(a) A list a1, a2, a3, a4 of rational numbers is defined so that if one term is equal 41 then 29 to r, then the next term is equal to 1+ 1+r For example, if az = 99 41 what is the value of a1? 1 If as 70 a4 =1+: 1+ (41/29) (b) A hollow cylindrical tube has a radius of 10 mm and a height of 100 mm. The tube sits flat on one of its circular faces on a horizontal table. The tube is filled with water to a depth of h mm. A solid cylindrical rod has a radius of 2.5 mm and a height of 150 mm. The rod is inserted into the tube so that one of its circular faces sits flat on the bottom of the tube. The height of the water in the tube is now 64 mm. Determine the value of h. 5.

Q: Suppose we have two n x n matrices and we plan to multiply them together. If we wish to remain…

A: For the solution follow the next step.

Q: Esther works at a clothing store which marks up its retail clothing by 40%. The store purchases…

A: Given, The store purchases pants for Php 500 The store purchases jackets for Php 400 The store…

Q: In Sl units, the position x of a spring-loaded electromagnetic valve varies over time t in the…

A:

Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

A:

Q: Find the number of zeros of f(z) = z' + iz – z + 2i in the upper half-plane.

A:

Q: Look into the polynomial p(x) It is known from the polynomial that p(-3)=-1 and p(0)=3 Based on this…

A:

Q: Evaluate the following limit using Taylor series. lim 3x X00 (.... Rewrite the given limit using a…

A: We will use taylor series of ex ex=1+x1!+x22!+x33!+......∞

Q: 4n +1 5.

A:

Q: This problem is related to core exercise 31 (module 5) in the textbook, and reguires you to do some…

A:

Q: For certain decisions, the time it takes to respond is a logarithmic function of the number of…

A: (b) The relation between number of choices N and the reaction time R in seconds is given as follows:…

Q: Find a root of an equation f(x) = 2x3 - 2x - 5 using Newton Raphson method %3D

A:

Q: MacQuarie Island is a small island about half-way between Antarctica and New Zealand. Between 2000…

A: We have given dRdt = kR The general solution for the given differential equation is R(t) = R0ekt

Q: Follow the solution procedure as seen in the image. Incorrect answers or not following the solutions…

A:

Q: 10 s(2-(z2 + 5)") dz =? 12z(z + 5)° +c (=+5) +c (22+5)

A:

Q: Jamal is creating a 5 digit passcode using the digits 0 through 9. How many 5 digit passcodes are…

A: Fundamental counting principle: If there are m ways to do a job and n ways to do an other job, the…

Q: Consider the linear DE system æ' = Aæ with -14 -90 and A = 2 14 If the initial conditions are given…

A: To find the solution for the below linear differential equation system. x'=−14−90214x,  x0=02

Q: Consider the two matrices: 2 4 1 -5 A = B = 2 Compute A + 3 B. The result is equal to: Select one:…

A:

Q: H-solve log , (log, (log x)) = 1

A: Given: log3log2logx=1 Concept: logax=logbxlogba

Q: Question 6. Given a group (G, *) and a nonempty set S. Let GS denote the set of all mappings from…

A:

Q: Q3) By using Graphical Method. Find the optimum solution of X1 and X2 that the maximize Z=X1 + X2…

A:

Q: Identifying The Characteristics of Exponential Functions Complete the table below for each…

A:

Q: (Prove that): く 107 112 :117 •122 (i) i (ii) i" +i" +i n + 1 n +2 n +3 = 0, %3D ne N .10 (iii) 1+i…

A: complex

Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

A:

Q: ne of the angles is 69 degrees and the hypoteneuse is 5m long to the nearest centimeter how long are…

A: Introduction: The trigonometric identity for the right-angle triangle with sides a, b, and c is…

Q: 1. Consider the initial value problem, 2y 3y2 13 1<t<2, (la) y(1) = 1. (1b) The exact solution to…

A: Note:- Due to time limit, i'm able to solve the problem for step size h=0.02. for the remaining part…

Q: Consider the system of linear differential equations: y' = 1 2 a. Which of the following is the…

A:

Q: Prove 1 +,+ i++ = 2 – for all positive integers n. |

A: We want to prove 1 + 12 + 14 + ... + 12n = 2 - 12n

Q: Find (do not do the Newton's iteration) the con- vergence order and the rate of the Newton's method…

A: See answer below.

Q: A set S of vertices is an independent set if there are no edges between any two vertices in S (e.g.,…

A: The statement is not true.

Q: Example 1.3.1 Check lim inf[0, n/(n +1)) = lim sup[0, n/(n +1)) = [0, 1). n-00 We can now give an…

A:

Q: S (z+1) (r+2)) dz =? 를 + 흘고 + c wherecis an unknown constant. (플+피) (를 + 2x) +c where cis an unknown…

A:

Q: Given: f(n) = 3n^3 + n^2 + 2 What is the O(n) of f(n) What are two constants c and k that prove…

A: The complete solution is in given below.

Q: Let S = {(x, y) : x and y rational numbers}. a. What is the interior of S? Justify your answer by…

A:

Q: If p = (u, v, w), show that Ipl < lul + |미 + |wl а. b. Ju| < \pl, ]v] < \pl, ]w] < \pl.

A:

Q: [17] For each of the following equations, • find general solutions; • solve the initial value…

A:

Q: Three cards are chosen without replacement from a deck of 52 cards and placed in order from first to…

A: In the deck of 52 cards, there are total 4 6's. (One for each of hearts, diamonds, spades and clubs)…

Q: ndwritten please Rew

A: Introduction: A Boundary price drawback may be a system of normal differential equations with…

Q: Question 3. measured at 140°C. 3 minutes later its temperature is 70° C. When a cake is removed from…

A:

Q: How can you relate the topic derivative in your life day to day as a student? Pleasee helpp me this…

A:

Q: PAPER 1 5. FACTORS OF POLYNOMIALS page 5 J2006 1 The cubic polynomial f(x) is such that the…

A:

Q: Solve 少, dx dy -logx

A: The given differential equation in the Bernoulli form,

Q: Find all proper nontrivial subgroups of Z, x Z, x Z. Find all subgroups of Z; x Z4 of order 4.

A:

Q: 8. Let f: R-→R be a field homomorphism. Show that f is identity.

A: Introduction: Like integral domain, a field also have homomorphism. A map f:F→K is referred to as…

Q: A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant…

A:

Q: For az _and _and_ _and_ X= y = z = = z' For a = Or there are no solutions. For a = Or . X= y = z =…

A:

Q: TABLE 18.1 Data to be fit with spline functions. i X; fi 1 3.0 2.5 4.5 1.0 3 7.0 2.5 9.0 0.5

A: Assuming first two points (3.0,2.5) and (4.5,1.0) has been joined by a straight line.

Q: 3n3 {an} = {n2+1 In²+1.

A:

Q: 8. Use Newton's method to approximate the positive solution of sin r = 0.8x correct to five decimal…

A: Given, Sinx=0.8x →Sinx-0.8x=0. ie., f(x)=Sinx-0.8x So,f'(x)=Cosx-0.8 Let initial solution x0=1 We…

Q: 1. Solve the following ODE by the method of variation parameters 4y" – y = 1. (Other methods are not…

A:

Q: The height, h(t), of a baseball, in meters, t seconds after it is tossed out the window can be…

A: Given that, the functions are ht=-4.9t2+7t+15 and gt=4t+1.5. Find the point of intersection of the…