Determine which Simpson's rule you are going to use and solve for the vehicle's displacement in the first 30 mins. Furthermore, solve for the average speed of the vehicle for the entire 30mins.

Q: Use two-timing (or averaging) to obtain the general solution of ï+ ε(x² + x² − 1)i + x = 0 with…

A: Please find the attached solution

Q: Consider the initial-value problem: y'-4 = x³y-2, y(2)=3 Using Euler's method we have. Oy₁ =26h +3 O…

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Q: Find all maximal independent sets of path Pio and C10.

A: Please find the attached answer

Q: (c) Let G be a group and a, b € G be elements of G each of order 3 such that a² = 6² and prove tha a…

A: Given: A group G, and a,b∈G order of a and b is 3 and a2=b2. To Prove: a=b.

Q: O(G) If G is a finite group, than o(G) = Σ- D(N(a)) where this sum is taken over one element of each…

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Q: Please do part C and D and please show step by step and explain

A: (c) Suppose the given structure {G = {a, b, c, d}, ∘} forms a group.       Now, a ∘ a = a. . . . (1)…

Q: 1. Let a, b, c E Z and n E N. Assume a = b (mod n) and b = c (mod n). Prove that a = c (mod n).

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Q: Let A E Cnxn and let XC Cn be a subspace of Cn. Recall that is said to be an A-invariant subspace if…

A: As per the question we are given a matrix A ∈ Cn×n and we have to show that : (A - λI)l • A = A •…

Q: Prove that 3" +4" ≤5" for all integers n ≥ 2.

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Q: Prove that pork = pur in O₂ if and only if 0 w = 2m for some m€ Z and k = 1 (mod 2)

A: To prove that ρθrk=ρωrl in Ο2 if and only if θ-ω=2πm for some m∈ℤ  and k¯≡ l¯mod 2.

Q: Determine whether the following statement is true or false: If both matrices A of the size 6 x4 and…

A: False

Q: -Solve the above linear system, by using the Gauss-Jordan reduction after you substitute k value…

A: We will apply elementary row operations on augmented matrices.

Q: Find the zeros and the corresponding multiplicity of the following polynomials and then draw the…

A: To determine zeros of polynomial f(x) then put f(x) equal to zero.  Multiplicity of a zeros is how…

Q: What functions in the range -π (1) Σ =o n= sin(2n+1)x 2n+1

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Q: smallest such k is called the index of nilpotency of N. (a) Show that if a matrix N is nilpotent,…

A: A matrix N is said to be nilpotent if Nk =0 for some integer k.

Q: Determine if the following sequence converges. If it does, find its limit. 8 √2n! \ (2n)! (n=1 2.…

A: (1) Let, the given sequence is {un}, where un = 2n n!2n!

Q: 2. y+3y"+4y+2y=0; y(0) = 4; y'(0)=-4; y"(0)=1 a. y=e* (4+sin x) b. y=4e¹ cos x c. y=e*(1+3 cos x) d.…

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Q: (b) Let I, J be ideals (two-sided) of a ring R and check as to whether In J is an ideal (two-sided)…

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Q: Use the inverse of the coefficient matrix to solve the following system of equations. 8x-y + 3z = 12…

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Q: find the inverse function for the following function(those are all bijective func- tion) (a) f(x) =…

A: Note- Given that All function are bijective.

Q: Show that the straight lines whose direction cosines are given by the equations al + bm + cn = 0 and…

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Q: how to find number of terms(n) when T1=15, D=3 and sum equals 870

A: The given problem is to find the number of terms when first term T1=15 and common difference d=3 and…

Q: A company produces very unusual CD's for which the variable cost is $ 15 per CD and the fixed costs…

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Q: 11.[2] Show that vectors A = 4ax - a₂, B = ax + 3ay + 4az, and C = -5ax 3a, 3az form the sides of a…

A: We know that if the vector form sides of triangle then A→+B→+C→=0 Given,…

Q: 24. Using the CAD drawing below, calculate the measures of angles C and E in degrees and minutes if…

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Q: Question # 1: A function is given by f(x) = 6e-3. Now Answer the following: 1. Calculate f'(x) at x…

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Q: = Solve the matrix equation AX = B for X. 14 -4 B= A=[-33] ³- (-22) -8 X=

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Q: 2. We already saw that the composition of bijections are bijections. In this exercise we will…

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Q: Prove that for any graph G, y(G) ≤ 2ir(G)-1.

A: Please find the attached solution

Q: 4. Find parameters a such that zero solution of the following system is asymptotically stable. * =…

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Q: Suppose A is a 3 x 3 matrix with real entries that has a complex -7-9i 1 -2i eigenvalue 7 +52 with…

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Q: (a) 5-2+0.8 -0.32+... D

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Q: pls answer 3&4

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find all integers n such that o(n) = 40.

A: Use the multiplicative property of ϕ:  if n and m are relatively prime then  ϕ(nm) = ϕ(n)ϕ(m). 40  =…

Q: 3. If the eigenvalues of A are 5 and -1, with multiplicities 2 and 3, respectively, find the…

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Q: If line k in the XY-plane has equation y = mx + b, and is parallel to the line y-x=b+1-mx, where m…

A: Slope intercept form of line is y=mx+c  Here, m is slope and c is constant.

Q: Each of the following points is given in polar coordinates. Find the rectangular coordinates of each…

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Q: Find general solution which starts at (x, y₂ 3) = (R₂0₂0) at t=0.

A: Please find the attached solution

Q: y(t) = y" - 7y' + 6y = et + s(t - 7) + 6(t-9), y(0) = 0, y'(0) = 0 ) + ( [ ])2(x-7)+ ( [ 1) 2(t-1

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Q: Let D be a dominating set of a graph G. Is V(G) – D a dominating set? Why?

A: please find the attached solution

Q: EXAMPLE 1. Use Inductive Reasoning to Predict a Number Use inductive reasoning to predict the next…

A: Given  First term a1=3 Second term a2=6 Similarly a3=8, a4=12, a5=15 a1=3        =2+1+12a2=a1+3…

Q: Verify whether the following sets are subspace of R³/R¹ or not. (i) S = {(x, 2y, 5) : x,y € R} (ii)…

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Q: Suppose x, y, z E R. Show that zz = yz if and only if either x=y or z = 0.

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Q: Polar Area. The graph of the polar function 3 +2²2 +2=²2COS (0) 1 +=cos 24 r = (shown at the right)…

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Q: Determine the pivot element in the simplex tableau. (If there is more than one correct pivot…

A: Given,

Q: n e induction on 17 to prove the Binomial Theorem (a + b)" = Σ C(n, k) an-kbk for all positive…

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Q: 2. sin x 3. dy dt dy dx + y cos x + 2xey + y² cos (2t) = 0 4. t²y' + 2ty - y³ = 0 - (1-x²ey) dy dx…

A: Since you have posted multiple questions , we will provide the solution only to the first question…

Q: Question 2 ! problem dy dx Consider the initial-value =1+2x−y, y(0) = 1. (a) Use the Euler's method…

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Q: 4. Prove that if G and G' are isomorphic groups, then Aut(G) and Aut (G') are also isomorphic.

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