Prove that Σ₁ iª = n(n+1)(2n +1) (3n² + 3n − 1) i=1 30

Q: Count the number of arrangements of the word EULERIAN that have no isolated vowels; that is, any…

A: The given word is EULERIAN. We need to find total number of arrangements of the given word such that…

Q: 3. Let P3 (x) be the interpolating polynomial for the data (0, 3), (1, 4), (2, y), and (3, 0). The…

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Q: 17.) Find the derivative using the quotient rule.

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Q: values ( Vinx dx usi x Rom brook method who Equal (A) 0.641 B0-65806 06637 O C 0-6112

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Q: - Divided differences of the second order for the following values تساوي------ -0.13333, 1.23333 (→…

A: Newton divided difference table for 3 data points can be made as follows. x y 1st order 2nd order…

Q: 5. (The hammer blow) Let p(x) = 0 and (x) = 1 for |x| 3a/2. Continue in this manner for each case.]

A: Given Data: ux,t=12c∫x-ctx+ctψsds =12clength ofx-ct,x+ct∩-a,a

Q: X log x-12 = If the root of the equati lies between 2.7 and 8, then the first approximation to the…

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Q: Does A(u x v) = Auxv +ux Av?

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Q: Quadrilateral ABCD shown in the coordinate plane below, is dilated with the center at the origin to…

A: Given:  The below figure: To find: The correct option for the scalar factor of dilation. The…

Q: Year Net Income Expenses 2013 $27,200 $19,800 2014. $23,700 $18,500 2015…

A: From data, a) Dana's net income ,in total, for years 2013 to 2019 =$(27,200 + 23,700 + 31,500 +…

Q: Use the Bisection method to find solutions to within 10-6 a. x³ + 3x² − 1 = 0, [−3,−2] - b. ex - 3x²…

A: a). Result is correct up to six digit.  Hence solution is -2.879583

Q: Consider a call option having the strike price K and exercise time t. Suppose further that the…

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Q: Let f(x, y, z): = x² - tany² 2xyz Solve for fry

A: Given :fx,y,z=x2-tany22xyz To find fzxy

Q: Let P, Q be two points on the sphere of radius 1. Assume that P # -Q. Show that there exists a curve…

A: Given Data: P and Q be two points on the sphere of radius 1 P ≠ -Q. Show that : There exists a…

Q: that the Lagrange Polynomial of values Know follows b) F a) T as 0 1 2 = (x²-19x + 6) :- 3 7

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Q: 15.) Find derivative. (+)

A: Given that ddxx1+4x

Q: The particular solution of the following equation by using the method of undetermined coefficients…

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Q: Find bases and dimensions for all four fundamental subspaces of A: 1 0 01 3 0 2 A= 5 100014 -3 1 1 0…

A: Basis: Let V be a vector space. Then, the set S is called a basis of V if S is linearly independent…

Q: Determine the coefficients of the rational expression below when expanded into partial fractions of…

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Q: 2. If TA'AA' = A', then K = TA' is the Penrose inverse of A. Use this principle to find the Penrose…

A: Given: In this problem, the given matrix is A=011011110 If TA'AA'=A', then K=TA' is the Penrose…

Q: Which of the following differential equations is NOT homogeneous? A B dy dx D x + y x-y (x²-xy + y²)…

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Q: If we have x = 0·3000 x 10³², x²=0.300 x10³ The relative error is!- a) 0.333x103 b) 0.33333 x 10 c)…

A: Formula of relative error  = (actual value observed)-(expected value)expected value given X=0.3000x…

Q: example of a function ti (n) such that t₁ (n) = 0(t₁(2n)).

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Q: The function f(x,y) = y²tan (y/x) is a homogeneous function of degree _____. A) 1/2 B 0 C) 2 (D) 1

A: Given: fx, y=y2tanyx To find: Degree of given homogeneous function.

