Use mathematical induction to prove that the following statement is true: 3 × 5 + 7 × 9 + · · · + (4n − 1)(4n + 1) = n(4n+1)(4n+5)/3 for all n ≥ 1.

Q: What is the effective annual interest rate of a 4% nominal annual interest rate compounded daily.…

A: Effective Interest Rate i=1+rMM-1×100 % where r is nominal interest rate M is number of compounding…

Q: Find all solutions of the given system of equations and check your answer graphically. (If there is…

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Q: Find all solutions of the given system of equations and check your answer graphically. (If there is…

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Q: The volume of the solid region in the first octant bounded by the x²+y², and z = √√√x² + y² and the…

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Q: Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika}, C = {Hans, Frans}.…

A: If A be a set of m element.  Then the cardinality of A is the number of element in A.  It is denoted…

Q: 1- Apply the backward Euler method to solve the initial value problem Consider the initial value…

A: Given Data:   Y'(t)=ata-1   Y(0)=0 Where, a>0       a=2.5, 1.5, 1.1 with stepsize  h=0.2, 0.1,…

Q: 7. ди du = 2, 0 0 Ət u(0, t) = u(36, t) = 0, t> 0 2x 362x u(x, 0) Find the solution of the heat…

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Q: 2. Suppose f is differentiable with f(0) = 0 and 0 0.

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Q: Internet Audience At the end of a certain year, the four companies with the largest number of home…

A: Given: The combined audience are 284 and  z-u=3x-y+22x+y=48+z+ux-y+z-u=54 To find: How large was the…

Q: A Bernoulli differential equation is one of the form dy dx + P(x)y= Q(x)y". bserve that, if n = 0 or…

A: y'-9xy=y4x17 divide by y4 y'y4-9xy3=1x17

Q: Which of the following statements is true? 1. The R (ie, R-squared) tells us the percentage of the…

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Q: Which of the following is false? a. (x-y+2) = (x-y-11) (mod13) b. (x-y + 2) = (x−y-32) (mod17) c.…

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Q: 17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the…

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Q: A large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $6…

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Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 3tk O 5 5 5 k k 2 -2 5 Z 2…

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Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then L−¹{F(s)G(s)} = f(t)g(t). O True O…

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Q: Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution,…

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Q: 3. Using the traces obtained in IV.1., provide a hand-drawn sketch of 3. Label all important points…

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Q: Use an appropriate series in (2) in Section 6.1 to find the Maclaurin series of the given function.…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4e* - 9

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Q: Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika}, C = {Hans, Frans}.…

A: The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A…

Q: Q4) Consider the DE y' = (5x + y + 7)², y(0) = 1 i) Solve it numerically using Euler's method (n=4)…

A: Given IVP is y'=5x+y+72, y(0)=1 Since n=4 So step size is h=upper limit-lower limitn⇒h=1-04⇒h=0.25

Q: 7. Consider Sø a. What is the order of the cycle (1457)? What is the order of a = (4 5) (2 3 7)? b.

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Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the…

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Q: QUESTION 3 Identify the order k of the Legendre equation (1-x²)y" - 2xy' + 20y=0 with general…

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Q: . Let 3 be the surface with equation given by 4x² - 9y² = 9 (2²+4). 1. Find an equation of the trace…

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Q: Need Use Cylindrical Shell Method, the region bounded by the curve y=x2 and the line y=1 and x=2 is…

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Q: Calculate the moment of inertia of the shaded area about the x-axis. 76 mm Answer: Ix= 76 mm 40 mm =…

A: Consider the following figure. We have to find the moment of inertia of the shaded region AEFCD.…

Q: How many ordered lists are there of three items chosen from four? ordered lists

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Q: Determine the periodic payments PMT on the given loan or mortgage. (Round your answer t $900,000…

A: Loan Amortization Formula PMT=Pr1+rn1+rn-1 Where 'PMT' is periodic payment, 'P' is loan amount, 'r'…

Q: Does n(CUN) = n(C) + n(N) − n(Cn N)? O Yes Ο No

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Q: b) Find -1. e-s ((s+1) e¯¹ s²+4s+6

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Q: A building contractor has a contract which will expire in 30 days. He has 80  men on the job and can…

A: according to question a contract will expire in 30 days contractor has 80 men on job and can finish…

Q: Question 2 Let y=ex + b(x+1)³. When x = 0, a) the possible values of a and b. suppose that dy - = 0…

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Q: 3/ Consider f(a)(x) = lim Auf(x) = lim h-0 h h-0 ha f(a)(x) = ka f(x) where f(x) = Emo (m) (-1)m…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Use a computer as a computational aid. Use U/+1, + U₁₁+1+ U₁-1₁j + U₁₁-1 - 4u,j = 0 to approximate…

A: We have to find the solution of the given laplace problem using mess size h=1/3

Q: Show complete solution. Solve for the roots using algebraic method. 16x+ - 1

A: To Solve: The roots of 16x4-1 using algebraic method.

Q: 13.) Determine the matrix: s P 6-8 3 ។ -3 the dimension X 10

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Q: Determine the moment of inertia of the cross-sectional area of the reinforced channel about the…

A: We have to find the moment of inertia of cross sectional area about x -axis  We find first Ix1…

Q: continuous at every number in its domain. State the domain. g(x) = 3r 1 22 + 2x - 15 b), Jse the…

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Q: Ordinary Differential Equations T′= t − t^2 + 1, t 0 = 0.5 Use the 4th order Runge-Kutta method for…

A: Given IVP is y'=y-t2+1, y(0)=0.5 and step size h=0.2 We have f(t,y)=y-t2+1 By forth order R-K method…

Q: 12. The trigonometric identities applicable to evaluate [sin'0 cose de 1. cos² 0 = (1+ cos20) III.…

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Q: Find f(0) and then find the equation of the given linear function. f(0) = f(x) = X f(x) 1 2 3 4 69…

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Q: O Let A = [a] (i) aij ≥ 0, Mnxn with the following properties. (ii) a₁ + a2 +...+ain = 1 for 1 ≤i,…

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Q: Let A = {H, T}, B = {1, 2, 3, 4, 5, 6}, and C = n(A x A x A) {red}. Find the number indicated.

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Q: n investment (in dollars). (I per year and is worth $50,

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