Prove that the transformation below is LINEAR. T:R² – → R3 R³ T(x,y) = (x + y, 3y, 2x – y)

Q: Cylindrical Shell Method 7. An oil tank in the shape of a sphere has a diameter of 60 ft. How much…

A: 7 Given that an oil tank in the shape of a sphere has a diameter of 60 ft. We have to find the…

Q: b) Consider the following LP problem. Maximize z = 3x1 + 4x2 + X3 Subject to X1 + x2 + x, 5 50 2x, –…

A:

Q: + 6х, — 5х, — 2x4 + 5x3 5x, + 10х, + 6x2 + 8x4 +

A:

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A:

Q: Use Green's Theorem to evaluate the line integral. v? dx + xy dy C: boundary of the region lying…

A:

Q: Consider integers from 1,000 to 9,999. Then, answer the following questions. a) How many even…

A: From 1000 to 9999 all are 4 digit numbers , So we need to filled up four places to get the number .…

Q: A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the…

A: The given volume of the tank is 100 L. Let v=1+cos2t and cs=0.21+cos2t. The initial time is 0 min…

Q: 2.f (t) = cosh wt sin wt

A:

Q: For the following differential equation y' = x * (x + y) + 2 and the following initial condition…

A:

Q: Let L= D^2(D^2-9).  Solve for Ly(t) = -2t(^2)*e^(3t) + e^-3t for t  is an element of (-inf,inf)

A:

Q: 14 if z +i 3. Let f(z) = 8i if z = i (a) Calculate limf(z) using properties of limits. (b) Use the…

A:

Q: Spline Interpolation Derive the linear system corresponding to the natural cubic spline through (0,…

A: As per the question we are given the following data points : x y 0 3 1 -2 2 1 And we…

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: The formula for percent error is: PE = (|Estimated value-Actual value|/ Actual value) × 100 Or…

Q: 3) Using the Power method, obtain the largest eigenvalue and the corresponding eigenvector for the…

A: We will use the basic knowledge of the power method and perform two iterations only, as specified in…

Q: evaluate log i^3 to base i

A:

Q: Q2. Evaluate | ydA in two different ways. Here R is the region in the first quadrant bounded by the…

A:

Q: 17. Evaluate L{y"(1) + 2y'(1) + y(1)}; y'(0) = -1, y(0) = 5. Let L {y()} = {s). A) (s°+2s+ 1)Y(s) –…

A: Here we use basic laplace transform

Q: t, 0st<1 3. f(t) = t21

A:

Q: Consider functions f: {1,2,3, 4} → {a, b, c}. i. How many such functions are there? ii. How many…

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

Q: What is the iterative method in system of linear equations

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

Q: a. Let V be any finite dimensional vector space. In class, we learned that for any finite set (w1,…

A: To Check: Whether the given statement is true or false. Statement: If W is a subspace of a vector…

Q: Circular Disk Method 1. R: y = √?, y = 4, y- axis               axis of revolution: y = 4

A: 1 Given that R:y=x, y=4, y−axis and axis of revolution is y=4. We have to find the volume of the…

Q: Which of the following is always true for a connected graph? Select one: O a. all vertices have even…

A:

Q: Question 7. Prove or disprove: (a) The union of two subgroups of a group (G, *) is a subgroup of G.…

A: 7)  We need to prove or disprove the given statements. a) The union of two subgroups of a group G ,…

Q: 9. Find the general solution of (D² – 2D+ 1)y= 6e*. A) y= (c, +c,x)e* + 3e™* B) y= (c, +c,x+ 3x² )e*…

A:

Q: PE02]Rbe function frx)={" if xs1 X. if x7L Indicate whet her the functionis Ca Pable o fin tegrable…

A:

Q: Prove the trigonometric identity  1+sec2x /over/ 1+tan2x=1+cos2x

A:

Q: Suppose a definite integral has lower and upper bounds as follows. 7.006 < < 7.018 If the midpoint…

A:

Q: a) Given the following Linear Programming (LP) problem: Minimize z = 2x, + 3xz Subject to x, + 3x, 2…

A: It is a Linear Programming problem and I solved it using Two-Phase method in the next steps.

Q: 4 0 b Let M 3 -7 be a three-by-three matrix with a =3 and b =0. What is the a -1 2 determinant of…

A: Here given that M=   4 0   b   3 a-7-1  2   1 be a three-by-three matrix with a=3 and b=0. We have…

Q: 1. Solve the system by Gaussian elimination x+y-5z =-18 3x-3y+z 6 x+3y-2z = -13

A: Consider the given system x+y−5z=−183x−3y+z=6x+3y−2z=−13.........1 We have to solve the given system…

Q: Let G be the group of symmetries of the graph Answer the following, giving a full justification for…

A: This is a problem of group theory.

Q: Evaluate the surface integral (x + y + z) dS where S is the part of a plane parametrized by S: r(u,…

A:

Q: Fund the ffirst three terms in the Fourier Sine series for the funotion: Cexterded as a 2ir periodic…

A:

Q: 2. Use first differences, second differences, and/or ratios to classify each relation as linear,…

A:

Q: Which expression is equivalent to [77 · (-65) + 147] mod 7? O 7 O [(147 mod 7) · (-65 mod 7) + (77…

A:

Q: Classify the quadric surface. 22 = x2+ y? O hyperboloid of two sheets O ellipsoid O hyperboloid of…

A: Solution :-

Q: Find the Fourier series of the given function. Show details of your work. So f(x) -T <x< 0 0 <x< T

A:

Q: The augmented matrix of a linear system has been reduced by row operations to the form shown.…

A:

Q: a = (5, - 1) and b = (-2, –2). Represent à + b using the head to tail method.

A: This is the problem of vector analysis.

Q: If A = 2xz 2 i - yz j + 3xz 3 k and ∅ = x 2 yz , find (a) ∇x A, (b) curl (∅A) , (c) ∇ x (∇xA), (d) ∇…

A: To find the above questions on vector

Q: Find the difference approximations of the solution y(x) of the boundary value problem y" +…

A:

Q: Determine the truth value of the statement and prove it on a sheet of paper: D = set of negative…

A: Set of negative integers and quantifier

Q: Suppose we have two 1 metre long rods. Each rod has a temperature of 0° on its left end with the…

A:

Q: Show that yrcos(x²) is asoktion to: xy"-y'+4x3y =0, and then use reduction of order to fond a second…

A: Given differential equation is ,                                   xy" - y' + 4x3y = 0 (.)  If  y =…

Q: Determine the periodic payments on the given mortgage. HINT [See Example 5.] (Round your answer to…

A:

Q: L{t(u0 – u1) + t²u1}.

A:

Q: 2. (G VH) →(G AH) - (GAH) :- (GvH)

A:

Q: 3. Prove that if E has finite measure and let {f.}be a sequence of measurable functions on E that…

A:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A: Introduction: When we apply force 'F' to a block, the body accelerates or speeds up or down…