Prove the following i 1. If 2 and a 2. If u and 640 3. If a E IR, then 9.0=0. are elements in HR w/ z+a=9, then 2=0. are elements in IR w/ u∙b=b₁ then us1.

Q: r=-6cos(theta) and r=6-6cos(theta) a. Graph each polar equation. b. Determine theta value(s) for…

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Q: Taxicab fares. In New York City, taxicabs charge passengers $2.50 for entering a cab and then 50.50…

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Q: Where does the point of inflection occur y = x³ - 3x² +2x - 3? A. (0,0) B. (1, 2) C. (1,0) D. (1,…

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Q: Find all prime ideals of (Z12, +12-12). Then find Rad (Z12).

A: Prime Ideal:  Let R be a commutative ring. An ideal P is called a prime ideal if P(not equal to R)…

Q: 1- For the non-linear ODE,determine the stability properties of all the equilibrium points.

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Q: 17.) Find the derivative using the quotient rule.

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Q: Let f and g be two arithmetical functions. We have f(n) = Σg(d) →g(n) = Σμα) (3) d\n d\n

A: This goes by the name of Mobius inversion formula a standard technique used in number theory. The…

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Q: 9.1 Explain whether a graph with each of the following characteristics exists. If so, give an…

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Q: Find the exact extreme values of the function z=f(x, y) = 30x+12y + 80 subject to the following…

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Q: Using the substitutionx = vyanddx=vdy + ydv, solve the homogeneous differential equation ydx + (2x -…

A: Introduction: An equation of the form y'+p(t)y=0 or, alternatively, y'=-p(t)y is a first-order…

Q: ?u а) t = 40 (г). Ət r Ər

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Q: 3. Let P3 (x) be the interpolating polynomial for the data (0, 3), (1, 4), (2, y), and (3, 0). The…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: dy/dx=2+√(y-2x+3).

A: Given differential equation is dydx=2+y−2x+3.......1. We have to find the general solution of the…

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Q: (d) t³y + 4t²y=et, (e) ty' + (t+1)y=t, y(-1)=0, -1<t<0 y(ln 2) = 1

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Q: lim f(x) 1. lim f(x)--1, lim f(x) - 0. lim f(x) 1. (2) 1. f(0) is undefined

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Q: Prove that Σ₁ iª = n(n+1)(2n +1) (3n² + 3n − 1) i=1 30

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Q: Let weight vector a = j i is equivalent to a) >0 az aly ai aj b) >0 c) ay-ay> 0 d) ay-ay 0 for all

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Q: Q4. B. Find the tangential vector (T), normal vector (N) and binomial vector (B) for the position…

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Q: TEST FOR HOMOGENEITY: 2. x² - 5xy - 4y²

A: The given function is x2-5xy-4y2 We need to test the Homogeneity.

Q: The preceding exercise tells us that the inverse of an elementary matrix is also elementary matrix…

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Q: 1. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at…

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Q: ; f= 3. the value of y that is a solution to the following two

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Q: Use the given information to draw a Venn diagram. (A0B0C)=3, n(An anc)-8, (nanc)-4, Ananc)-9, (Anne)…

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Q: Determine if the following graphs are planar or not. Try to find a proof of planarity (planar…

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Q: Let R be the region bounded by the curves y = 3x² -2 and y=2-x² Let S be the solid of revolution…

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Q: Let x = log 3 and y = log 4. Express the following in terms of x and y.     Please provide all…

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Q: 2 (-3) - = (- (-1)² 8 = {) 1 -1 if p= ±1 (mod 8) if p= ±3 (mod 8).

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Q: 1. We can generalize our approach to warto for any state function. Consider: f = 3x²³ - 2xy² for X₂…

A: As per the question, we will verify the above for f=3x3-2xy2. We are given that xi=1, yi=2; xf=5,…

Q: Convert the following polynomials to factorial polynomials 1. x³ + 8x² - 4x - 1 2. 2x45x³ + 2x² - 4x…

A: The given polynomials are: 1. x3+8x2-4x-1 2. 2x4-5x3+2x2-4x+9 3. x4+2x3+x2-6x-4 We have to convert…

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Q: 150x₁ - 15x₂ + 8×3 = 1500 2x₁ + 120x2 - 9x3 = 1200 2x₁-22x₂ + 110x3 = -900

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Q: Problem 10.1 2 Simplify 5 + 5i the following complex number. 20 + 3 - 4i 4 + 3i

A: solution : Given that the complex number  5+5i3-4i+204+3i

Q: 1. Convert the following linear program below into standard form. Solve the standard form problem,…

A: The given linear program problem is: maximizex1, x2, x3 3x1-x2+4x3   s.t.…

Q: 7. According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million…

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Q: 110x20y = 20 80x-70y = 0 -30x-50y + 110z = 500 Using Gauss Gordan Method?

A: The given set of equations is ,                       110x - 20y = 20          80x - 70y =…

Q: 3. Let m =(√2/2) (e₁ + e₂) where e₁ and e2 are orthonormal vectors. Is there a tensor A such that…

A: We are given that m=22e1+e2 where e1 and e2 are orthonormal vectors. Now, we need to find if there…

Q: Q4. B. Find the tangential vector (T), normal vector (N) and binomial vector (B) for the position…

A: The main objective is to find tangent vector, normal vector and binomial vector at t=0.

Q: Let A B denotes the tensor product of matrices Amxn and Bpxq defined by the block matrix A & B :=…

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Q: that value K, in a way RK-4 when solving the issue y' = Y-x Y+x , Y (0) = 1 where h=0.25 15:- a) 0.2…

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Q: What fallacy does this syllogism commit? All mothers are females; But all actresses are females;…

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Q: Solve the differential equation: (x + y)dx + (x + y²)dy = 0 By using the exact equation.

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Q: 3 9 -3 -2 -5 5 1 1 -6 0 0 0 A=10 0 0 000 5-6-8 +A=-4-10 4 1 48-4

A: Given: The equation is 39-3-2-5511-6-1+A=-45-6-8-104148-4. To find: The matrix A.