(a) Describe the terms Whole Life Annuity and Present Value of money in actuarial calculations. (b) Ms Smith plans to take out a loan of £15000 from her bank which is to be paid back over 3 years in 36 equal monthly payments. The monthly payments are to be paid at the end of each month throughout the specified loan period and the interest is charged monthly at a rate of 9% per annum. Calculate the amount of the monthly payment for Ms Smith's bank loan. Show all your working.

Q: solve the differential equation x²y" - 3xy' + 3y = 2×4 ex

A:

Q: 1. Derive a forward finite difference approximation of f" in the following form: a3f3+ a2f2+ a1f1 +…

A: The final answer is:The forward finite difference approximation of f′′(x) is:…

Q: The question involves finding the inverse Fourier Transform of the following functions:

A: see the attachment given below for details.Explanation:

Q: Please answer question B

A: The ratios |f''(x) / f'(x)| provide insight into how rapidly the function's slope is changing…

Q: 6 10 2 1.0 A = 10-2 10 -2 10 20 -0.5 2 10 6 0.1

A: A number  is said to be an eigenvalue of the matrix A if we can write  for somenon-zero vector x and…

Q: 3. Solve the following differential equation: +32 + 2x = t where x(0) = 1, (0) = 0. (For the…

A:

Q: Suppose T = L(V) and U CV is a subspace which is invariant under T. Prove that U is invariant under…

A: The answer for the given question has been solve step by step below please find the attachments…

Q: Question 1: (a) Consider the n-point Newton-Cotes quadrature rule n [^ f(x)dx ~ Σ wif(xi). i=1 (1)…

A: The solutions have been attached below.Explanation:Approach to solving the question: Detailed…

Q: Monique works as a librarian and earns $1,300 on a bi-monthly basis. What is her average monthly…

A: The objective of this question is to calculate Monique's average monthly income based on her…

Q: Find the transformation matrix for the following figure: B'(-5,3) A(-5,0) C(-3,0) B(-5,-3) A(-3,-3)

A: Given the triangle A(−3,−3),B(−5,−3),C(−3,−6).We need to find the transformation matrix so that we…

Q: use the method of undetermined coefficient to erational equation [1² + 3D + 2] y = 10€² 3t

A:

Q: 10 Exercise 3.- Calculate the mean value of the function f(x) = |2|on the interval [3,10] and…

A: Mean Value Theorem for Integrals: If is continuous on the closed interval and differentiable on…

Q: Can you check if I have done it correctly.

A: This is not correct.Explanation:No need to expand 2/z² and 3/z in Laurent series expansion. Also…

Q: Ind a recursive relation satisfied by sn n-1 + 3n-14-1, for n Є N. 3n−1 + Hint: Reverse engineer the…

A: If a recursive relation has auxiliary roots  then the general solution is

Q: ssume f: RR is strictly increasing. et g: R→ R be defined by g(x) = ff. Which, if any, of the…

A: Assume f:R⇒R is strictly increasing .Let  g:R⇒R be defined by g(x)=∫0xf.Lets check each options one…

Q: Use the Laplace transform to solve the given initial value problem. For technical reasons, write uc…

A:

Q: Consider the following bases for R4 23 = and let = (a) P→E and D = 320 0032 (1, 2, 3, 4) be the…

A: Dear Student,     As per our guidelines we can answer only first three subqustions. So kindly…

Q: In the initial value problem, use the Runge-Kutta method with step sizes h = 0.2, 0.1, 0.05, and…

A: Given in the interval [0,2].The Runge-kutta method is given by where,

Q: Prove Prop 11.4: If a and n are positive integers such that a | n, then a ≤ n.

A:

Q: Using the first method of Algebraic and Transcendental Equation (Fixed point iteration) solve the…

A: The objective of the question is to find the real root of the equation x * log10(x) - 1.2 = 0 using…

Q: Laplace equation Uxx + Uyy = 0 in polar coordinates U(1, Theta) = f(Theta) for a disk where the…

A: Laplace's equation in R2 in terms of the usual (i.e., Cartesian) (x, y) coordinate system is:…

Q: (a) Determine if the transformation defined by each of the following standard matrices is injective…

A: 1) NOT INJECTIVE/SURJECTIVE2)BIJECTIVE 3) NOT INJECTIVE/ SURJECTIVE4) SURJECTIVE Explanation:Step 1:…

Q: Can you please use this data to determine the power at a wind speed of 14 m/s using linear spline…