Q: Find all parameters a ∈ (0, 4] for which the logistic family ga(x) = ax(1 − x) has an attracting…

A: Given: Logistic family gax=ax1-x To Find: All the parametersa∈(0,4] for which the logistic family…

Q: (a) If f, is integrable on DCR, n € N, and if Ef uniformly converges to f, then f is integrable on D…

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Q: (b) = 15251-11 |x| o otherwise

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Q: 6 For each of the following functions, find all local maximum and minimum values. (a) g(x) = x ln x…

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Q: JJJ Evaluate the triple integral E tetrahedon with vertices (0, 0, 0), (6, 0, 0), (0, 4, 0), (0, 0,…

A: Given information Vertices of tetrahedron are 0, 0, 0, 6, 0, 0,  0, 4, 0,  0, 0, 9. Triple…

Q: -18 [] 12 Let u= 40 and A= 2-4 9 Is u in the plane in R³ spanned by the columns of A? Why or why…

A: Given : u=-184012   , A=2-4-5922 To Check : A. u is a linear combination of the Columns of A…

Q: / 1 التاريخ : and the number using the central differences of the Prablem where - y = x الموضوع y (H…

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Q: Prove that if Σan converges, then Σa also does.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: [5] For each of the following functions f find a simple function g such that f(n) = (g(n)). (a)…

A: Given Data: We need to write Θ(g(n)) for given functions.

Q: Q3.) In an experiment, the following reading were recorded: Xi Yi 3.6 9.3 4.8 10.2 7.2 11.5 A 6.9 12…

A: Given Data: (a) To derive the normalized equations for this reading if (y=a+bx) by LSA method. (b)…

Q: To the right are two different models of the same rectangle. If the width of the model on the left…

A: Introduction: Units of measure are needed so as to live these values. Sometimes the units of…

Q: 4. Vertex is at (1, -2) and focus at (1, 0) Equation in standard form: Opening/Concavity Vertex…

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Q: For all x > 1 we have Στι(n) = 6(2) x2 + O(xloga). ηΣα

A: We recall some basic facts and then proceed to solve the problem. The detailed solution is given as…

Q: How many shortest lattice paths start at (2, 2) and a. end at (12, 12)? 184756 b. end at (12, 12)…

A: The number of Lattice Paths from (c,d) to  (a,b) is given by the equation; N=a-c+b-da-c

Q: Anna wants to make an open wooden bin with a square bottom, rectangular sides, and a height of 3 m.…

A: Let the length of the square bottom is a m. So the area of the bottom is a2 s.m. Now the cost for…

Q: 5. Get the sum of the first six terms and compare with the eight number. Repeat the procedure for…

A: q-5 get the sum of first six term and compare with the eight number. repeat the procedure for the…

Q: Prove that if n is composite, then n has a prime divisor p satisfying p ≤ √√n.

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Q: Find all prime ideals of (Z12, +12-12). Then find Rad (Z12).

A: Prime Ideal:  Let R be a commutative ring. An ideal P is called a prime ideal if P(not equal to R)…

Q: 3 9 -3 -2 -5 5 1 1 -6 0 0 0 A=10 0 0 000 5-6-8 +A=-4-10 4 1 48-4

A: Given: The equation is 39-3-2-5511-6-1+A=-45-6-8-104148-4. To find: The matrix A.

Q: When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was…

A: Given: When water flows across farmland, some soil is washed away, resulting in erosion. An…

Q: dx2 2. What is the particular solution of: d'y + 4y = e³x dr

A: According to our guideline, we can solve only first question of multiple questions. Here we solve…

Q: Use iterative methods to solve the following 1. √90 to 6 significant figures 2. √125 to 6…

A: Given : Let x=90 To Find : Using the iterative method, find the value of 90 up to 6 significant…

Q: The following table shows the weather forecast for the statistical data of precipitation for the…

A: Note: In the table, the value of 2012 should be 746 instead of 476. Otherwise, the value will not…

Q: If a 1 : 192 movie set scale model of the Empire State building in New York City is 84 inches tall,…

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Q: Suppose that you are thinking about buying a car and have narrowed down your choices to two options.…

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Q: Q4. B. Find the tangential vector (T), normal vector (N) and binomial vector (B) for the position…

A: Given: R(t)=cosh(t)i-sinh(t)j+tk We have to find tangential vector ,normal vector and binomial…