Here is a two-variable function: f (x, y) = Vx2 + y² – 1 This is the upper half of a quadric surface. What is the name of the quadric surface? Sketch in the domain of f. y 1 X -1

Q: (2x- y+2z =5 1. Solve the system using Cramer's Rule: 4x-3y=17 x-y+z=2 2x+6y-3z=-8 2. Solve the syst...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

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Q: Obtain the moment of the area generated by x = 2a, bounded by x =y and x2 = 2av.

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Q: Exercise 1. Let R = {(x, y) | x, y E Z and x + y = 0, } be a relation on Z. Prove or disprove if R i...

A: Let S be a non-empty set and R be a binary relation on S. (a) The relation R is said to be reflexive...

Q: Exercise 5. Prove that given positive integers a and b, there is a positive integer d such that • d ...

A: Given two positive integers a and b, let us choose d = gcd(a, b) [greatest common divisor] Then obvi...

Q: What is the differential equation of the family of parabolas with their vertices and foci on the y –...

A: We need to find differential equation of the family of parabolas with their vertices and foci on y -...

Q: Construct a matrix system Ax = b, who has a particular solution Xp |1 and the nullspace of the 3 mat...

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Q: min 4a1 + 5xз subject to 2x1 + x2 – 5x3 -3x1 = 1 + 40з + х4 — 2 x; > 0, i = 1, 2, 3, 4.

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Q: Which of the following differential equation has a solution of y = e"(c, cos 2x + c, sin 2x) ?

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Q: Sketch two functions F such that F' = f. In one case let F(0) = 0 and in the other, let F(0) = 1. -1...

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Q: Which of the following is the general solution to the differential equation = ()* +2 ( Cx(x + y) = y...

A: Given differential equation is dxdy = xy2 + 2xy

Q: Which of the following differential equation has a solution of y = C,x³ + C2x ? 4y = 3x?y' – x³y" 3y...

A: To find which option is correct: We first find y' and y'' of  y = C1x3  +  C2 x and then we will che...

Q: Solve. Express your answer using interval notation. Illustrate your solution on a number line. 5x +1...

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Q: Let M and N be 3 x 3 matrices with det(M) = 64 and det (N) = 81. Calculate det Also show whether NT ...

A: Let M and N be are 3×3 Matrices. We have given that ,  detM = 64  and  detN = 81 We need to find ,  ...

Q: w to find this? P is 12, Qis-2

A: (18) Given,                     p5+1+45-1=q+45

Q: Determine all the roots of z +1 = 0

A: The given question is related with complex analysis. We have to determine all the roots of z4 + 1 = ...

Q: Determine the values of a, if any, for which all solutions of the differential equation y" – (2a – 1...

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Q: Find the derivative of each function using the definition of derivatives. Use the formula of defini...

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Q: Consider the following statements: 1. If A is a square matrix and Av = λv, for some nonzero number ...

A: 1.  If A is a square matrix and Av = λv, for some nonzero number λ, then v is an eigenvector of A.  ...

Q: Prove that if a = b mod n and c= d mod n, then ac bd mod n.

A: Given if a≡bmodn and c≡dmodn We have to show that ac≡bdmodn. Now, a≡bmodn ⇒n/a−b⇒a−b=nq1,q1∈Z⇒a=nq1+...

Q: 1. In class, we talked about how to solve the homogeneous second-order differential equation ay" + b...

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Q: 3. Which sentences below are paradoxes? • This sentence is false or 1+1 = 2. • This sentence is fals...

A: Solution:-

Q: All changes saved 18. For the three-part question that follows, provide your answer to each part in ...

A: We will use calculator to approximate this

Q: 1 2 1 1. A = 1 -2 -1 -1

A: This is the problem of linear transformation.

Q: min X2 subject to X2 = 1 X1, X2 > 0

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Q: Find the surface normal vector to the surface z 4-(x +y²) at the point (1, 1,v2) by (a) Vf (b) N = 7...

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Q: Find Taylor's expansion of 1 about the point z =- i. i) f(z) = (z + 1)2 2z3 +1 i) f(z) = about the p...

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Q: (a) {(m, n) E N × N|m < n}. Hint: A subset of a countable set is countable. (b) {2 |n € N}. (c) {r E...

A: This is a problem of set and function.

Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A O (A)° = A – int A (ii...

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

Q: A machinist creates a solid steel part for a wind turbine. The part has a volume of 1,015 cubic cent...

A: It is given that the volume of the steel part is 1015 cm3 and the density is 7.95 g/cm3. Let us deno...

Q: Prove that fdr %3D dSxVf

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Q: 3. Find the solution of the given initial value problem using MVP: 4y(2) – 8y(1) – 5y = x³e2x – 8x y...

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Q: 2. Show that the set of all diagonal matrices of order 2 x 2 is a subspace of M2x2. That [ ] a is, s...

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Q: Construct a matrix system Ax = b, who has a particular solution x, = antd the nullspace of the %3D {...

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Q: Given the differential equation x*dy – tan(y) dx – xsec²ydy + 2xydx = 0 then what is y(x + y) = tan(...

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Q: /hich of the following is the general solution to the differential equation dx =? + ex? y e x + In x...

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Q: min 4x1 + 5x3 2x1 + x2 – 5x3 -3x1 subject to = 1 + 4x3 + x4 = 2 Xi > 0, i = 1, 2, 3, 4.

A: The following steps are used to convert the primal problem as the dual problem. Write the given pri...

Q: Consider the simplex tableau given below. X1 X2 S1 S2 S3 5 1 4 1 3 1 10 2 1 4 - 6 - 2 5 (A) The pivo...

A: From the given table, we have to find the column where the pivot element is located.  

Q: 3/2 Evaluate xp (1+x)'

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Q: Let -8 -2 -9 6. 4 8 and w = 1 4 4 -2 Determine if w is in Col A. Is w in Null A?

A: We can solve this using given above information

Q: Find Vf (Gradiant f) for f(x,y, z) = ysinx + yz at p(0,1,2) Please choose one: a.(1, -1.2) b.(-1,1,0...

A: The gradient of a function: f(x, y, z) is defined as: ∇f=∂f∂x,∂f∂y,∂f∂z, where ∂f∂x,∂f∂y,∂f∂z are pa...

Q: Convert the system to a single second-order homogenous equation and use the methods from the previou...

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Q: (a) Let N E R. Consider the matrices cos(2) - sin(2) ) sin(N) cos(2) cos(N) sin(N) sin(N) - cos(SN) ...

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new ques...

Q: Find the volume of the indicated region. the region bounded by the paraboloid z 1- 36 x2 and the xy-...

A: Solution:-

Q: 2. Find the solution of the given initial value problem using Method of Variation Parameters (MVP): ...

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Q: Eleven members of the executive committee of the Student Senate must vote for a student representati...

A: Option D is correct answer

Q: cos e - sin 0 cos O A = sin 0

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Q: By eliminating the arbitrary constants of y = Cqx + C2x² through isolation, then which of the follow...

A: Differential equation obtained by eliminating constants

Q: Use sigma notation to write the Taylor series about x = 9 for the function. 1 x + 5 Σ k

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Q: 13 cOs(TT) -13 7? Po(x) =| 13 P1(x) = 2! -13 76 -13 n4 x4 4! P3(x) = 6! P2(x) =

A: This is a problem of Mclaurin expansion.