1. Given the following differential equations, determine the transfer function if the input is X and the output is Y. a. y'" + 6y" - 3y' - 4y = 2x" + 5x' - 2x b. 2y" + 6y" - y = 6x" + 3x' + 8x

Q: V = {ax³ + ax² + bx − 2c|a + c = 0, b ≤ R} ≤ P3.

A: Solution

Q: A=UEVT 0.5 0.5 0.5 0.5] [20 -0.5 0.5 -0.5 0.5 0 15 [0.8 -0.6 0.5 -0.5 -0.5 0.5 0 0 0.6 0.8 -0.5 -0.5…

A: Given that A=U∑VT=0.50.50.50.5-0.50.5-0.50.50.5-0.5-0.50.5-0.5-0.50.50.520001500000.8-0.60.60.8…

Q: Let n and k be integers. Disprove: nk−n is always divisible by k. Problem 2 Let x be a non-zero…

A: 1. Let n and k are integers. Then nk-n is not divisible by k when n is not divisible by k. To show…

Q: Let a be a complex zero of x2 + x + 1 over Q. Prove thatQ(√ a)= Q(a).

A: given equation x2+x+1 let a be the complex roots over ℚ

Q: Question: Find the order of every element in the symmetry group of D4. I know the order each group…

A:

Q: Your instructor treats your section with a Pepperoni Pizza. Suppose that your plate is the Cartesian…

A:

Q: please answer question 5

A: We know that the tank will be full in 8 days. We need to determine the recommendation regarding the…

Q: Suppose that F is a field and there is a ring homomorphism from Zonto F. Show that F is isomorphic…

A: It is given that F is a field and there exists a ring homomorphism from ℤ onto F. Prove that F is…

Q: Determine the validity of an argument using Euler diagram. Premise 1: Some real numbers are…

A:

Q: Problem IV Consider the set of a s. Determine whether it is a subspac 61. z-y +z = 0. 62. x+y+z= 1.…

A:

Q: Determine the nth term of the given sequence (answer varies). a1 = 0, a₂ = 3, a3 = 8, a4 = 15, as =…

A:

Q: Show that the following vectors are linearly independent 2 [943 - • Let W = {A E M2x2 (R) | A = AT}.…

A:

Q: Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of…

A: The details are provided in step 2.

Q: Question 2: Which of the following sequences are bounded (and divergent), in- creasing, or…

A:

Q: fourier series function, f(x) = {x − 2} if −2 < x < 0 {x+2} if 0 < x < 2 sketch the 4 periodic…

A:

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A:

Q: A simplified version of input-output analysis of a national economy has the following input-output…

A:

Q: (a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive…

A:

Q: -3x dy dx + = 1 + 3x

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: coin is biased in such a way that the probability of tails is 0.6. If the coin is flipped 540 times,…

A: Probability and expected number

Q: 4. Linear Equations a. (y - cos²x) dx + cosxdy = 0

A:

Q: a. 3y(x²-1)dx + (x³ + 8y − 3x)dy = 0; x = 0, y = 1

A: Given differential equation is  3y(x2-1)dx+(x3+8y-3x)dy=0 ; x=0,y=1 This can be solved by using…

Q: Let f(x) = sin 2x. (a) Find the Hermite interpolating polynomial of degree at most three using xo =…

A: We are given the function f(x)=sin 2x. For (a), The Hermite interpolating polynomial of degree at…

Q: 10. Prove: "If line m is parallel to line 7, then all the points on m lie on the same side of I."

A: Suppose, if possible, there exists a pair of points on the line m, say u and v, such that u and v…

Q: b) an unbounded sequence with a convergent subsequence.

A: A sequence (x n) of reals is bounded iff there is some M≥0 such that |x n|≤M for all n≥1. A sequence…

Q: In Exercises 9-14, reduce the given payoff matrix by dominance. 12. a b 1 0 2-3 3 2 -1 -10 10 3-4

A: The given matrix 0-1-5-3-101023-4 This payoff matrix is solved using the method of dominance.

Q: I meant 16 not 14!

A:

Q: 4. 5. (1 + Inx+) dx = (1 - Inx) dy dy ax = 3x + 2y e

A:

Q: There are fallacies associated with conditional statements. The three most common are Fallacy of the…

A:

Q: 4. Consider the the linear maps f: R² R² and g: R² R² given by f((x, y)) = (x-y,2+ y) and g((x, y))=…

A:

Q: Given the triangle in 3-space that has vertices A(2, 6, -1), B(1, 1, 1), and C(4, 6, 2), solve the…

A:

Q: {,-5,-4,-3,-2,-1} U [0, +∞0) in E₁

A:

Q: what six transformations (reflection, shift, translation, etc.) that have occurred to produce this…

A:

Q: Determine the Galois group of x3 - 1 over Q and x3 - 2 over Q.

A: In this question, we have to determine the Galois group of x3 - 1 over Q and x3 - 2 over Q.

Q: 1. Define the multiplication operation as modulo 10 in G = {2,4,6.8}. Determine whether the system…

A:

Q: If a > 0 show that a¹/n → 1 as n → ∞.

A:

Q: How many edges does Cn have

A: We know that Cn is a cycle graph on n vertices. The cycle graph Cn is a circular graph with V=0, 1,…

Q: 4(dq/dt) + 2q - 4 = 0 Construct a slope field for the differential equation. Do not sketch solution…

A:

Q: 4.2 Use 3 iterations of the power method to approximate the dominant eigenvector and eigenvalue of…

A:

Q: Suppose Set B contains 67 elements and the total number elements in either Set A or Set B is 145. If…

A: as given nB=67nA∪B=145nA∩B=12 claim- to find nA

Q: x+2y+3z=4 19. 3x+6y+z=2 (no solution) 2x+4y+z=-2 [x-2y+3z=4 20. 3x-y-z=2 x+y-3z=-2

A: Total Equations are 3x+2y+3z=4→(1)3x+6y+z=2→(2)2x+4y+z=-2→(3)Converting given equations into matrix…

Q: In each of Problems 17 and 18, determine the values of a, if any, for which all solutions tend to…

A:

Q: Let U={1,2,3,...,10}, A={1,3,5,7}, B={1,2,3,4}, and C={3,4,6,7,9}. Select (A∩B)^c from the choices…

A:

Q: Find the area of the region bounded below by the curve y = 2, to the left by the curve y = cos(x)…

A: Explanation of the answer is as follows

Q: A fair cubic die is rolled twice. Determine the probability of rolling two even outcomes given that…

A: Probability= Number of Favourable OutcomesNumber of Total Possible Outcomes

Q: y'' +4y' +5y=3e-2x cos x solve the above differential equation

A: The given differential equation is ,      y''+4y'+5y=3e-2xcosx then the solution is given by ,…

Q: Prove the validity of the compound proposition. Either Gryffindor wins or Slytherin wins. If…

A: Let us define the following symbols.  G : Gryffindor wins S : Slytherin wins Gd : Gryffindor…

Q: Nolsten home's for any frimme, p=5 P-1 Σ sid k= > sem. we have. (P-1)! k 。 (p²)

A:

Q: Define an operation ∗ on Z+ as follows: For a,b ∈ Z+, a∗b = a−b+1.  Show that ∗ is a binary…

A: Define an operation ∗ on Z+ as follows: For a,b ∈ Z+, a∗b = a−b+1.   Show that ∗ is a binary…

Q: The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the…

A: The cardinality of a set represents the number of elements in that set. We need to calculate the…