prove that: if n is a natural number and r is the remainder when n is divided by 3 then if t=5 or 11 the sum r^2+r+t is prime.

Q: Find all x in R4 that are mapped into the zero vector by the transformation x-Ax for the given…

A: Here we have to find all x in R4 .

Q: 3. Find the value(s) of x when f(x) = 5e* is parallel with 5x - 2y = 1.

A: (3). Given function is f(x) = 5ex.       We have to find the value of x when f(x) is parallel to the…

Q: SS, [(2x - z)dydz + x²dzdx -xz²dxdy],

A: We use divergent theorem. This theorem change surface integral to volume integral.

Q: ques2  plz provide answer asap

A: We know the definition of subspaces, A non empty subset S of a vector space V is said to be subspace…

Q: π.Χ. B: Solve the equation f(x) = e-* + sin n use Newton Raphson Method Xo= 0. "

A:

Q: Question 5. Prove that every integral domain D=D, +, the ring of integers Z., can be embedded in of…

A: Given that ℤp,⊕,⊙ is a ring of integers. Also D=D,+,· is an integral domain of prime characteristics…

Q: -) Write the Cayley table for the group U(15).

A: U(15) is the set of all elements in ℤ15={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14} ; x≡x ,such that…

Q: 1. Find the equation of the plane that passes through the points (1,0,-1), (0,2,3) and (0,0,5) in

A: Introduction: An indefinitely long, smooth, two-dimensional surface is known as a plane. A point, a…

Q: 4. Write the surface z = x² + y² in cylindrical coordinates (simplify its expression if possible). 2…

A:

Q: Find the equilibria of the autonomous system of equations, classify them and x=2-2√1+x+y sketch the…

A: The given system of equations is: x˙=2-21+x+yy˙=exp54x+2y+y2-1 Therefore the equilibrium points can…

Q: 3. Let h(x, y) x + y sin²x 2¹+ y² 0, if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

A:

Q: Q5. Find the directional derivative of the function [f(x, y, z) = xy + y.z + z.x] at the point x-3…

A:

Q: Let X= [0,100] x [-2,2] with the Euclidean metric d on X and T: X→→ X be defined by T(a,b) = (2+ √a²…

A: As per the question we are given a Banach space X = [0, 100] × [-2, 2] with the Euclidean metric d…

Q: Consider the following binary operation (denoted *) defined on R. Determine whether or not the…

A: Solution

Q: If their positions are po = (-²) ₁₁ = (6)₁ ,do they collide?

A: The general equation of the circle whose position: p⇀=ab and radius: r can be defined using the…

Q: Solve the differential equation 10y" - 15xy' + 60y = 0 using appropriate method. Then evaluate the…

A:

Q: "36. Prove that a square matrix A is invertible if and only if A^TA is invertible

A:

Q: As you saw in Session 3.2, we can extend the notion of a linear approximation to a quadratic…

A:

Q: Construct the truth table for (p→→q) → [(pv-q) → (pv q)].

A: We have to construct the truth table.

Q: In a dance crew with 32 members, 9 are are part of unit A, 10 are in unit B, and 6 performs solo. 3…

A:

Q: Let f(x, y) = √x² + y² - 4 y 2 - Identify the equations of the level curves of f for k = 0, 1.…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: The temperature C of a fresh cup of coffee t minutes after it is poured is given by C = 125e-0.03…

A: Given that The temperature C of a fresh cup of coffee 't' minutes after it is poured is…

Q: Let A = (ajj), B (bij), C = (Cij) be real n × n matri- ces, where B = CT, Cij is the cofactor of the…

A:

Q: Evaluate the solution of: 2(D^2)I - 2Di – 4i=0.

A:

Q: Find the first two derivatives: Leje d. k dejé c. beje d. Leve Assume 0, b, and d are functions of…

A:

Q: II. Suppose that the total worldwide sales for a song album are approximated by the function: 250x³…

A: The relation between no. of Sales S(x) in x number of months is given by S(x)=250x3x3+7. (a) To…

Q: Find the value/s of x that make/s the given functions discontinuos

A:

Q: Suppose that there exist integers x and y such that ax + by = 12. What can you deduce about (a, b)?

A:

Q: Find and draw the domain of m (x, y) = √x-y+√x+y.

A: For a function: z=f(x, y), the set of real values of x, y for which f(x, y) is defined is called the…

Q: - Find all the second-order partial derivatives of the function: f(x, y) = sinxy

A:

Q: Two students are discussing the need for mathematics to be a core course, that is, ALL university…

A: Given: Lets consider two students statements, Student A: I don't use trigonometry, logarithm, or…

Q: B: Solve the following equation by Finite Differences Method, choose h = 0.25 d²y dx²-y=x+y . y(0) =…

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Q: The manager of an employee health plan for a firm has studied the balance B, in millions of dollars,…

A:

Q: Please do number 4-6

A: Given,  The Venn diagram of of the set A,B,C and universal set U is given. To find the B' , C' ,…

Q: (b) Give the Dedekind cut for 1+ 3. (Of course, your answer should not refer to 3 or other…

A: (b) A dedekind cut is defined as a partition of rational ℚ into two subsets A and B such that (i) A…

Q: In a Hilbert space. Prove that x →x provided ||x₁||→||x|| and (x₁, x) → (x, x). n

A:

Q: Prove the following statements by divisibility. 1. If a/b and a/c, then a/ (bx + cy) where x, y € Z.

A:

Q: Mu=Φ x 0.85 x fc' x a x b x (d - a/2) 266000000 = 0.9 x 0.85 x 21 x a x 366 x (486 - a/2) a= uknown…

A: The False-Position method uses the formula: xr=xl-f(xl)⋅xu-xlf(xu)-f(xl) to perform the iterations…

Q: Mu= x 0.85 x fc' x axbx (d-a/2) 266000000 = 0.9 x 0.85 x 21 x ax 366 x (486 -a/2) a= uknown "x"…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: y'-2y = y²; y = 3 when x = 0

A: A differential equation can be solved using the variable separation method. In this method, the…

Q: 3. Show that the area of the optimal rectangle inscribed inside a semi- circle of radius 2 (found in…

A: Concept: Critical point: A critical point is a location on the graph of a function y=f(x) , such as…

Q: Let A be an operator on a Hilbert space H. Show if ||Ax||=||A^x|| for every x = H, hen A is normal.…

A:

Q: Q1. Find the general solution for the following differential equation: -y² (x²ex² - y²)dx + xydy=0

A: Solution :  Given differential equation  x2 e-y2x2-y2dx+xy dy=0

Q: Let X be a vector space. Let || and || || be two norms on X. When are these norms said to be…

A:

Q: Calculate SS, (x²z+y²z)dS ds, where S is the surface determined by² + y² = 9, z ≥ 0

A: Introduction: The surface integral in vector calculus is a generalization of multiple integrals to…

Q: II. Suppose that the total worldwide sales for a song album are approximated by the function: 150x³…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find all distinct (non-isomorphic) trees of orders n = 5, 6, 7

A:

Q: 7. Find the equation of a line tangent to the graph of f(x) = cotx at x = π/4. Show all steps to…

A: Introduction -   Equation of Line tangent:         Using the equation y - y1 = m (x - x1), where m…

Q: CLASSIFICATION OF DIFFERENTIAL EQUATIONS Classify each of the following differential equations by…

A:

Q: y²dx + x(x+y) dy=0 A xy²=c(x+2y) B x²y=c(x+2y) C xy²=c(2xy) D x+y²=c(2xy)

A: Let us consider the differential equation of the form dydx=f(x,y). Such that f(x,y) is a homogenous…