How many strings of 8 letters from the English alphabet contain exactly 3 different vowels and 5 different consonants? Give your answer in terms of combinatorial numbers. Then, write the answer in a different way, using complementary combinations.

Q: 8. Find the principal value of Arc tanh(1 + j2)

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Q: Correct answer is q imples p

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Q: D) Calculate the following definite integral: [* (/{√x - 1) dx

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Q: 4. Given the functions f(x) = x + 2 and g(x) = x², determine all values of x for which f(g(x)) =…

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Q: Find the values for a, b, c and d in the diagram below. Give reasons for your values. 2430 34° 59°…

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Q: Find the Laplace transform of F(s) = = f(t) = = t 5

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Q: Line integrals can look a lot alike! But they represent very different things. Consider: (i) [f ds…

A: Given That  Different Representation of Line Integral is as follows : i) ∫Cfdsii) ∫CF·driii) ∫nF·nds…

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A: Given That : ∂u∂x+∂u∂t+u=0 ,x>0,t>0u(0,t)=0 ,u(x,0)=sinx To Find : Solution of the Partial…

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Q: 8.17 Let f(t) be a T-periodic signal and let g(t) be the signal given by 1 8 (t) = ² ft = ² ft f(u)…

A: In this question, the concept of Periodic function is applied. Given, gt=1a∫t-atfudu.

Q: Let a and b be any two positive integers. Define the least common multiple of a and b to be the…

A: As per the question we are given the least common multiple of two integers a, b as : l = ab/gcd(a,b)…

Q: (b) d²y dy Find the solution for cos(x) ² − (1 + x²) dx − 2xy = 12 with the conditions - dx² dx 1+x²…

A: Given cosxd2ydx2-1+x2dydx-2xy=11+x2y1=-1, y2=2, h=0.25`

Q: 3. The iteration formula X+1=X-Rsin²x +(cosx) (sin x), where R is a positive constant, was obtained…

A: Newton's method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to approximate…

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A: a) 148+25 (i) combine sets for a total of flats , longs and units given sum can be written as…

Q: 7. 2) Write the difference equation for the systems shown below. ii) Find yon) / xen). yon) x(n) 3…

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Q: Variable Separable Find the general solution of the given differential equations. B. x sin sin x edx…

A: Given: Let us consider the given differential equation, x sin sinxe-y dx=ydy To determine: The…

Q: 1. Consider the matrices 10 A₁ = -( : ) - ( ) - ( 1 ) 020 A3 3 3 A₂ 02 00 -1 0 0-2 1 Compute the…

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Q: (1093x-21093x+5) The equation log3x-2 X exactly three real solutions at least one real solutions =…

A: Consider the given equation, xlog32x-92log3x+5=33 Let us assume that log3x=m,…

Q: 2. Sketch a graph of y = cos x and y = − cos(2x − n) + 1 for 1 full cycle. -

A: What is a Cycle: Cycle is important in trigonometric functions. When a trigonometric function…

Q: : Find a solution op of the I.V.P.: Y₁ = −y₁, y₂ = y₁ +ty₂, y(0) = []

A: To solve this problem using the following steps  First we find the particular solution of the first…

Q: Solve the following optimization problem subject to max-(₁-4)²-(₂-4)² 21,22 x₁ + x₂ ≤ 4,2₁ +372 ≤9

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Q: Compute the first 5 Legendre Polynomials, Po(x), P₁(x), -P₁(x). (These These are > Solutions, P,…

A: What is Legendre Polynomial: Legendre polynomial is a collection of orthogonal polynomials of degree…

Q: Which of the following is equivalent to the conditional statement p→ q? O a. Contrapositive q→ p O…

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Q: Find the Laplace transform of F(s) = = f(t) = = t 5

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Q: (b) Find the equation of the sphere in R³ that has the diameter from A(1, 2, -1) to B(5,-2,0).

A: Part (b):- Given co-ordinates of diameter are  A1, 2, -1   to   B5, -2,  0.

Q: 5. Prove that (-1)v=-v for every vector v in a vector space.

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Q: A recruiter who can walk is interviewing a job seeker who uses a wheelchair. Summarize your…

A: Giving an opportunity for the disabled person and interviewing him is one of the good thing .…

Q: Prove by induction that 7"-4" is a multiple of 3, for all ne N.

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Q: How can I simplify f(x) = arctan(2(x-1)) - ln IxI such that I can describe the intervals of the…

A: Given below clear explanation

Q: In Problems 41-46 use Theorem B.3 to find A¹ for the given matrix or show that no inverse exists.…

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Q: So, L' (e^ F (4)) = f (t-a) ua (t) Now 2 [(5m) in en -e. it los (i) L uk [sint} 2k --(4-k)s - ille…

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Q: Restate the contraction mapping principle, and list what it tells us about the mapping g.

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Q: As a detective, you are tasked to solve the case handed over to you by your senior officer: A dead…

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A: Part(4):- To show that:- a0 = 0 for every scalar "a" in a vector space. Here, "0" denotes zero…

Q: 2. Let V = M₂ (R). Show that the symmetric bilinear form : VxV→R given by (X,Y)= tr(XY) (X,Y)=0 for…

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Q: 6. Find complementary function and particular integral of the following differential equation: (D- d…

A: Given : D-12 D+12y=sinx To Find : Complementary function (C.F.) and particular integral (P.I.)

Q: For Questions 5-7 below, consider the following description of a two-goods example: Assume two…

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Q: Variable Separable Find the general solution of the given differential equations. A. (xy² − 4x)dx +…

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Q: (a) Prove that : (a-1)² a²+1 a (6-1)² 6²+1 b (c-1)2 c²+1 c = 0

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Q: How many kg of rice costing *8 per kg must be mixed with 36 kg of rice costing * 5.40 per kg so that…

A: The expression y percent gain on x is same as: x1+y100.

Q: a. The function f: [0,1] → R given by f(x)=x¹/² is Lipschitz. b. The function f: [0,00) → R given by…

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Q: Given the observed values of a function 168, 120, 72 and 63 respectively at the four positions 3, 7,…

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