1. Use Dijkstra's algorithm to find the shortest path length between the vertices a and z in each of the following weighted graphs. (a) (b) a a 2 b 2 di 3 2 4 4 5 b 3 C e 7 1 2

Q: you have wrong 3rd derivarive and 4th as well

A:

Q: 2. (a) Let A = {1, 2, 3, 4, 5} and B = {6, 7, 8, 9} and C = {1,4}. Let f: C → B be the function…

A: Let A = {1, 2, 3, 4, 5} and B = {6, 7, 8, 9} and C = {1, 4}. Let f : C → B be the function given by…

Q: Construct a simple graph that is a tree with vertices P, Q, R, S, T, U such that the degree of T is…

A:

Q: 3. A cosine function has a maximum value of 1 and a minimum value of - 5, and a phase shift of 2,…

A:

Q: The Critical Values of the Objective Function: Now we need to find our derivative, C'(x). Again,…

A: As determined previously: Total cost is given as: T=181.6x2+152xy+21.6xy+191.6x2 Constraint: x2y=150…

Q: Compute T₂(x) at x = 0.5 for y = e and use a calculator to compute the error lez - T₂(x)| at x =…

A: Taylor series for y = ex is      y = ex ≈ 1 + x + x2/2! + . . . .    So, T2(x) = 1 + x + x2/2 Then,…

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 6y' +34y=116e¹,…

A:

Q: Solve the initial value problem d²y dt² Select one: O& Ob Od - dy + y(t) = et; y(0) = 2, y'(0) = −1…

A:

Q: use variation (D²-1) = ex - e-x of parameters. r to solve the equation 2

A: Find Roots of auxiliary equation Complementary solution Particular solution by variation of…

Q: JO the MacLaurin polynomial of degree 7 for F(x).

A: Given,          F(x)=∫0xsin6t2dt.

Q: 2. a. Use a computer algebra system to evaluate the following integrals. fsi i. sin x cos 2x dx ii.…

A: Given :  a Following integrals : i ∫sinx cos2x dxii ∫sin3x cos7x dxiii ∫sin8x cos3x dx b∫sinax cosbx…

Q: Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix is (i) b₁ = 2…

A: The given incidence matrix is: A=-1100-1010010-100-11 We know that the incidence matrix A is a n×m…

Q: Describe the set by referring to the numbered regions. XOWOY' W IS 13 If Is X 14

A:

Q: 10. A professional athlete invested $2.5 million of a bonus in an account that earns 6.8% compounded…

A: To find semi annual years when the account will be $0 We use ordinary annuity formula

Q: d) x" - 2x² + 2x=0, e) x" - 2x' + 2x = e-t, x(0)=0, x'(0) = 1. x(0) = 0, r' (0) = 1. f) x" - x' = 0,…

A:

Q: If two inlet pipes can fill a pool in one hour and 30 minutes, and one pipe can fill the pool in two…

A:

Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

A:

Q: (c) ry"+y = 36x

A:

Q: Suppose that $25,000 from a retirement account is invested in a large cap stock fund. After 25 yr,…

A:

Q: Consider a linear transformation Find the matrix A of T. A= *(E)-A· ¹(E) - ¤). ¹(E) - 4) =

A:

Q: The graph of the function f is shown on [0, 2] Match the graphs with the corresponding extension of…

A: Given: Graph of function f in [0,2] and  Option A ,B,C are also given .To do: Match the graphs with…

Q: A. Is it a Subspace? Consider the following vector spaces V and subsets U. Determine if U is a…

A:

Q: The left end of a rod of length I is held at temperature 130, and there is heat transfer from the…

A: Given: The left end of a rod of length L is held at temperature 130, and there is heat transfer from…

Q: Solve the linear programming problem.. Maximize P=40x+50y Subject to 2x+y = 10 x+y ≤ 7 x+2y s 12 x y…

A:

Q: Consider the vector field Find a direction (8) sin (a) in which the directional derivative of…

A:

Q: A function f : N × N → N is defined by f (m, n) = 2ᵐ−¹(2n − 1). (a) Prove that f is one to one and…

A:

Q: Find the point P(z, y, z) at which the paraboloid has a tangent plane parallel to the plane (z, y,…

A:

Q: A store store is looking to stock the following: necklaces, bracelets, rings, and earrings. The…

A:

Q: From smallest to largest, the eigenvalues are A₁ <A₂ < X3 where X₁ 1₂ 5 X3 = Find the eigenvalues…

A:

Q: how can one combine power series? what is the convergence of the combination?

A: To Explain: How can one combine power series? What is the convergence of the combination?

Q: A = 060 4 1 2 20 04

A:

Q: Convert the rectangular equation to polar form, or the polar form to rectangular form and sketch the…

A: The given equations are: (a) y=4 (b) y2=9x (c) r=θ We have to convert the rectangular equation to…

Q: Let V be a vector space over F, and let U and W be subspaces of V. The sum of U and W, denoted by…

A:

Q: Find the general solution with the given set of auxiliary roots. m = 0, 3,-1,1± √√√2 A B C y=c+ce 2…

A:

Q: * U V Q Consider the graph given above. Add an edge so the resulting graph has an Euler circuit…

A:

Q: S(curl F) · n dS  where F  =  4yz i  +  6x j  + 5yze x2 k  , S is the portion of the paraboloid  z…

A:

Q: Building the most economical shed (or minimizing the cost of building a shed). A shed is to be…

A: Length x Height y Depth z The depth of the shed is 1.6 times of the length The volume of the shed…

Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve the…

A:

Q: 9. Let F be the function such that F (n) is the sum of the first n positive integers. Give a…

A:

Q: Sketch the graph of the function and check the graph with a graphing calculator. Before doing so…

A: Fx=e-x+1

Q: The rate of a continuous money flow starts at $1300 and increases exponentially at 6% per year for…

A: Solution:-

Q: Part 1 of (a) For each function given in the table, write an equivalent function using base e. That…

A:

Q: If AT y = b has a solution and Ax = 0, is (x¹ b = 0) or (x y = 0)? Justify your answer…

A: Given ATy=0 has a solution and Ax=0. We need to determine whether xTb=0 or xTy=0 is true.

Q: If f : X → Y and g: Y→ Z are functions such that g of is one-to-one, then f is one-to-one.

A:

Q: I'm confused on how to do the second part of the problem still.

A: Given: The system of equations is given by:          x'=-2565310-25x Also, it has been calculated…

Q: 46. Find the order of 7 modulo 172.

A:

Q: THEOREM 7.4.1 Derivatives of Transforms If F(s) = {f(t)} and n = 1, 2, 3, . . . , then L{t¹f(t)} =…

A:

Q: Let x, y, z be (non-zero) vectors and suppose w = 12x + 8y + 2z. If z = -3x - 2y, then w x+ y. Using…

A:

Q: A string of length L is secured at both ends. The string has no initial displacement, but has…

A: