Solve for a and b so the points (1,-1, -3), (2, 0, -1), and (a, b, 3) will lie on a straight line.

Q: Suppose a 5x8 matrix A has two pivot columns. Is Col A =R2? Is Nul A=R6? Explain your answers. Is…

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Q: F(s) F(s) = = s²-1 1-2s s²+4s+5

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Q: Emilio is using pennies to make a pattern. He arranges his pennies as shown below. 00 O O O Figure 3…

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Q: Prove that n²¹ +n²+1 n = 0(n³).

A: To Prove: n4+n2+1n=Θ(n3).

Q: For which real number a, the solution of the Initial Value Problem da dt x (0) = 1 is such that x(2)…

A: The Initial Value Problem is given by:  dxdt=axtx(0)=1 We have to find the value of a such that:…

Q: e following systems, the origin is the equilibrium point. dž Write each system in matrix form = Ax.…

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Q: Evaluate the surface integral ff 5y2 d.S, where S is part of the surface of a paraboloid with…

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Q: Determine whether the given graph has an Euler circuit. Construct such a circuit when one exists. If…

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Q: (a) Find the approximate integral of the following function using Simpson's 1/3 rule and (b)…

A: Given: fx=2x2  , x=0, 4 , n=4 To find:  (a) Approximate integral by Simpson's 1/3 Rule. (b)…

Q: Two large containers A and 8 of the same size are filled with different fluids. The fluids in…

A: Answer  We get  t= 6.868192 Now step by step approach is as follows

Q: Find the lines that have four point contact at (0, 0, 1) with the surface x + 3xyz + x² - y² - z² +…

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Q: Show that the function 200 loins of a continuou) is closed.

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Q: 3. When we refer to "The vector spaces" Rn (of column vectors), or Mnxm(R) (n x m matrices), or Pn…

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Q: pairwise co-prime and m = m₁m₂ mk. Then f(x) = 0 (m) has a solution if and only if each of the…

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Q: -x² The rectangles in the graph below illustrate a right endpoint Riemann sum for f(x) = The value…

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Q: Question 2 Find the value of P when Q = 2 and R=-3 in the formula below. Leave your answer in exact…

A: Given formula 4PQ-RP/3=QR^2  To find the value of P when Q=2 and R=-3

Q: The temperature at a point (z, y, z) is given by where T is in degrees Celsius and z, y and z are in…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: State the equation of the rational function that meets these conditions: 1. Vertical asymptote at x…

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Q: Problem 4 (Extending continuous functions). Suppose KC Rm is compact and f: KR" is continuous. Show…

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Q: Problem 3. Evaluate the following (please do not use a calculator): (a) 11 11 11 11 11 (mod 10) =…

A: We know that modulo is remainder after dividing one number by another. Let a, b, m are integers with…

Q: What is the value of k in the function f(x)= (2, 4.2)? a) 21.2 b) 6 c) 17 d) none of the above 2x +…

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Q: A function : [a, b] CR → R is called a step function if there is a partition C0 < x₁ << Xn = b of…

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Q: Show that the osculating plane at P has three point contact in general contact of second order) with…

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Q: rst four terms in each portion of the series solution a ential equation. x²y" 5x y' + 6y = 0

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Q: Prove that; It pis prime 0217. - 2 (류) (1) 8 1 ; PE+Imed B ; p= ± 3 mod

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Q: a raindrop falls, it evaporates while retaining its spherical shape. If we make the further…

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Q: 1. Let f (0, ∞)→ R be the function with f(x) = |1 ln x]. Sketch the graph of y = f(x). Give a brief…

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Q: Alexa and Erik plan to send their son to university. To pay for this they will contribute 9 equal…

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Q: Consider the following matrix: A The following vectors are linearly independent eigenvectors of A:…

A: The given problem is to find invertible matrix P and diagonal matrix D for the given eigen vectors…

Q: x' + x + y = et x"+x+y=y=t

A: This is a question of the system of the differential equations.

Q: sin' (t) -√√² x→0 xm t integer m. With such m, find the limit. Round your answer to 2 decimal…

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Q: 3 Z3 [x]/(x² + 1) (not reduced mo coefficients did modulo 2).

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Q: As the equation is exact, there is a function f such that. = M(x, y) and = N(x, y). af ax af ду To…

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Q: Sketch the following function and find the Fourier series, given that f(x + 2) = f(x) 1 0 for n≤ x…

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Q: Let m be an odd positive integer. Then we have (-)-(-1) and 3 N 2 m = (-1) ™³²-¹.

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Q: (p-1)(q-1) 4 = (−1)|

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Q: 3. Create an infinite series by letting n→∞. Find the interval of convergence for this series.

A: This is a question of infinite series.

Q: se co-prime and m = m₁m₂ mk. Then f(x) = 0 (m) has a solution if and or h of the congruences f(x) =…

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Q: Problem 1: Determine whether graphs G and H are planar or not. To show planarity, give a planar…

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Q: How many numbers are there in the set {1,2,3,...,200} which are divisible by neither 3 nor 4 nor 12?

A: To find: We have to find out how many numbers are there in the set 1,2,3,.....,200 which are…

Q: (a) 8 (mod 3) (mod 3) = (b) 7 (mod 5) (mod 5) = (c) 3 (mod 4) (mod 4) = || = 11 12 (mod 3) 23 (mod…

A: As per our guideline, we are supposed to solve only first three subparts. Kindly repost other…

Q: We have found that the solution to the exact differential equation is of the form f(x, y) = xy +…

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Q: how that the given equation is not exact but becomes exact when multiplied by the given integrating…

A: Given a homogenous differential equation x2y3+x3+y2y'=0. ⇒x2y3dx+x3+y2dy=0 Compare it with Mdx+Ndy=0…

Q: Determine a, h, b so that the paraboloid 2z = ax² + 2hxy + by ² may have the closest contact at the…

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Q: To obtain some idea of the possible dangers of small errors in the initial conditions, such as those…

A: We can solve the given differential equations.

Q: Identify the type of frieze pattern illustrated in each of the following design. Frieze Pattern…

A: The first frieze group F1 contains only translation symmetries Hop The  fifth frieze group F5…

Q: Find the area of the plane z 2y + 5z = 13 cut out by the cylinder x² + y² = 9. area=

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Q: dy For the differential equation = (y - 3) (+2) there is equilibrium solutions. The positive…

A: The given differential equation is: dydx=y-3y2+2. To find: The positive and negative equilibrium…

Q: 1. Let A = Z+x Z. Let R be a relation defined on A as follows: For all (a, b), (c, d) € A, (a, b) R…

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