A 2nd degree palynomial passes through the points (1,-1); (2,-2); (3,-1) and (4,2) Find the polynomial eqution

Q: Transformers for underground works were planned to be provided. Type A has an initial cost of…

A: Solution:-

Q: ABCD is a square and E is the intersection point of the diagonals. If N is any point on AE, show…

A:

Q: The set is called the standard basis of the space of 2 x 2 matrices. Find the coordinates of M=…

A:

Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: 1. The vertices of a quadrilateral PQRS are P (0, -1), Q (- 2, 3), R (6, 7) and S (8, 3). The two…

A:

Q: 2. Find the eigenvalues and eigenvectors of A = 2 1 0 121 O 1 2

A: Solution :-

Q: Describe the transformations of the functions. State the domain and ran

A: (b) Given,           y+4=-2x

Q: Solve the following PDE (Paryial Differential Equation) for t > 0. Express the final answer in terms…

A: Introduction: One of the most important applications of Laplace transformation is solving partial…

Q: Caitlyn sells her drawings at the county fair. She has portraits and landscapes and she is required…

A:

Q: Solve the partial differential equation: a²u azu by the method of separation of variables for a…

A: Given: ∂2u∂t2=c2∂2u∂x2 To find: ux,t=0

Q: Q2. At a price of $7.00 per box of apples, the supply is 320,000 boxes and the demand is 200,000…

A: To determine the price-supply equation.

Q: Q3) A building was photographed using an aerial camera from a flying height of 1000 m. The photo…

A:

Q: Mathematics of Apportoinment A small country consists of five states, whose populations are listed…

A: Given that the population of five states and total legislature seats in the following table…

Q: Question: Find the mass of a plate bounded by one arch of the curve y = sin x, and the x-axis, if…

A: Solution:-

Q: 4. To lease a new car worth $19995, a customer agrees to pay a $3000 down payment and 48 monthly…

A:

Q: g(t) = -{ = t², -8 + 3t, (t− 6)² + 2 cos (²-1), 0 2

A: Solution

Q: What is the value of k such that the lines 3x + 6ky-7 and 9kx + 8y=15 will have the same positive…

A:

Q: Evaluate the integral: */ - — csc? rdr. π/4 Find the derivative of the integral function: g(x) =…

A:

Q: Compute the following Laplace transforms: Problem 12 (a) L{3t4 + 4t² - 6t+8} (b) L{4e-3t-sin 5t)}…

A:

Q: Q3: Solve (x + y)dx - x dy = 0

A:

Q: (29) π/3 177³- _csc ada π/4

A:

Q: 8. Solve for the quadratic equation x²-6x-8= 0 using the quadratic formula. 9. Solve for the…

A: Solution

Q: Verify that the given functions are linearly independent by evaluating the Wronskian at a = 0. {ex,…

A:

Q: Consider the curve defined by the equation y = 5x + 1x. Set up an integral that represents the…

A:

Q: ▪ Homworke Example 2 The point P(x, y) is given an anticlockwise rotation of radians about the…

A:

Q: ) Solve by using Laplace transform the partial differential equation 8² 2² = 9. y(0,1)= 0, y(2,1)=…

A:

Q: (B) Explain the relationship between any three of the following a) Ideal and subring. b) Prime ideal…

A: Solution :-

Q: Given the force field È (x, y, z) = .) Show that FdR is independent of path without computing for…

A: Please find the answer in next step

Q: 6. For any n x n matrix A over C, there exists a positive semi- definite matrix H and a unitary…

A:

Q: Use Laplace transform to solve the partial differential equation: d²u du ди(x,0) t> 0, 0<x<1, u(x,0)…

A:

Q: x²-x+1 x² + 2x + 2 -२ хр.

A: To solve: ∫x2-x+1x2+2x+2dx

Q: Let Find a basis for the null space of A. A = -2 3-1 -6 9 -3 33

A:

Q: Compute the determinant det 2 n n+1 n

A:

Q: Supppose A is an invertible x n matrix and is an eigenvector of A with associated eigenvalue-2.…

A: Here we use the properties of eigenvalues of matrix to answer the appropriate question as below.

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

A:

Q: Write 843 in scientific notation

A:

Q: In a certain geometry, define the distance d(P₁, P₂) between two points P(x, y,) and P(x, y₂) as…

A: We will use the basic knowledge of metric spaces to answer this question completely and correctly.

Q: Q: Define the concept of the ring. Is (Z, +,.) a ring? What's about (Z, +,.)?

A:

Q: Let Find a non-zero vector in the column space of A. A = -8 -8 12 -12 2 -2 -3 0 10 0 15

A: Solution

Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: Exampley Consider the following nonlinear sine-Gordon equation Utt-Uxx+5 inu zo subject to the…

A: Solution: Given the Sine-Gordon equation utt-uxx+sinu=0   - - - - - (1) and initially conditions;…

Q: 7. Find the value of K, so that (x + 4) is a factor of P(x) = 2x³ + x² - kx + 20. 8. Find the value…

A:

Q: (B) Let I be a maximal proper ideal of commutative ring with identity R. Prove that R/I is a field.

A:

Q: 1. Find the zero-divisors of Z6- 2. Let D be an integral domain. Show that if a E D such that a² = a…

A:

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

A:

Q: 2. Find the volume of the solid generated when the region enclosed by the curve y = x² + 1, y = 4x −…

A:

Q: Show that if 4, and A, are two events, then P(A₂)+P(A₂)−1≤P(44₂).

A: First we will write Inclusion-exclusion principle for two sets.

Q: (A) Let R =(Z12, +12,-12). 1. Find all maximal ideals of R. 2. Evaluate char. (R). 3. Is R a fi-

A: Z12 maximal ideals and characteristics R

Q: 是 Suppose the differential equation = 2x²-1 where y(0) = 0. dx 8) Create a slope field the…

A: To plot the slope field for the differential equation of the form y'(x)=f(x) recall the following…

Q: c) Find the curve length of the lemniscate of the area Inside the lemniscate r² = 6 cos 20 and…

A: Solution:-