V1 V3 V2 V4 a) Find the adjacency matrix A for the directed graph shown. b) Compute A³. What do the entries in A³ represent?

Q: A 2³-2 design was used to investigate the effect of A = condensation temperature, B = amount of…

A: Since, you posted multiple questions, we will solve 3rd question for you.

Q: . Let P(r) = 5x³ – 3rª + 3x³ − 9r + 5. Give a step-by-step € – 8 proof that - - lim P(x) = P(1). I→1

A:

Q: Estimate 3x + x² using Mid-point method (n=6), then find the error estimate.

A: Given integral is ∫143x+x2dx. We have to estimate the given integral by using Mid-point method.…

Q: QUESTION 9 Question 4 (Answer Questions 4.1 4.2 based on this Question) Consider the Logistic…

A: To solve the given logistic difference equation.

Q: Use the root test to find the radius of convergenc n n Σ (m+-+²1) ² = xn 9n +4 n=1

A: Introduction: The radius of convergence of a energy collection is the diameter of the most important…

Q: Consider the following optimisation problem min f(x, y) = x + y − x2 subject to x + y ≤ 1 x ≥ 0, y ≥…

A:

Q: b) Using only Laplace transforms solve the following Samuelson model given below i.e. the second…

A: Given: yt+2-5yt+1+6yt=4t To find: Second order difference equation

Q: Find an equation for the plane that is tangent to the surface z= In (x²+y^) at the point P(0,1,0).…

A:

Q: Let Us Assess Take your time and study the figure below. Show your solution in calculating its area.…

A: Let us consider the rectangle of length L and breadth B  The area of rectangle is obtained as Area…

Q: 1. Consider the system X(t) = AX(t) where A = ( a) - (1) ª and a a constant. (a) For which values of…

A:

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

A:

Q: a. Let A be an p × k matrix, with columns a₁, A2, . ...,ak. Let x = (X1, X2, ... Xk) be a vector in…

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

Q: 0 10 0 0 1 0 0 0 0 0 0 0 0 0 ω Ν -3 0 0 2 1 0 0 3 0 1 -1 2 0 0 0 0 0 0 0 0 X1 X2 X3 ΧΑ X5 Χ6 Χτ = 32…

A: Given that, Convert the matrix term into system of equations.…

Q: An airplane has an airspeed of 500 km/h. The pilot wishes to fly to a destination the the plane's…

A: Formula for resultant of two vectors R=A2+B2+2ABCosθ where A represents magnitude of A and θ is the…

Q: pro Determine whether each of the following NLP's is a convel (f) May 62 X, +123 X₂ In (x₁) + In…

A: As per the question we are given an nonlinear optimization problem. And we have to find whether the…

Q: Paper sheets are required to make a stack of 8cm height. Each paper is 2.5x10-4. How many are…

A: Solution

Q: Prove the theorems: i) "If n is an integer, and if n² is even then n is even". ii) "If n is an…

A:

Q: H.W: Use the chain rule to find the derivative of w= x² + y² with dw respect to t (dr), with x =…

A:

Q: 1. Compute the Frenet apparatus k, 7, T, N and B of the following curve √2 a(s) = (1 – ½ c cos s, 3…

A: Given: αs=1-22cos s,3+22cos s,sin s To find: Center and radius

Q: 4. Find the distance from the pole to the vertices, and then find the equation of the ellipse in…

A:

Q: For which of the following series the radius of convergence is 5? (1) Σ#ight (x – 9)", (11) Σ+1 (x –…

A:

Q: a) Determine whether S = {(1,0,-1), (2,1,0), (3,1,−1), (1,1,1)} spans R³. b) Find all c ER for which…

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

Q: The figure below is a net for a right rectangular prism. Its surface area is 208 m² and the area of…

A: In this question, the concept of area is used. The area of the missing edge and dimension of the…

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x, y) = 10xye-(x²…

A:

Q: Use Runge-Kutta 2nd order to find y at x=2, given that dy=e* +0.1y dx. y(1) = 0. (Use h = 0.2) 1 1.2…

A: We can write the given differential equation as y'=ex+0.1y, where y'=dydx. We have to find the value…

Q: Q.3 Show that Je dx=r

A:

Q: Solve the following differential equations: dy 1.1 (x³ + y²)-(3xy²) X dx [Hint: Let y = vx].

