Show that there are no integers a, b such that a² + 2ab+26² = 100000000003. Hint. Use mod 4 congruences.

Q: Show that is conservative by finding a potential function for F.

A:

Q: For small z, the approximation good to a relative accuracy of sin z = sinzz is often used. For what…

A: For small x, the approximation sinx≈x is often used. Consider Taylor's series for sin(x) up to the…

Q: N z=y+ =2-hx2 x=0 - z=4-y

A:

Q: Convert to cylindrical coordinate. 1. z = x2 + y2

A:

Q: Find two linearly independent vectors perpendicular to the vector -B]₁ V = 7

A: Two vectors u, v  is called perpendicular if u.v=0. in the given problem we have to find two…

Q: Express the limit lim n→∞ Provide a, b and f(x) in the expression a = (³ (x ) ³ - 4(x²) ¹) Ax; over…

A:

Q: 8z Compute the inverse z-transforms of z²-6z+25

A:

Q: If (x + iy)³ = u + iv, then show that И V ---- + w y = (x² - y²).

A:

Q: The acceleration of a particle moving along a horizontal line at t seconds is modelled by the…

A:

Q: Determine which of the matrices below are mutually commuting, and, for those that are, demonstrate…

A:

Q: is an imaginary root of unity. Prove that (1)(a + bo+cal) + (a + but co? 50 - (2a-b-c) (2b-a-c)…

A:

Q: How do you find the radius of convergence of a power series ∞ Σen n=0 cn (x − a)"?

A:

Q: 5. Prove that a symmetric matrix P is positive definite iff all eigenvalues of P are positive.

A:

Q: 4. Find the volume of revolution generated by rotating the region bounded by y=x²-x²-9, y = 18-x²…

A: Given : y = x3 - x2 - 9 , y = 18 - x2 and y=0 and the axis x = 1.   To find : The volume of the…

Q: If (x + iy)³ = u + iv, then show that И V - X + = (x² - y²). - y

A:

Q: N How many solutions are there to the equation X₁+X2+X3+X4+X5+X6=41, where each x; is a positive…

A:

Q: Evaluate (x+y-52) dV where E = {(x, y, z) | − 7≤ y ≤0,0≤x≤y, 0≤ z ≤ x + y²}

A:

Q: Mary Branson invested her summer earnings of $3000 in a savings account for college. The account…

A: Given   Principal amount = $3000  Interest rate r = 3.5%  Time t  = 6 months  We need to find amount…

Q: Prove that the inner derivations ad x, x∈g are an ideal on Der(g)

A: Prove that : The inner derivative adx , x∈g are an ideal on Der(g).

Q: Solve the initial value problem. y(x) = = x³y" + 7x²y" - 2xy' - 10y = 0 y(1) 1.3, y'(1) = -10.1,…

A:

Q: 5. Solve the initial value problem (a) y" - 4y' + 3y = 0, y(0) = 7, y′(0) = 11.

A:

Q: Graphing Quadratics Standard Form Identify y-int, x-int(s), axis of symmetry, vertex from the…

A: 4. Given the equation is                          y= -x2+6x-5.

Q: -TI/3 17- -6- 5 4 3 2 1 -2 it/3 2Tt/3 T 4Tt/3 5Tt/3 2n 7Tt/3 8Tt/3 3it 10 t/3 11m/3 ५० 47

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a) Solve it using Gauss' method. Solution: x + 3y + z + w = 6 -Y +2w=-4 2x + 5y + 2z+4w = 8 X +7w=-6…

A:

Q: Stems Leaves 2 8    3    0 6 2    3    3    1 8 2  7      Part 1 The mean of the data is ​(Round to…

A:

Q: 4x y" - 5y + 4y = ¹, y(0) = 0, y'(0) = 10/3 e

A: Please find attachment

Q: Ņ 4 2- -2 OA. lim f(x) = (Type an integer.) a. Find lim f(x). Select the correct choice below and,…

A:

Q: Problem 4. know about, ∞ If the power series Σen" has radius of convergence 3, what do we n=1 ∞ (b)…

A:

Q: Complete the following table. Population Growth Rate, k Doubling Time, T 2.7% per year Country A…

A: A=Pert where P =starting population at time t=0, t=years, r= interest rate ( in decimal) e =about…

Q: Verify that the Divergence Theorem is true for the vector field F(x, y, z) — xzi + yz j + 3z² k on…

A:

Q: 1. Let S = C[0,1] be the set of real-valued continuous functions defined on the closed interval…

A:

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

A:

Q: 2. Use spherical coordinates to evaluate fff (9-x2 - y2) dV where E is the solid hemisphere x² + y²…

A: That is circle or radius 3 in xy plane and the equation of the circle is x2+y2=9

Q: Let At be a matrix that depends on r and is given by 4-[30] At = t (a) For which te R matrix At has…

A: At=-13t-21

Q: Use properties of logarithms to condense the logarithmic expression below. Write the expression as a…

A:

Q: Let x, y, z be (non-zero) vectors and suppose w = 6x - 6y - z. If z = 3x - 3y, then w3x+-3 y. Using…

A: The given nonzero vectors are x, y, z and w=6x-6y-z. The vector z=3x-3y. Therefore, w=3x-3y. The…

Q: Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be…

A: As per the question we are given the covariance matrix of a students' data and the index : y = c1x1…

Q: f(x, y, z) fxyz In (4xy) 22 Let + sin(xy² + ye²). Find

A: Note:    We use the following notation fxyz=∂∂z∂∂y∂f∂x

Q: 3. Let (X, d) be metric space, prove that for any P1, P2, P3,..., Pn E X, we have d(p1, Pn) ≤d(p1,…

A: We prove the result by mathematical induction We know the triangle inequality of metric space If x,…

Q: • Matrix N € Cnxn is said to be nilpotent whenever Nk = Onxn for some positive integer k. • The…

A:

Q: Power Series. Find the general solution near x = 100. d³y dx3 dy + (x - 100)². = 0 dx

A: The given differential equation is dy3dx3+(x-100)2dydx=0. The objective is to calculate the power…

Q: Problem 4. know about ∞ (2) Στ3η n=0 If the power series en " has radius of convergence 3, what do…

A:

Q: Using the inner product (,): P₂ (R) × P₂ (R) → R, (p, q) = p(0)q(0) + p(1)q(1) + p(2)q(2) calculate…

A:

Q: Q4: Sketch the phase plane portrait of equation (without explicitly computing its solutions), x"(t)-…

A: Given: x''t-2x'+2x=0 (a) Sketching the phase plane portrait of a given equation. (b) Find Solution…

Q: Find the work done by the force F = xyi + (y − x)j over the straight line from ( − 1,0) to (0, − 1).

A: In the given problem, force is given and the displacement straight line is given. We have to find…

Q: D B E A Find an Euler path for the graph. Enter your response as a sequence of vertices in the order…

A:

Q: Show that (cos+ i sin 0)" = cos no + i sin ne for 0 € R and n € Z.

A:

Q: In a recent year, 37% of all college students were enrolled part-time. If 6.7 million college…

A:

Q: Let 2₁, 22, 23 be three complex numbers and a, b, c be real numbers not all zero, such that a+b+c=0…

A:

Q: Describe the cosets of VEIK where U is the solution subspace of the equation 8x + 2y + 5z = 0

A: A subspace U of R3 is given, which is a solution subspace of the equation 8x+2y+5z = 0. Our aim is…