A: The power at a wind speed of 14 m/s is 535 W.Explanation:To perform linear spline interpolation, we…

Q: Use the substitution z = e to turn t'a eciation below into a linear equation in z: dy =…

A: Given differential equation .We have to linearizing the differential equation using

Q: Match each formula for A with the correct name. Match each variable with its description. 1. A =…

A: Formula: A = P(1 + rt)Name: Simple Interest FormulaVariables:A: Total amount accumulated after…

Q: Draw the null-clines and determine equilibrium of d +x(t) = x² - y d y(t) = x(y-2x). Use these…

A: Consider the given system of differential equation.We need to use the null-clines to sketch the…

Q: x(t) = x1(t) X2 2(t) Find the general solution of x' 2 = 23 13 ☑

A:

Q: Problem 5. Let V and W be two vector spaces. A = {a1, a2, a3} is a set of basis for V and B = {b1,…

A: Given that

Q: - Let S be a subset of a vector space V over a field F, then a) if S is linearly independent then S…

A: Given that S is a subset of vector spcae V over field F. Note: Since you have posted more than one…

Q: Find the area under the curve

A: To find area under the curve defined by the points (20,85), (15,83), (9,80) & (7,78)We can use…

Q: Following an exponential distribution, the average lifespan of a smartphone battery is 2.3 years.…

A: Following an exponential distribution, the average lifespan of a smartphone battery is 2.3 years.…

Q: (xsinx+2y)dx+xdy= 0

A: The given differential equation is

Q: Individuals with multiple sclerosis were classified according to the presence or absence of brain…

A: The objective of this question is to find the probability that either the person experienced Early…

Q: Solve by using the sinking fund or amortization formula. (Round your answer to the nearest cent.)…

A: Sinking Fund Payment CalculationTo solve for the sinking fund payment given the conditions, we can…

Q: PLS HELP ASAP ON ALL GIVEN QUESTIONS PLS

A: Equation of f(−x)=−3x+1.Explanation:Approach to solving the question:  Detailed explanation:

Q: Let (f : [0, infinity) -> R be an arbitrary continuous function, which is differentiable on…

A: Given that  is continuous on  and differentiable on , we can assume that .To show that  for all ,…

Q: 2. Show that the complex conjugation function (as discussed in class) is a bijection.

A:

Q: Let A = {−7,−2,0,2,7,8,10}, and define an equivalence relation R on A as follows: (x,y) ∈ R if and…

A:

Q: Give an example (any representation is allowed) of a function from Z to Z that is a) one-to-one but…

A: (a). For one-to-one and not onto:      Suppose that be function defined from

Q: Show that: a) Every element of A belongs to some equivalence class. b) Two elements are equivalent…

A: Equivalence Relation:An equivalence relation on a set A is a binary relation that satisfies the…

Q: Show that (N,|) is a poset.

A: Let A be a set and a relation ≤ be defined on A. Then (A,≤) is called poset if it satisfies the…

Q: 1 The general solution of the equation = (1+ y²) cos x is y(x) = tan (C + sin x). With the initial…

A: The differential equation given as:Given that with the initial condition , there is a vertical…

Q: ii) xy' + 3y = 2x5, y(3) = 2

A: We have to solve the differential equation.

Q: Find the general solution of x' = Find the general solution of tx' 2 -1 4 -2-2 -2] = X 2 3

A: (1)Consider the system . Let  be its solution.We have eigenvalue λ=3 with algebraic multiplicity 2.

Q: Let a and ẞ belong to S. Prove that a 1B-1 aẞ is an even permutation.

A: Given,

Q: Let T: R3 R³ be given by [1 0 1 T(x) = 1 1 2 x 0 1 1 and (1, 2, 3) be the standard basis for R³. Let…

A: Given that, and  be the standard basis of .We know that .Then, and Therefore,

Q: (e) Which error is more serious?  Why?

A: Radon is a colorless, odorless, invisible gas that seeps into residential homes and has been linked…

Q: Stella's friends got her a skydiving lesson for her birthday. Her helicopter took off from the…

A:

Q: Please solve and show all work.

A: The answer is given below.Explanation:

Q: Show that the block graph of any connected graph is a tree

A: Since the block graph B(G) of any connected graph  G  is both connected and acyclic, it is a…