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

Q: Evaluate [²²* 0 3 y² sin z6 dx dy dz

A: Consider: ∫01∫0z2∫03 y2 sinz6 dx dy dz So, evaluating this we get: ∫01∫0z2∫03 y2 sinz6 dx dy…

Q: The real part of cot(1 + j2) is.

A:

Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: Question 4. Compute the density, the characteristic path length and global clustering coefficient…

A:

Q: Let G be a graph with n 1 vertices. (a) If x(G) = 1, what can you say about E(G), the edge set of G?…

A: Given : G is a graph with n≥1 vertices We have to answer the following : (a) If χG=1, what can be…

Q: [*f(x) dx = Given that $f's is 54 wha f(w)dw

A: Properties of Integral 1. ∫abf(x)dx=-∫baf(x)dx 2. ∫abf(x)dx=∫abf(w)dw

Q: dy Use Picard's method to solve -xy, y(0) = 1 dx Find y3(1)?

A:

Q: Find T(10 + 7t) when T is a linear transformation from P₂ which is a vector space of polynomials…

A: A linear map (additionally called a linear mapping, linear transformation, vector area homomorphism,…

Q: Find the Laplace Transform of e-t sin2t 2 2s 2 A. ²/+ B. S (s+1)²+4 (S-1)²+4 C. S+1 s(S²+4) D. None…

A:

Q: A boy is pushing a box with a force that can be described by the function: (x) = x³ − sin 2x + 1,…

A: To find: Work which is required to be done when force F is applied to move the box from x=1 to x=3.…

Q: c{(a,b), r} circle of center (a, b) and radius r 2 2 (x-a)² + (x−b)² = r² Convert to polar…

A:

Q: Given the function below f(x, y, z) = 2 cos (r) + xy - xz - y² - e²% +2% (a) Show that the origin…

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

Q: 1 = Σ x with convergence in (-1, 1), find the power series for 1-x n=0 1-2x3 n=0 Identify its…

A: Follow the steps.

Q: Using Limit Comparison Test (LCT) the following series +∞ n2 + 3 Σ; ηνησ + 5 n=1 test is…

A:

Q: If f(x) = – 1 1 + 8x f'(x) = Σ – Σ n=1 = Σ (-1)"8"an n=0

A: Follow the steps.

Q: Q1. Compute the following limits if it exists. √x+2-3. 1-lim( x-7 2-lim (7x²+x+1) x→∞0 4x²+3x

A:

Q: Maciek swims in a 25 m long pool. At one end of the pool the depth is 3 m, and at the other 1.5 m.…

A: Given: Length of  pool BE=25m To find: Capacity of pool

Q: +x+y² = 0

A: Given as, 3. cx2+x+y2=0

Q: Suppose that an equilateral plate that is 2 feet high is standing straight on the bottom of a 6 feet…

A: We will find force on horizontal slice of plate and then integrate it to find total force . 56u

Q: Chapter 9.2, Question 6 If Shanta deposited $2800 in an investment fund that was earning 5.5%…

A:

Q: (y')2+y'-x=0    solve the differential equation

A: A differential equation is an equation that relates one or more unknown functions and their…

Q: that set of of degree subspace of P₂ Prove or disprove all Spolynomials is 43 not? Or

A: P2 is vector space of real polynomial of degree less or equal to 2. That is P2=px=a0+a1x+a2x2:…

Q: Find the interval of convergence for each power series. Include endpoint convergence tests when…

A: To find the interval of convergence of the given series :-