Factor the rational expression by dragging the correct integers to the corresponding boxes.

Q: Define f:R → R by f (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is…

A: Given, f:R→R by f(x)=5x if f(x) is rational and f(x)=x2+6 if x is irrational.To prove that f is…

Q: (c) Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy…

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Q: 30. (Remainder Theorem) Let f(x) e F[x] where F is a field, and let a E F. Show that the remainder…

A: Here we have given that fx∈Fx, where F is a field and α∈F. it is required to show that the remainder…

Q: the va q² +y? +æy ) at x = 1 and y = 3 is %3D

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Q: Find the partial fraction expansion of the following and evaluate: i. 21 (x2 – 1)2 1 i. 21 dx J,…

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Q: 9. Tell whether the correlation coefficient would be closest to -1, O or 1. 150 b. 150 150 100 100…

A: Given, Different Scatter Plots a, b and c. To find: The closest value of the correlation coefficient…

Q: Show that if u, v, w, and r are any vectors, then a) u x (v x w) + v × (w × u) + w × (u x v) = 0 b)…

A: Given a u×v×w+v×w×u+w×u×v=0b u×v=u.v×ii+u.v×jj+u.v×kkc u×v.w×r=u.wv.wu.rv.r

Q: Sketch the domain and three-dimensional (3D) graph in first quadrant of the following function: z2 =…

A: This is a problem of set and functions and calculus of several variables.

Q: (a) Find the coordinate vector of z = with respect to the ordered basis 4. E = 6. of R [æ]E = (h)Lot

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Q: (a) Find the eigenvalues of A. (b) Find two eigenvectors v and w of A with respect of the two…

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Q: Relation -4 -1 -6 6. -39 3 -15 -8 -26 10 5- -10 -5 10 -5 ddit gaph on desmos 10 A) determine the…

A: A. Using a graphing calculator (ex. desmos) we can see that all given points lie on a quadratic…

Q: 2 (a) Find of the following functions: dx zxa+1cos y? = sin(yº + 22z) where A=2 C=6| 一

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Q: If possible, write -4 – 2x – 3x as a linear combination of x - x?, -a? and 1 + x². Otherwise, enter…

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Q: 2200x A firm has the marginal-demand function D'(x) = where D(x) is the number of units sold at x…

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Q: Let T : R" -→ R" be a linear transformation. Which of the following statements is false? OT can be…

A: The linear transformation T:ℝm→ℝn can be represented by n×m matrix. Therefore option (1) is wrong.…

Q: Prove by contradiction that if 3x? 2 is irrational then r is irrational.

A: We have to show that x is irrational if 3x2-25 is irrational. We have to prove the statement by…

Q: 10. Let v = [1, 1] and w = [2, 1] be two vectors: find the project of v into w d bu [1 11. 11. 1, 2,…

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Q: Solve the following system of differential equations. dx = x + y, dt dy - 2x + z, dt dz = 3x – y +…

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Q: For each of the regular solids, take the number of vertices, subtract the number of edges, and add…

A: Consider a regular solid Cuboid: here we can observe that, Number of vertices is 8. Number of edges…

Q: Let A be a square, invertible matrix and let A' be its transpose. Which of the following statements…

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Q: Let A = Amxn be such that xo is the unique solution to Ax = b for some b e R". Which of %3D %3D the…

A: Given A=Am×n be such that x0 is the unique solution to Ax=b for some b∈Rn. we have to find the…

Q: Q4 Find the solution of the linear system by using 1) Gauss elimination method 2) causs Jordan 3)…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: rea of the closed region det

A: Given, the equation of the circle is                                        (x+2)2+(y-3)2=4

Q: Find all solutions of quadratic congruence x^2+85x+2=0(mod401)

A: We follow the method of completing the squares of the equation x^2+85x+2. Note that 85 is odd so we…

Q: Use the geometric series to derive a power series for the function f(x) = 1 / (1-x). What is the…

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Q: 2.) Use the comparison test to determine if the series is convergent or divergent: 2n+3 Σ 3n2 +2 n…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

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Q: -3 -2 -1 1. -8642 -2 3 * 6 4 2 0 2 46 8 10 2 2- -8-6 -4 -2 8 4 2 -2 4 -6 5 Determine whether these…

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Q: If f(1) and g(1) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-1)g(-1)+…

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Q: C. VARIATION OF PARAMETERS 2. (D² – 3D + 2)y 1 1+e-x

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Q: Use the shell method to set up and evaluate an integral that gives the volume of the solid generated…

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Q: 1 s S xe^ dx dy xy 0 0 –1 2.

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Q: How many units has the quotient ring Z/I, where IC Z is the ideal generated by the integers 36 and…

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Q: What is the probability of failure in the binomial probability expression below? 100 54 )…

A: In case of Binomial distribution, we write generally,      P(number of success = x) = NCx px (1 –…

Q: Analyze the approximate value and the exact value for (7.2, 4.06) for the function z = x³y? sin(xy)…

A: Given below clear explanation

Q: Sketch the domain and three-dimensional (3D) graph in first quadrant of the following function: z? =…

A: The function in the form f(x,y,z)=C is called a multivariable function. If z=g(x,y), then the…

Q: 2 - y = 3 – z and l4(s) = (1 – 2s, 4s,1+ 2s). 2 3. Consider the lines defined by the equations l3 :…

A: Hint: If l3 and l4 are two lines is said to be parallel if the cross product of a directional…

Q: Solve the following system of IVP: -3 1] -2 -1 1 and x(0) 2] 3 x' = Ax where A = 6

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Q: Prove or disprove: For n>2, 2 is a generator of Zn if and only if n is odd.

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Q: 6. If c is a positive integer and a and b are integers with a = b(mod c), show that a2 = b²(mod c).…

A: Let c is positive integers and  a and b are integers with a ≡ b ( mod c)

Q: Let A be a 4 x 4 matrix with eigenvalues =-3, X2=-2, X3 1, M=4 and corresponding eigenvectors…

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Q: Using the infinite transaction method, he question y" + y = cos(3x)

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Q: Solve the given IVP. Write your answer in terms of Sine and Cosine if applicable. y" – 4y" + 29y' =…

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Q: Build a Venn diagram. Use the names of the sets to label the regions. Place the numbers in the…

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Q: Analyze the approximate value and the exact value for (7.2, 4.06) for the function z = x3y2 sin(xy)…

A: Given below clear explanation

Q: Determine whether or not the vector feld is comervative. t is conservative, find a function / such…

A: Conservative vector field and scalar potential function

Q: uch th

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Q: 3 2x Estimate the value of the definite integral dx with n=4 subintervals, taking x+1 the sample…

A: Introduction: The endpoint formula and the midpoint formula are related. A midpoint is the point in…

Q: Let C1 be the circle r = cos 0 and C2 be the petal of the rose r = V3 cos (20) that is to the right…

A: If f is continuous and non negative on the interval α≤θ≤β with 0<β−α≤2π. Then area of the region…