It suspect that the five data points: (-2, y1), (–1, y2), (0, y3), (1, ya), (2, y5) lie on the curve y = ax + bx² + cr³. (i) What is the system of equations that would need to be satisfied if the points did lie on the line? (ii) Write down the normal equations for this system and explain why they have a unique solution.

Q: Use Laplace transform and find f(t) of the function. 53+3s2-2s+4 F(s) = s(s-1)(s-2)(s²+4s+3)

A: Solution

Q: Consider the nxn matrix with entries Aij = 1/(i+2j-1), set x = [1, ..., 1]', and b = Ax. You act as ...

A:

Q: GENERAL MATHEMATICS Identify the domain and range of the following logarithmic functions. y=log 5(x-...

A: The given logarithmic function is: y=log5x-1+3

Q: 6. Mat A = magic(4) , Mat B = | 5 8 l10 7 [3 1. 6 3 4 20, Mat C =|11 11 30 l-2 5 11

A:

Q: 3.5 A-4.5 5/K 225

A:

Q: Suppose f : ℝ ®ℝ is given by f(x) = x3 and g : ℝ ®ℝ is given by g(x) = 3x + 2. Then determine the co...

A:

Q: Use the method of variation of parameters to find a particular solution to the following differentia...

A: We have given differential equation, y'' - 18y' + 81y = e9x25 + x2 We need to find particular soluti...

Q: 1. Simplify: 12 O6 3 O6 5 O6 24 2. Problem: Use the encoding formula y = x + 15 (mod 26). 1. Encode:...

A: 2 use the encoding formula y = x+15(mod26) 1. Encode DAWN first we will convert each letter in plain...

Q: Look for the Fourier transform of the pulse waveform below. v(t), -T/2 0 T/2

A:

Q: Use technology to maximize the following. You may round answers to 2 decimal places if desired. Maxi...

A:

Q: 0.31x + 2.73 If the coefficients are rounded off of find the absolute and relative in y x + 0.35 whe...

A: Solution:-

Q: -4 - n<t < 0 f(t) = { 4 0<t<n

A: Given periodic function is:f(t)=-4   -π&lt;t&lt;04          0&lt;t&lt;πWe have to find b1

Q: b. Recall that f(x) = 2*-1 - 1. Graph of f,(x) = f(-x) + 2, f2(x) = f(-x+ 1) +1, and fs(x) = f,(x) +...

A:

Q: f(x) = -5x6 + 8X5 + 9X4 -10X3 +2X2 -22X +45

A: To do the calculations in Excel, first enter the numbers in separate cells. Each number is identifie...

Q: -10r+12s -6 S =

A:

Q: If a fifth degree polynomial is divided by a third degree polynomial, what is the degree of the quot...

A: Let there be two polynomials fx=ax5+bx4+cx3+dx2+ex+f and gx=mx3+nx2+px+q where a≠0, m≠0.    

Q: The position vector r of a particle (relative to the origin) at time t is r = k cos ot i+ k sin ot j...

A:

Q: Inverse Laplace Transform Given F(s) =L (F), find f (+). a, b, L, n are constants. Show the details ...

A:

Q: 13. (a) To buy a Treasury bill (T-bill) that matures to $10,000 in 6 months, you must pay $9750. Wha...

A:

Q: Suppose that Ax=b has no solution and the columns of A are linearly independent. Let t(A) denote the...

A:

Q: 4. Write the following (0, 1, 2. ..., 10) in set-builder notation. 5. Write out the set (x: x is an ...

A: Set theory

Q: Find the products AB and BA for the diagonal matrices. 5 A = -3 0 B = 0 -2 0 4 AB = I 1 BA =

A: Given Matrices are A = 500-2  ,   B = -3004

Q: The graph of an exponential relationship is shown in the following applet. P1 = (0.00, 2.00) P2= (2....

A:

Q: (b) +V-2y-3t y(0) 0 v(0) = 1

A:

Q: 2x + 3)y’ = y + (2x + 3)1/2

A: Given differential equation can be reduced in linear differential equation 

Q: 7 45 and fourth term of (3x -) 6. Find the product of expressed 2 as P.

A: The complete solutions are given below

Q: GIVEN COMPLEX NUMBER 3 1. 2 - 5i

A:

Q: Given the function fx)=x cosx. Use the centered-divided-difference formula f '(x) = 2h to compute th...

A: We will use center difference formula  f'(x)=f(x+h)-f(x-h)2h

Q: Find the orthogonal trajectories of

A: Given,          y=ax2+4ax+4a, where a being paarameter.

Q: 1. The partnership of Nina, Sarah, and Tessa earned a net income of Php 30,000.00 they agreed to div...

A:

Q: Alfred Wegener was a German meteorologist and geophysicist primarily known for his contribution on C...

A: We have to find the error. Then, we solve the problem.

Q: Part 4. Prove the following mathematical statements, Let n be any integer. a. If n – 1 is odd, then ...

A: The given problem is to prove the given following statements. With given n is any integer.

Q: The root of the equation is estimated using the point of intersection of y = e^x and y 3x + 2 Using ...

A:

Q: +y-y K0)-1

A: This is a problem of IVP.

Q: A particle moves in the x – y plane with velocity v = = (1-t)î + (4 – 21 + t² )i 4. where t is the t...

A:

Q: M stand for slope b stand for y i

A: Given,               x+y=3                         ...(1)x-2y=-6                     ...(2)

Q: A consumer has preferences described by utility function u(x1,x2)=In(1+x1)+x2. Suppose p1=1, p2=3, a...

A:

Q: find the equation in the form:y zab th lexponential). > points: (0,83), (30, 63) and (70,47)

A:

Q: Find x such that the matrix is singular. A = -3 -2 X =

A: Given A = 6x-3-2

Q: 1-1

A: If we subtract 1 from 1, then it will be 0. i.e. 1-1=0

Q: 4. Use the Fixed-Point Iteration Method to find the solutions to the equation sin x –e-* = 0 in the ...

A: a)

Q: GIVEN COMPLEX NUMBER 3 - i 2. 2 - i

A:

Q: Exercise: Solved the following problem: The average cost per unit C(x), in dollars, to produce x uni...

A: Given that the average cost per unit C(x), in dollars, to produce x units of toy cars is given by S=...

Q: Question 3 Compute the Laplace Transform of the following differential equations dy(t) + 3y(t) = u(t...

A:

Q: b. Recall that f(x) = 2*-1- 1. Graph of f(x) f(-x) + 2, f2(x) = f(-x+ 1) +1, and f3(x) = f,(x) + f2(...

A: Only digital solutions are allowed as per the guidelines.

Q: Find the harmonic conjugate of the following. 10. х-у2+у

A:

Q: (a) Radius of the circle = 2 ..... (a) Circumference (b) Diameter (c) Arc (d) Chord (b) is the longe...

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

Q: Suppose that Ax=b has no solution and the columns of A are linearly independent. Let t(A) denote the...

A: This is a problem of Linear Transformation.

Q: 2. The differential equation x2(x- 2) y" + 3(x – 2)y' + y = 0, has the singular points at x = 0 and ...

A:

Q: Consider the function f(r, y, 2) = ry + y² + z². (a) What is the gradient grad f of f, and what is i...

A: Given: f(x,y,z)=xy+y2+z2a) To find, grad f and its value at point 2,1,1