x2+y2≤9,x≥0,y≥0…

Q: Convert the given integral into an integral in spherical coordinates. 2 - 2 - 680 x - 68 /*-* I (x2…

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Q: Evaluate the triple integral JILzy where W is the solid determined by the inequalities zy dv, 0≤x≤…

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Q: Simplify your answers if possible (write the answer in the simplest form, cancel all common factors…

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Q: 8. Decide which of the following sets are linearly independent in Rn. Justify your answer in each…

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: Calculate the median of the following data: X f 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 3 7 12 16 22 20…

A: As per the guidelines I have solved first problem.

Q: Exercise 2: Congruence classes 1. Let m € N, m > 1 be odd. Prove that the sum of all elements in Zm…

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Q: If possible, find a complete set of mutually incongruent solutions of each of the following…

A: The given congruences, a) 9x≡12mod 15. b) 81x≡57mod 117. We have to find the solution to the…

Q: Problem 4 from Section 4.1: "Let, A, B, C be sets. Write the following in “if... then" format and…

A: The sets A, B, and C are given. We have to prove that (a) x∈B is a sufficient condition for x∈A∪B.…

Q: Show that if {fn} converges uniformly on {fn} converges uniformly on [a, b]. (a,b) and {fn(a)},…

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Q: P₁₁ = P₁2 = P₁3 = P₂2 = P₂3 = DE P32 = P3 3 = -9 What is the projection p of the vector b = -7 P₂1 =…

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Q: b) { / - n (-1)") n+2

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Q: Let L₁ be the line passing through the points Q₁-(-1, -3, 1) and Q₂=(-4, -6, 2). Find a value of k…

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Q: Exercise: Let A = 35 2 3 3 1 2 32 1 2 1 0 3 -9 18 -57 18 -2 14 -28 -1 2 -4 6 12 -2 -30 -10 5 -9 -2 2…

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: Find the absolute maximum and minimum of the function f(x) = 4x-x² on the interval [0,6]. Give your…

A: Given: The given function is fx=4x-x2. To find: We have to find the absolute maximum and minimum of…

Q: 1 Define the function of by cos(27") 3n f(x) = Σ n=0 a) Use the Weierstrass M-test to show that f is…

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Q: In Exercises 21-26, evaluate det(A) by a cofactor expansion along a row or column of your choice.…

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Q: Solve the given initial value problem using the method of Laplace transforms. z" + 4z +…

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Q: 9.) Find the function whose 2nd derivative is given by f"(x) = 1 - 4x where f(−1) = 1, and f(-1) =…

A: Given that , f''(x)=1-4x  ------(1) Now integrating both sides of (1) with respect to 'x' we get,…

Q: Find the area of the region inside the lemniscate ²-6 cos 20 and outside the circle r=√3. Sketch a…

A: Given curve, r2=6cos2θr=3

Q: A pulse (gas) travelling along a fine straight uniform tube filled with gas causes the density at…

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Q: answer all five parts only HANDWRITTEN answer needed ( NOT TYPED)

A: Concept to be used: Let us assume that the pair of linear equations in two variables x and y is…

Q: Let X = {a, e, h, l, r, t, w}, Y = {1, 2, 5, 7, 17, 18, 21, 27, 30}, and ƒ : X → Y with ƒ = {(a,…

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Q: (a) sequence #1 is provable if and only if sequence #2 is not. _ (b) If sequence #3 is provable,…

A: As per the question, we consider the provability of four different sequences in propositional logic…

Q: Convert the polar equation to rectangular form and sketch its graph. r= 70 -14 14 л 7 -7 у -14 л 14…

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Q: AB4: Evaluate ef (x) f'(x) dx. -3

A: Given: The given definite integral is I=∫-36 efx f'x dx. To find: We have to evaluate the given…

Q: 3. Use logarithmic differentiation to compute the derivative of x²(x − 3) arctan (2x) √1+x² f(x): No…

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Q: If ƒ(x) = (x² + 5x + 6)², then f'(x) = f'(1) =

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Q: b) Differentiate the function below with respect to x. f(x) = (2+3x) sin (8 + 2x) Note: In Text mode…

A: The given function is f(x)=-2+3xsin8+2x. To Find: Derivative of above function.

Q: [S₁² f(x, y, z) = 1 -√√√x² + y² + z², B = {(x, y, z) | x² + y² + z² ≤ 25, y ≥ 0, z ≥ 0} Interactive…

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Q: Suppose f: [0, 2π] → R is defined by f(0) = 2 cos(30) + 3 sin(20) for every angle 9. Which one of…

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Q: B: Find Inverse Laplace Transformer for the following function:- 345 F(s) = 3s3-s²-3s + 2 s² (S-1)²

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Q: dy dx dy dx + + 318 2y X = y = sin(x) 1 x² " given that y = 2 when x = 1 dy dx + 2y tan(x) = sin(x),…

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Q: Prove that (F,|.|) is Banach space where FE{C, R}

A: Definition required:  Let X be a metric space and let xn be a sequence of points in X. (a) Cauchy…

Q: The equations that represent the balance in three different savings accounts x years after 2012,…

A: Given: The equations that represent the balance in three different savings accounts x years after…

Q: Problem. Calculate the Laplace transform L{y"}(s) with data y(0) = 2, y'(0) = -1, y"(0) = 1.

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Q: Consider the sequence (yn) defined recursively by, Y0 = 2 for n ≥ 0, _Yn+1 = Yn². Show that for all…

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Q: 1. Using the abbreviations specified below, symbolize the following English sentences in the…

A: Given: The abbreviations A,B, and C for three statements.To find: The truth-functional logic for :a)…

Q: Find all values of x so that the triangle with vertices A-(-5, x. -2), B-(-5, 5,-1), and C-(-6, 2,…

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Q: In Exercises 11-12, use the inversion algorithm to find the i verse of the matrix (if the inverse…

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