Factorising quadratic polynomials using the factor theorem

Q: Prove that |A U B| + |A n B| = |A| + |B|

A: Let A and B are two sets. A = number of elements in the set A. B = number of elements in the set B.…

Q: 36. The problem below shows steps in finding the product of two two- digit numbers using this…

A: First we need to find first entry and then we do normal multiplication as always do.

Q: 3. x³7x² + 14x6 = 0

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Q: e the recursive formul

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Q: (b) Let D be a circular domain of radius R with center at the origin. Show that sin(r² + y²) dr dy…

A: We will first transform the coordinates from Cartesian to polar using x= rcos\theta, y= rsin\theta.

Q: Determine the values of partial fraction decomposition for the function F(s)=5+3

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Q: 1. Consider the 2nd order differential equation d²f 2 df + Af (=)=0 dz² z dz To solve the problem…

A: As per the question we are given a second order linear homogeneous differential equation. And we…

Q: e expression 3:30 is a row vector containing integers from (30 to 3) False True O * x=z', array z =…

A: In the first question, the given command will give us the numbers from 3 to 30 as a row vector. I.e.…

Q: Let V=R²³ be a vector space over R and w = {{ x, y, z) € R³ : x = y +z, y, z, XER} show that w is a…

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Q: struction site, there are 4 excavators. Each one must be allocated to exactly one job. The time

A: The given data is as follows   Job1  Job 2 Job 3 Job 4 1 4 2 5 7 2 8 3 10 8 3 12 5 4 5 4…

Q: 6. A 200 g sample of polonium has a half-life of 40 days. This means that every 40 days, the amount…

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Q: -sin20 B)Evaluate the integrals: i) f/2 sinze rdrde, 0 ii) f/2/2 finx 2² siny dz dy dx. 0 0

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Q: (a) Assume that f(x, y, z) and F(x, y, z) are arbitrary differentiable functions such that f(x, y,…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Use a parameterization to find the flux *SSF. F-n de of F=xy i-z k outward (normal away from the…

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Q: c. Given f(x) = 2x - 3, g(x) = -4x² + 9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

A: 1) Given  f(x) = 2x - 3 g(x) = -4x2 + 9   f(x)*g(x)  = (2x - 3)*(-4x2 + 9)  = 2x*(-4x2 + 9) -3*(-4x2…

Q: (s-14)4 te-14 6 tBe4t 5) 6 t324t =) 6 a) then the function f(t) can be: 82 +58 + 14. 8 7 31 s²+ } 8²…

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Q: b) Find the area enclosed between f(x)= = -x² + 4x and g(x) = x² - 6x + 5, over the interval 0≤x≤ 1.

A: Sol

Q: B)Convert r = √2 cos(0-7) = √2 cos(0-) to cartesian.

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Q: using secant method to find a root, an initial guess Xo = 2, X1 = -1 and X2 = -2 with f(X1) = 4 and…

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Q: A) Find area bounded by y = 0, y = √x - x² using double integration. V

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Q: 6. Factor fully x³ - 1

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Q: y X = + 2.2 When solving the differential equation y' singular solution, depending on the parameter…

A: For non linear equation there exist a general solution and may be particular solutions.

Q: +1 * +7 و 2 {مد 2

A: We have to solve given problems;

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.…

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Q: Define := +₁0=1+√, and 7:= 1+5. Determine IQ..](Q).

A: Please find the answer in next step

Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

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Q: .L{cos 5x) = p²+25

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Q: Define the linear transformation 7 by T(x) = Ax. -1 -2 1 1 -4 -3 -1 -3 A = 1 2 -1 4 3 1 2 -1 (a)…

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Q: S Js V is the volume enclosed x (axr)ds = 2aV, where a by the closed surface S.

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Q: Fernando runs a restaurant that sells two kinds of desserts. Fernando knows the restaurant must make…

A: Please see the attachment

Q: Evaluate the double integrals ffe Se-x²-² dxdy, where D = {(x, y) | x² + y² ≤ 4, x ≥ 0, y ≥ 0}.

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Q: Q2 Using the fixed point iteration method solve the equation 2x³-2x-5=0 in [1,2] with € 0.00002.

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Q: Solve the following differential equation ÿ+y+y=e-2x (9x + ln(x))

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Q: (d) (e) n=1 n=1 3n²+ 1 2n² +3 2¹ (n!)² n2(2n!)

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Q: Use the first derivative test to determine the location of each local extremum and the value of the…

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Q: Z {a} is a z-a True False

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Q: .. Evaluate. a) 2³ x 4² x 2-3 b) 81¹/4 - 81/3

A: Evaluation of numbers

Q: Laplace transform of 8(ta) is ea as True False

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Q: 3. Let A be an m x n matrix and be Rm. Given that Ax = b has two distinct solutions u and v. Explain…

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Q: B)Convert r = √2 cos(0-) to cartesian.

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Q: (a) Assume that f(x) is function defined by J - ² 4 f(x) = for 0≤x≤. (i)Expand the function f(x) in…

A: According to guidelines we can solve only one problem.

Q: Let KCC be an arbitrary non-empty compact set. BEB(P), 1 ≤p≤0, such that o(B) = K. Construct an…

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Q: c. Given f(x) = 2x - 3, g(x) = -4x² + 9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

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

Q: simplification is to isolate terms and identify the dominant term. For instance, we might want to…

A: fx(n) =log2log2n+3for n→∞log2n+3 =log2n

Q: Q5: a) Show that the vector field F = (x² - y² + x)i - (2xy + y)j, is irrational.

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Q: 5 Given A=-2 6 0 2 92719 2, and X= x₂ show that XTAX = 27, suggest that 5X + 6X3+7X3-4X₁X₂ + 4X₂X3…

A: Solution:

Q: 9. Find the center and the radius for the sphere: x² + y2 + 2²-6y + 8z = 0.

A: Given, Equation of sphere is x2+y2+z2-6y+8z=0                   (1) Since general equation of sphere…

Q: Prove that (X + Y) (X+Y) = X

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Q: Given Σ(x-μ)² = 78 and N= 80, then the standard deviation, a, is approximately a) 0.994 Ob) 0.110 c)…

A: We have to find the correct choice.

Q: Solve differential equation dy -(x²+y) x+siny

A: We have given a differential equation , dydx = -x2 + yx + siny This is exact differential equation.…