5. By considering Z[¹+√5]*, or otherwise, show that if n and m are expressible as 2 a² + ab-b² and c² + cd-d², respectively, then nm is expressible as e²+ ef -f² for some integerse and f.

Q: Find the eigenvalues and eigenfunctions for the boundary value problem, x2y′′+xy′+λy=0, y(1)=0,…

A:

Q: Given the vectors A = (–2, 1, 3), B = (–5, 3, 0) in R³, then B x A is 9i - 15 j + k -9i - 15 j - k…

A: Vector cross product

Q: Where possible, evaluate the following improper integrals: (a) //dx. (b) ¹₁x² In |x| dx. x2 (c) √2…

A:

Q: Let L: R³ R4 be a linear transformation defined by Which of the following is a basis for the range…

A: Range of linear transformation

Q: f(x)= 300x 1+ et

A: The given function is f(x)=300x1+ex. The given interval is 2, 4 and the number of segment is 8. The…

Q: 6. Write an equation, h(t), modeling the height of your ball as a function of time. h()=4.9t² +9,42t…

A: The height of the ball as a function of t is given by  ht=-4.9t2+9.42t+1.95

Q: Please answer the question. Asap. Thank you.

A:

Q: Consider (₁9₁2) = And the curve C: √(t) = oltzan Evaluate Include A Graph of the Vector Feild And…

A:

Q: If L : R6 → R³ is a linear transformation and dim(range L) = 2, then how many vectors are in the the…

A:

Q: 1. Evaluate the following complex numbers below. a. loge(5 + 3j) b. In (4 + 5j)³j c. log(-15) d.…

A:

Q: Suppose f: A → B is an injection g= B → C is a surjection. Must and gof: A ⇒ C your answer. be an…

A:

Q: Let ax + by + cz + d = 0 be the plane. Then the points (x₁, ₁ (x₂, 2, 2₂) lic on the same side or…

A:

Q: Determine if F(x, y, z)= yz²i+xz²j+ (2xyz-5)k is a conservative vector field. If it is, find a…

A:

Q: B. Find the volume of the indicated solid i) under z = x² - y² and above the square R = [1,3] ×…

A:

Q: 14. Evaluate surface integral z²ds where is the surface of the cone z = (x² + y2)1/2 between z = 1…

A:

Q: Given the vector field F(x, y, z) = (x², 2xy + x, z). Use Stokes Theorem to evaluate the circulation…

A: To find the flux

Q: answers only pls submit asap 7. Vectors

A:

Q: Use Green's Theorem to evaluate the line integral [(cos y + 3xy²)dx+(4x²y-xsin y)dy where C' is the…

A: we have to use the greens theorem to evaluate the line integral  ∫C(cosy+3xy2)dx+(4x2y-xsiny)dy…

Q: 2. Solve (D²+3D)y = -18x

A:

Q: rcentage a) Which table has linear growth? b) For the table with exponential growth, what is the…

A:

Q: True or false? A matrix is diagonalizable if all roots of its characteristic polynomial True False…

A: Diagonalization of the Matrix

Q: Solve the problem. Describe all solutions of Ax = b, where 2-5 31 A-2 6-5 and b = -4 7 0 b-[:]…

A: Here we have to find general solution of given Ax=b in parametric form.

Q: Consider F(x, y) = (y² − 2xy) i + (2xy — x²) j. (a) Show that F is a conservative vector field in…

A: the given vector field is F(x,y)=(y2-2xy)i+(2xy-x2)j we have to show that the vector field is…

Q: Given the set of positive integers Z+, which of the following properties does not hold for Zt to be…

A:

Q: Write an equation for the polynomial graphed below. You can leave the function in factored form. -5…

A:

Q: Which of the following sequences represents an arithmetic sequence with a common difference d = −5?…

A:

Q: PEAK TRAM The Peak Tram in Hong Kong connects two terminals, one at the base of a mountain, and the…

A:

Q: Using the Method for Variation of Parameters for the differential equation y" + P(x)y' + Q(x)y =…

A: To find solution of non homogeneous differential equation,  we use method of variation of…

Q: The parametrization of a straight line in 3D space is given by r = CT, were T = [t 1], and C = [1…

A:

Q: 8. A company wants to assign 8 salespeople to 4 regions of a state (see table below). Region…

A:

Q: Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line…

A: The plane ax+by+cz+1=0 The plane makes an angle of 60° with the equation of the line x=y=z and 45°…

Q: 3- Using echelon form solve the following linear system o equations (c) 3x₁ + 6x₂ x₁ + 3x₂x₂ - 4x4 =…

A: Note :As per our Guidelines we can solve first parts as your all parts are not small. Please repost…

Q: Find all the values of a such that the given series would converge. 6 (x)(n+1) (n +9) ∞ n=1 The…

A:

Q: For each positive integer n > 0, find the greatest positive number integer mn such that 1 tan ¹(n+1)…

A:

Q: In the United States, 40% of the population has brown eyes. If 15 people are randomly chosen, what…

A:

Q: 18. An ecologist has received permission to fence in a small rectangular plot of land at a state…

A:

Q: A tank is full of water. Find the work (in J) required to pump the water out of the spout. (Use 9.8…

A:

Q: Part 2 -45 + 7(x + 2) - 6x (no justification needed) = -45+ (7x + 14) - 6x = -45+ (14+ 7x) - 6x =…

A:

Q: 2. Prove that √2 & Q

A:

Q: For each function below, find all points where the function is discontinuous and classify the type…

A: To Check: whether the following function are continuous or not. If they are discontinuous we need to…

Q: Find the area of region enclosed by x = t-tº, y=t-t³, 0≤ t ≤ 1 using Green's Theorem.

A: to find the area by green theorem

Q: II. ROOT FINDING METHOD - Find the root of e-²x - e-x-2.

A: The given equation:     f(x) = e-2x - e-x - 2 Initial interval points:     xl = -0.6  ,   xu = -0.8…

Q: and P² = B C 0.20 0.52 0.28 0.21 0.31 0.48 A to state B in two trials is

A:

Q: II. ROOT FINDING METHOD - Find the root of e-²x - e-x-2.

A:

Q: (c) 2x1 + 2х2 - 4x3 = 14 3 = X3 8 X2 + 2x3 = -1 3x1 + X2 + 2x1

A:

Q: • Formulate the system as x = Ax, by explicitly writing out the matrix A. • Find the eigenvalues and…

A:

Q: 3. Find an equation (x(t), y(t), z(t)) of the line that is the intersection of tangent planes at (1,…

A:

Q: Determine the Annihilator of the given function: ( Find Q(D) F(x) = -2x³ + cos(4x) +10

A:

Q: 10. Examine the tables below and answer the questions that follow. Table B Table A Year 0 1 2 3 4 5…

A:

Q: Let X have a Weibull distribution with the pdf below. α f(x; a, B) = Ba Verify that μ = Br 1+…

A: