Prove a^2 +4a+3 is odd if and only if a is even.

Q: Let A = 1 01 -2 0 0 -1 1 1 TO 0 2 -2 2 0 2 o Find the eigenvalues for A. Carefully show your…

A: Given,       A=10-110101-202-20202.

Q: 6). State whether the series converges absolutely, conditionally, or not at all. ∞     n = 1 (−1)n…

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Q: Consider the system of equations Find all basic solutions. x1 01 x2 -1 2 x3 x4 [21 1 12 = 2

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Q: How many WAYS can you make P17 using only P10, P5 and P1 coins? SHOW the different ways.

A: Solution:   Given : P10, P5 and P1    And we have to make P17. Now,        P10 P5 P1   Total 1…

Q: A stretched rubber band is fixed at x = displacement is given by f(x) 0 and x = L and is initially…

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Q: 99 The deflection of a beam yox), satisfies the differential equation 26 d"y dx4 ои = W(x) 0<x< 1…

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Q: finitely many prinies of the form in 4n  +3.

A: Suppose there are only finitely many primes and let p be the largest one. Define q by…

Q: Given that the Laplace transform of f(t) is S -7 877 s² + 7 F(s) = then the Laplace transform of…

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Q: the differential equation. (D²+1)y=secx tan x

A: The general solution of a differential equation  is given by; y(x)=C.F+P.I where C.F is the…

Q: 5s The inverse Laplace transform of s² + 81 is A cos(bt), where A and b are constants such that b >…

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Q: characterize the following differential equation (what order is it, if it is linear or not, if it is…

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Q: {"By experiment method"; Make a series of drawings and briefly explain each ...) You have a drum of…

A: Given that, You have a drum of water, a 5-quart pail, a 3-quart pail, and an empty drum. 1 quart of…

Q: X 0 1 123 2 3 4 5 сл f(x) 0 0.5 0.8 0.9 0.941 0.962

A: There doesn't exist any exponential function which transform zero to zero. Here I have considered…

Q: II. Let G₂ be the solid above the xy-plane that is inside the sphere x² + y² + z² = 16 but outside…

A: The given problem is to evaluate the given triple integral of z over the given region above xy plane…

Q: Find the lowest possible root of the function f(x)=x² + 12x4-10x³ - 7x² - 10 using Bisection Method.…

A: Given function: f(x) = x7+12x4-10x3-7x2-10 At x = 0, f(0) = -10 &lt; 0 At x = 1, f(1) = 1 + 12 - 10…

Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: 1. Express f(t) in terms of the unit step function uc(t) f(t) = 1, t 1, t-3, 1, - if t 5

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Q: e) A manufacturer produces three products: Product A, Product B and Product C. To be able to produce…

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Q: =o ex) Solve the D.E. (x+y) dx + (x+zy) dy - that satisfies the initial condition y ez) = 3 ?

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Q: Find the order of 5 modulo 2^100.

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Q: η 1 Σ;( + 1) = =n(n + 1)(n + 2 i=1

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Q: (4) Let f : [0, 1] → [0, 1] be the function given by f(x) = x². (a) Use induction to prove that for…

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Q: here are infinitely many primes.

A: We shall prove it by contradiction. Suppose there are only finitely many primes, say 2,3,5,,p. Let…

Q: x+3x+2x = 2√e¨¬dt Find x(t). Note that x = dx/dt, etc. (b) What is the value of x(t) ast →∞ ?

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Q: Step 3 of 4 The approximate Riemann sum of f(x) = x³ - 9x on [0, 7] using n rectangles with right…

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Q: a.) Use long division to rewrite the function f(x) = 6x−3/2x+1 as the sum of a constant and a…

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Q: (3) Let G be the group Sn. Let S be the 3-fold Cartesian product of {1,...,n}. Describe the orbits…

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Q: Consider the plate bounded by y2 = 8x and x = 2 with density 8 = 2-x. (a) Sketch a graph of the…

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Q: Transform: f(t) = sin 2t cos 2t F (s) F (s) F (s) = F (s) : F (s) = = = = F (s) = = F (s) : = F (s)…

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Q: 1. Taylor Approxmations Use sympy to find the Taylor Approximations to sin x with 1 term, 2 terms, 3…

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Q: 3. f(t) = cos 4t-cos 2t t

A: We know that  LFt=fs=∫0∞e-stFtdt           aLcosat=ss2+a2                         bL1tFt=∫s∞fxdx…

Q: Q2: given that G=40 1=55 C = 0.8Yd + 25 T = 0.1Y+ 10 Calculate the equilibrium level of income(y)…

A: Given: G=40, I=55, C=0.8Y+25, T=0.1Y+10   To Calculate: The equilibrium level of income (Y) To find:…

Q: You are given 12 points in the plane, no three of which are collinear (i.e., no three of the points…

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Q: Prove the following using the Mean Value Theorem: (a) For any real numbers x and y with x > y, we…

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Q: use the building block - I In problems Σ", x < 1, together with the result differentiating and…

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Q: The bar graph below shows trends in several economic indicators over the period 1997-2002. Over the…

A: Introduction:        "A bar graph is a chart that compares different categories of data using…

Q: Differentiate y=sinx+cosx+tanx

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Q: 25. F(s) = = 7s² +23s + 30 (s − 2) (s² + 2s + 5)

A: F(s)=7s2+23s+30(s-2)(s2+2s+5) Then solve it

Q: Calculate the following integrals. You may - and in many cases, should use results from Sections 3.2…

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Q: (10) Let f RR be the function given by f(x) = e and g (1,7) →R be given by g(x) = tan x. (a) Is fog…

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Q: Let f (x) and g(x) be differentiable functions in (a, continuous at a and b, and g(x) #0 in [a, b].…

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Q: Suppose that a computer supplier has two warehouse, one located in city A and another in city B. The…

A: Ware house\Customer location C D Supplysi A 1 2 80 B 3 2 90 Demanddi 70 50…

Q: 1. How many games will be played by 8 players in a ping-pong tournament if each player plays with…

A: A combination can be defined as an arrangement of objects where the order in which the objects are…

Q: Find an orthogonal basis for the column space of the matrix to the right. 1 - 1 ܝ ܘ ܝ 1 1 3 6 - 4 1…

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Q: 1. Let p be prime and let a 0 (mod p). Let b = a 2 (mod p). Show that ab = 1 (mod p). 2. Use the…

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Q: Find the lowest possible root of the function f(x)=x² + 12x4-10x³ - 7x² - 10 using Bisection Method.…

A: As per the question we are given the following 7th order polynomial equation : f(x) = x⁷ + 12x⁴ -…

Q: 3) (- .) How many ordered quadruplets (a1, a2, a3, a4) of non-negative integers, where at least one…

A: We have to find the how many ordered quadruplets (a1, a2, a3, a4) of non-negative integers, where at…

Q: 1f \ x | < 1 and 1= x < < 1; then: 2 ₂ F₁ (a, b ; c ; x ) = (1 − x)¯ª₂ F₁ [a, c − b; c; X _— — ₁) X-

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Q: I. Let G₁ be the solid in the first octant that is inside the paraboloid 2x² + 2y²=8-z and below the…

A: As per our guideline we can solve only furst question with all subparts. Please repost for another…

Q: The inverse Laplace transform of 9s² + 76s + 320 (s + 4) (s² + 4s + 40)

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