Who is Leonhard Euler and what was one of the significant contributions he made to the field of mathematics that we explored in this module. Give a mathematical example and explain.

Q: QUESTION 12 The following matrix is the adjacency matrix corresponding to a directed c raph.…

A: (a) In the matrix the element M21 = MBA = 1       => Vertex A is reachable from vertex B.…

Q: Given the initial conditions y=1 at x-1, estimate y at x=1.2 using a stepsize h=0.1. Use…

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Q: Answer the following questions for the graph G below: (1) Find a vertex cover for G. (2) Is V={a, c}…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Using the answers obtained in getting the LU decomposition, solve the following system of equations.…

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Q: Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a)…

A: The following steps are used to evaluate the determinant of the 4×4 matrix by diagonal method. Use…

Q: what notation is used in sequences and functions?

A: The notations used in sequences and functions are given below.

Q: Rowena would like to invite 7 friends to go on a trip but has room for only 4 of them. In how many…

A: Here we can use combinations to find the required number of ways. We can choose r things out of n in…

Q: 9. From a class of 32 girls and 18 boys, how many study groups of 3 girls and 2 boys can be formed?

A: Given: A class consists of 32 girls and 18 boys.

Q: dy 3. Find if y= sinh(sec 2x) . Simplify your answer. dx

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Q: 8. Determine the truth value of the each of these statements if the domain consists of all integers:…

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Q: Determine if the events below are mutuall 1. Tossing a 4 or a number greater than 3 if one die is…

A: To determine if the events are mutually exclusive or not mutually exclusive: 1. Let Event A: Tossing…

Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: Please provide justified answer asap:::: Show that n is odd if and only if n^2+4n+1 is even.

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Q: Example 12.8. A firm uses milling machines, grinding machines and lathes to pro- duce two motor…

A: Let us take x to be the number of parts 1 to be manufactured and y to be the number of parts 2 to be…

Q: Let S be a subset of the metric space M = (X, d), with point p E X. Question 4. Prove that p is a…

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Q: wwws 23 う dl %00 Use the circle to answer the question. 15 ft The circumference of a circle is C =…

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Q: Determine the four roots of – j625 in rectangular form. The final answer should be rounded-off to 2…

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Q: M. 50 140 o oo OOO

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Q: 3. Let f : [a, b) -R be integrable. Show that f(t)dt = lim,b Sa f(t)dt. %3!

A: Recall the results mentioned below

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in.…

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Q: Solve the following exponential equation: 7+(5).34x-1= 27 O a. log,(4)+1 4 O b. log,(5) 4 None O d.…

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

Q: Q:Determine a solution for the pDE, and canjecture the form of the general Solution マン fnbtれてhiy h-

A: Given, homogenous Partial differential equation  uxx-4uyy+2ux+4uy=0 Substitute uxx=D2u, uyy=D'2u,…

Q: Calculate x-z lmage 24 ) 8х -2 2x + 1 z + 22 3z O 10 O 10

A: Solution

Q: 25. A number is drawn at random from the set {1, 2, 3, .., 40}. Find the probability that the number…

A: Given: the set 1, 2, 3, …, 40.

Q: 13 in 12 in 9 in CamScanner 5 in

A: To find the surface area of the given triangular prism :-

Q: Determine if the given function is continuous and differentiable at the indicated values of x. Show…

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Q: Given the following time-cɔmplexity functions, fiE O(Wn) f2 E O(n) which algorithm is faster for…

A: Solution :-

Q: Solve the Laplace equation u + Uy O given that

A: Let us consider the step size h=1 i.e. ∆x=∆y=1. To solve the Laplace equation and find the values…

Q: H.W. Solve the fallowing first order DE.

A: Introduction: Integration will be used in some steps to solve a differential equation, both general…

Q: 3 1 4 1 | |(2x – 4y)dydx (2х — |x²ydxdy 3. 4. - 1 2 0 2π π |(sinx + cosy)dxdy 5.

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Q: 14. A box with 12 articles contains one that is defective. In how many ways can Martin select 5…

A: Given: A box has 12 articles such that one of the article is defective.

Q: Solve the initial value problem from t = 0 to 2 when y(0) = 1. dy = yt³ – 1.5y dt Using the methods:…

A: The initial value problem from t = 0 to 2 when y(0) = 1. Solving using Analytically and fourth order…

Q: If W is an invariant subspace for T, t Thus, for each a in V, the conductor S

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Q: f birth? (Use a calculator when necessary) day: month: year (two digits only): my birth date is…

A: To find the age when the date of birth is given as 2nd of  June 2001 We calculate the age from the…

Q: Question 3. 900 Estimate the integral f(x)= fe sinx dx by using trapezoidal rule. You can use…

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Q: For the differential equation y" + 4y + 4y = x² Part 1: Solve the homogeneous equation The…

A: The given differential equation is y''+4y'+4y=x2 To find: the solution of differential equation.

Q: A = {1,2,3,4,6,8,12} a.) Relation on Z Refleksif Symmetric Transitive

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Q: dy Plot the slope field for the differential equation = y2 – x and sketch the solution for the…

A: we will find equilibrium solution curve and then decide region for positive and negative slopes to…

Q: Find the volume of the solid that results when the region enclosed by the given curves y = e-2*, y =…

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Q: 24. Box A contains 7 balls and box B contains 16 balls. How many different selections of 10 balls…

A: Selection of balls, probability

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in.…

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Q: Find the first four nonzero terms in a power series expansion about x=0 for a general solution to…

A: Write y(x) as a power series around 0 and then put this y(x) and their derivatives in the given…

Q: 19. What is the graph of a qua A. Straight Line B. Hyperbola @ Pa D. Sinusoidal ob i2 bol 20. How…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 1 6. Find dx. V2x2 -8x +2

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Q: For the differential equation y' + 14y + 49y = sin(7x) Part 1: Solve the homogeneous equation The…

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Q: Q, has how many edges ? k

A: Let us determine the number of edges does Qk has.

Q: dt dy la) what is associated dineorijed System ar Hhe equilibrium lo,0) ? 10,.0) ! 11 ity of the…

A: This is a problem with the system of differential equations and their stability.

Q: H.W: Which of the sequences {a„} converge and which diverge: 1. a, = 2+(0.1)" 2. an =|1+

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Q: 9. : (y²dx + x²dy) = 0 (x – y)²

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Q: Show algebraically that f(x)-2 x| -9 is an even function. Solve the equation algebraically for x.…

A: A function is an even function if f(-x)=fx. It is known that if logab=c, then b=ac.