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Q: k 1. Prove that \k

A: In the first part, it is required to prove that knnk=n−1k−1 We know that nk=n!k!n−k! Now take Left H...

Q: QUESTION 2: (Interpolating and Polynomials approximation) Use Lagrange's formula and estimate from t...

A: Given: A data Income not exceeding (in JD) 295 410 585 730 No. of workers 36 44 51 62 To fin...

Q: If ? be an ? × ? matrix, then rank (?) + nullity (?) = ?. Do you agree or disagree? Explain briefly....

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Q: (a) Write the following expression in the forms of x+ yi where x and y are real numbers. +3i 5i (V5+...

A: Complex numbers

Q: Solve for x= 0.1 the intial value problem (1.v.p) and Use Taylor series -3 Siny y6) = W %3D

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Q: Let q1, q2, q3, . . . be defined by q1 = 2, qn = 3qn−1 − 1 for n ≥ 2. Show by induction that for all...

A: We are given a sequence of qn and we have to use induction to prove that : qn = 1/2(3n + 1)

Q: If functions f and g are continuous on the interval [-1, 1] and differ- entiable on (–1, 1), and the...

A: Rolle's theorem is very significant in differential calculus. It gives the idea of the tangent line ...

Q: Match each problem with its correct answer. A. 0.543 + 10' 0.0021 B. 62.93 + 10³ 0.543 C. 987.33 + 1...

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three ...

Q: Eight men have enough food for 29 weeks. How long would the food last for 10 men?

A: 8 men have enough food for 29 week 1 man have enough food for 298weeks  

Q: Find the harmonic function which vanishes on the hypotenuse and has prescribed values on the other t...

A: The harmonic function which vanishes on the hypotenuse and hasprescribed values on the other two sid...

Q: (a) Construct the image of the point A under the composition of ƒ =ref (the reflection with respect ...

A: As per the question we have to construct the image of the given point A , after being reflected by t...

Q: Use (a) fixed - point iteration and (b) Secant method to determine a root of f(x) = - x2 + 1.8x +2.5...

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Q: 4. Prove that a function which is harmonic everywhere on a plane and is bounded either above or belo...

A: The given problem is to prove that a function which is harmonic everywhere on a plane and is bounded...

Q: sin e cos (cos a cosec 0) de (1-cos a). 2 ||

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Q: (a) Using Crammer's Rule or any other method for matrix determinar 2x –1 2x+1 = 0 values of x for wh...

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts ...

Q: 2) у(и? + 1)du + (из — Зи)dy — 0 %3D

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Q: a) Check that the line r: (x, y, z) = (1,0,1) + t(1, –1,0) is parallel to the plane n:x + y +z = 0; ...

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Q: If a television program has an audience of 2 000 000 people with 30% of the viewers being in your ta...

A: Given the total audience is 2000000 Given percentage of viewers = 30% Therefore, the remaining perce...

Q: Answer this question Determine the loo = ||x - y ||. distance between the vectors x = (4,–2,–3)* and...

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Q: 1 1 3 1 6. 2 A = -3 -1 1 -2 -1 1 1 4 1 6. 1 A) Find the rank (A) B) Find the basis and dimension of ...

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Q: We would like to solve the following boundary value problem using the weighted residual method: d'u ...

A: The given problem is to find the exact solution of the boundary value problem with given boundary co...

Q: dx n+1

A: By Bartleby policy I have to solve only first one as these are unrelated and lengthy problems.These ...

Q: 1. Which of the following sets of vectors a = of R (n 2 3)? (a1, .. ., an) in R are subspaces boa W ...

A: A subspace is a non-empty subset of a vector space which is itself a vector space. When a non-empty ...

Q: Deter mine Whe ther the difle ven tral Equation (5x -2ny +3) dx + (sy-+5) dy = is Exa ct. I H 1S Cr9...

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Q: (a) Show that the vectors (1,1,0), (1,0, 1) and (0,1,1) form a basis or not for R' (b) Define subspa...

A: Let us consider a set of vectors say S then S is said to be the basis of the vector space V .If  S ...

Q: If z1 = 3 + j2 and z2 = 5 – j3 , what is the simplified form of z1 z2 ?

A: We know that the rectangular form of a complex number is written as z=a+jb where a and b are real nu...

Q: Problems 4.1. Show that the entropy of a system in the grand canonical enscmble can be written as S=...

A: Solution 

Q: What will be the maturity value of ₱16,000 invested for 5 years at 15% compounded quarterly?

A: Formula: The compound interest formula is given by, A=P1+rnnt, where A-maturity value, P-principle a...

Q: Consider the divisibility partial order on N. Find a, b E N so that the interval poset a, b has heig...

A: The divisibility is obviously partial ordered relation on ℕ that is it satisfies, 1)Transitive Relat...

Q: What sum of money is required to pay a loan of P20,000 on May 20, 2018, if the loan was made on Octo...

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Q: 08. Σ 3n 1 Arcsin 2n n=1

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Q: Let X, Y be two sets. Prove that X × Y C P(P(X U Y )).

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Q: A simple graph T has 26 edges and degree of each vertex is 13. Find the number of vertices. (recall:...

A: We need to determine the number of vertices using the number of edges and degree of each vertex.

Q: In the comer of a cellar is a pyramidal heap of coal. The base of the heap is an isosceles right tri...

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Q: a) A disc jockey decides to play 7 songs in a birthday party. If there are 13 songs available, in ho...

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...

Q: What is the interest rate compounded quarterly if P 2,500,000.00 is invested and the amount became P...

A: Formula: The compound interest formula is given below: A=P1+rnnt, where A-final amount, P-Principle ...

Q: 2x e D ze find D? గలగోల గాల

A: The given problem is to find the determinant of the given matrix of exponential functions.

Q: Find e^t where A is the matrix 2 1 2 1 2 0 1 1 2 A =

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Q: Solve an = an-1 +3n² – 3n+1 with A, = 0

A: We will find the solution of given recurrence equation by rearranging terms on the non homogeneous p...

Q: y = 6*

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Q: Let f be a function defined on ]0, 1[ by : 0, if x is irrațional f (x) = {1/q, if x=p/q; where p and...

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Q: Answer this question Determine the loo = ||x – y||. distance between the vectors x = (4, –2, –3)ť an...

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Q: solve the first and second derivative of Y= (1+lnx)  /  x

A:  If y=f(x), then the independent variable x is called the input of the function, and the dependent v...

Q: A bacteria culture is known to grow at a rate proportional to the amount present. If the population ...

A: This is a problem of the application of differential equations.

Q: LA wheel has a diameter of 100 centimeters. If the wheel is supporting a cart moving at 45 kilometer...

A: For the solution follow the next step.  

Q: J Q2) Which of the following sequences and series is converge and which is diverge? (choose five): 1...

A: According to our guidelines we can answer only three sub-parts and rest can be reposted. 

Q: k log k Show that diverges. 1+ k2 k=1

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Q: Calculate ff F.n dS where F x'yzi + 2xj + y?k in the solid region S bounded by the parabolic tube z ...

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Q: Given the following periodic function, find its Fourier sine series. 0, <. f(x) = I - x, 0 <x <

A: The given problem is to find the Fourier sine series of the given periodic function, we have to use ...

Q: find a re: 1ons.

A: