Use mathematical induction to show that: (n(n+1)(2n+1)) 12 + 22 + 32 + ….. + n² = 6

Q: The integral , cot(x + 1) dx is transformed into , g(t) dt by applying an appropriate change of vari...

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Q: Let a be a natural number such that gcd(a, 10) = 1. Use Euler’s theorem to prove that a^40n+1 and a ...

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Q: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully si...

A: This is a problem of point-set topology.

Q: Question 3: Let ť = |1 a) Is there any linear transformation L such that L(u) = v and L(w) = t? If y...

A: For any finite dimensional vector space, any linearly independent subset can be extended to a basis ...

Q: A parachutist of mass 68.1 kg jumps out of a stationary hot air balloon. Use Eq. (1.10) to compute v...

A: The complete solution is in given below

Q: i (2 + i) z = (-1+ i)*

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Q: Allison wants to pay off the loan on her jet ski that she has owned for 18 months. Allison's monthly...

A: Given,  Allison's monthly payment is $284.67 Loan duration :- 2 years (24 months)  Annual rate :- 8....

Q: In the following ordinary annuity, the interest is compounded with each payment, and the payment is ...

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Q: 1. A small town has only 500 residents. Must there be 2 residents who have the same birthday? Why? 2...

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Q: – 3t +2 (b) 24 (a) 15

A: Here we can use the following formula: 1. Lafx+bgx=aLfx+bLgx2.  Ltn=n!sn+1

Q: a) Find the center of mass of the unit square if p(x, t) = 3 – 2P,P2 P1 r = Position vector m 2 b) W...

A: To find: The value of density of the unit square if its center of mass is at the point 0.5,0.5.  

Q: Problem# 2: Solve the following modulo equations/congruences: a) 6x=-107 mod 15. b) 5x+23=-102 mod 7...

A: (a) 6x = -107 mod 15      => 6x = 13 mod 15     As gcd(15, 6) = 3 (not equals 1), thus 6 does not...

Q: Which of the following does not denote a set?   a. N={x|x≥0} b. S c. {1,2,3} d. 2R3

A: "Since you have asked multiple question, we will solve the first question for you. If youwant any sp...

Q: Find the argument of the complex number 3 + 17i 4 4. 47

A: Argument of the complex number

Q: 9. 3cos(@t – a), where w and a are constants.

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Q: 亭 t. e 12 cos 7t + sin 5 - 3

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Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is

A: 1)  The statement is true  Now to see  ho the given polynomial is irreducible or not 

Q: Evaluate and simplify sinh

A: we know that sinhix=isinx therefore  sinhπ3j=jsinπ3

Q: (b) Now consider two different schools, C and D. Suppose that: • In school C, the fraction of studen...

A: Given: From the given,  From school C, the fraction of students with grades below s=s10 From school ...

Q: {(x, y) | y = 3x² – 3x + 4}. Let the relation H defined as H = Write the domain and range of H. a. b...

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Q: The Particular solution of the boundary value problem (D +4)y = 0, with y(0) = -2, y = 0 is 2 %3D %3...

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Q: (a) Students in school A and school B took a standardised math exam. The lowest possible score is 0;...

A: Given:   Students in school A and school B took a standardized math exam. The lowest possible score ...

Q: simplify 520 63 13 ,0.3805i )-5 2i O 5 2i 292-21.8°

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Q: Question 12 Leading coefficient in row echelon form matrix is 1. O True O False

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Q: 6. For a positive integer n 2 4 and a prime number psn, let U, denote the union of p,n all p-Sylow s...

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Q: Solve the differential equation in which y is the displacement of a object at timet. * + 64 + 7y = 1...

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Q: Let a * b = 2ab be defined on Z†. 1. Compute a * (b * c) 2. Compute (a * b) * c

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Q: [(A ^¬B) → C] (¬C→ ¬D) b. ¬[(A → B) → C]V ¬ {[A→(B ^ C)1→¬D}

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Q: rope 'B' to the length of rope 'A'. An alloy contains 2.5 kg of copper and 500 g of zinc. 8. a. Find...

A: Given that the weight of copper is 2.5 kg=2500 gm and zinc is 500 gm in the alloy.  

Q: 3. (a) e' cost (b) 3e2' sin 21

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Q: Consider the differential equation ay“ dæ + 6xydy = 0, with a a real constant. If u(x,y)=xy is an in...

A: By multiplying integrating factor, making it exact we have to find value of a

Q: Solve the differential equation in which y is the displacement of a object at time t. d'y dt2 + 10y ...

A: Second order differential equation

Q: 1) 1+e" |dx+e" (1- xydy =0

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Q: In the set of {1,2,3,4,5,6} can we use the formula 2^n (n stand for how many even number inside the ...

A: This is a problem of set theory.

Q: Try this: Solve the following DE. 1. (x2 + y2)dx + x(x- 2y)dy = 0

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: The object shown in the figure is axially symmetric and its curved surface is described in cylindric...

A: The given problem is to find the volume of the given surface described in cylindrical coordinates r=...

Q: 8.6. What is the conformal transformation sending the first quadrant onto the unit disk? [Ans. f(2) ...

A: To find: The conformal Transformation that map the first quadrant onto the unit disk. First we find ...

Q: The ODE (3x44xy-6) dy+[6xY+2= 5 Sofue by 9. F méthed:

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

Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x) = ...

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Q: Consider the series where (-n-3)" (-4n - 1)" In this problem you must attempt to use the Root Test t...

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Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers. *)(i...

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Q: Prove that the planes (i) 12x – 15y + 16z – 28 = 0, (ii) 6x + 6y – 7z - 8 = 0, and (üii) 2x +35y – 3...

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Q: Let h : R → R be Thomae's function: if x = 0 h(x) 1/n if x E Q and x = m/n in lowest terms with n > ...

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Q: Jillian has just turned 16 years old and has her mind set on buying a new car by the time she is 20 ...

A: To calculate the future value and the interest earned over the investment.

Q: Use the fact that matrices A and B are row-equivalent. 1 2 1 2 5 1 1 A = 3 7 2 2 -2 4 9 3 -5 12 1 0 ...

A: Multipart :    We have given a matrix ,  A = 12100251103722-2493-512 We have given a reduced  row ec...

Q: Construct a truth table for each of the following compound statements, where p, q, r denote primitiv...

A: “Since you have asked multiple question, we will solve the first question for you. If you want any s...

Q: Q. 8. A gas cooking range is available for Rs. 2500 cash or for Rs. 520 cash down payment followed b...

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Q: In an RLC series circuit, L = 1H, R = 42, C = 0.5F and the voltage in a circuit is V(t) q on a plate...

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Q: Compute the thrust being produced by the Lear Jet in Problem 6.21. Given f(x) =f(a) +f'(a)(x – a) an...

A: We have to approximate the f(x).

Q: Q2: Let X and Y have a bivariate normal distribution with parameters µ = H2 = 1, 0} = 16, o = = 25 a...

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