Advance Math question and answers for July 21, 2023
- Q 3.) You have a loan for $20,000 on which you are charged 6%compounded quarterly. What payment amount at the end of every sixmonths would reduce the loan to $15,000 after...
- Q Let X = R and A = {disjoint union of the intervals of the form(a, b], (−∞, b] and (a, + ∞)}. Prove that A is an algebra but not...
- Q Solve Laplace's equation inside a rectangle 0 ≤ x ≤ L, 0 ≤ y ≤H, with the following boundary conditions [Hint: Separatevariables. If there are two homogeneous boundary conditions in...
- Q (a) Find a linear transformation T : R2→R2 that (i) maps thex1-axis to itself, (ii) maps the x2-axis to itself, and (iii) mapsno other line through the origin to itself.For...
- Q Students at the Akademia Podlaka conducted anexperiment to determine whether the Belgium-minted Euro coin wasequally likely to land heads up or tails up. Coins were spun on asmooth surface, and...
- Q 1-f(x) =1/8(7x-2), x ≤ 3a-absolute maximum value b-absolute minimum valuec-local maximum value(s) d-local minimum value(s)2-Show that the equation x3 − 16x + c = 0has at most one root in...
- Q study of the effect of college student employment onacademic performance, the following summary statistics for GPA werereported for a sample of students who worked and for a sample ofstudents who...
- Q Solve IVP for y(x): dy/dx + (3/x)y = 8y^4, y(1) = 1
- Q The differential equation ay\" + by' + cy = f(t) hascharacteristic equation aλ2 + bλ + c = 0 whose roots are given ineach part below. The forcing function f(t)...
- Q This is one question about 14-bit stringsHow many 14-bit strings that have more 0’s than 1’s?How many 14-bit strings that have even number of 0’s?How many 14-bit strings that have...
- Q Discrete math : Show your work please.Consider a set X of 10 positive integers, none of which isgreater than 100. Show that it has two distinct subsets whoseelements have the...
- Q For all integers n > 2, show that the number of integerpartitions of n in which each part is greater than one is given byp(n)-p(n-1), where p(n) is the number...
- Q Consider an n×n square board, where n is a fixed even positiveinteger. The board is divided into n 2 unit squares. We say thattwo different squares on the board are...
- Q 4-Consider the following problem:max − 3x1 + 2x2 − x3 + x4s.t.2x1 − 3x2 − x3 + x4 ≤ 0− x1 + 2x2 + 2x3 − 3x4 ≤ 1− x1...
- Q Give the Laplace transform of the solution to y\"+2y'+3y=0y(0)=-5 y'(0)=4
- Q USE NEWTON'S METHOD TO APPROXIMATE THE SOLUTION TO  2COSX = 3X .  LET X0 =pi/6 .  ANSWERUP TO 3 DECIMAL PLACES.USING REGULA FALSI METHOD, SOLVE THE EQUATION x^3 - 4x + 1 =...
- Q 2. Firm I has variable cost VCi = yi^2/10 and fixed cost FCi =2000.(1) Find total cost Ci(yi), average cost ACi, marginal cost Mciand the firm supply function Si(p)(2) There...
- Q The SIT Drug company produced two types of liquid pain killer,N(normal) and S (super). Each bottle of N requires 2 units of drugA, 1 unit of drug B and 1...
- Q Which of the following sets are closed under addition?(i) The set of all vectors in R2 of theform (a, b) where b = a.(ii) The set of all 2 × 2 matrices that...
- Q Plot the Euler’s Method approximate solution on [0,1] for thedifferential equationy* = 1 + y^2 and initial condition (a) y0 = 0 (b) y0 = 1, alongwith the exact solution...
- Q prove that if you multiply 4 successive integers and take thesquare root of that + a number, the only number for whichroot(product + x) is a perfect square is 1.
- Q Hi, can you please verify with the basic code of a beginnerMATLAB user, and try explaining how to approach if possible. Thanksa lot! :)1. Answer the following questions regarding complex...
- Q A mass that weight 5lb stretches a spring 3in. The system isacted on by an external force 6sinâ¡(8sqrt2 t)lb. If the mass ispulled down 4in and then released, determine the...
- Q Let f(x) = sin(πx).• x0 = 1,x1 = 1.25, and x2 = 1.6 are given. Construct Newton’sDividedDifference polynomial of degree at most two.• x0 = 1,x1 = 1.25,x2 = 1.6...
- Q Select a product or service of interest, and develop asegmentation scheme chart with 16 segments for the market, thatinvolves at least 4 variables. Select and justify the choice of atarget...
- Q Construct a conformal equivalence between a “half-strip†S1 :={z : 0 < Im z < 1,Re z > 0} and a “full stripâ€S2 := {z : 0 < Im z...
- Q 7. Consider a two-step, serial, productionprocess with one resource at each step. The processing time at step1 is 10 minutes and the processing time at step 2 is 5 minutes.There...
- Q ntor the data of the variable, if the value of the original variableis the method there, I 24 January 1980 and 20 dst Student ID: Name:M. De Vna 1.1.60 people...
- Q Using the successor function prove distribution over addition.Do this in a detailed proof.
- Q Lydia saved $1,345,000 for retirement. The money is deposited inan account earning 3.2% compounded monthly. She is going towithdraw $5500 per month for living expenses. Create a tableshowing how much...
- Q Both parts.a) identify Fourier series for full wave rectified sine functionf(x) = | sin(x) |.b) f(t) = cos(t) but period of 6, so t = [-3,3] (L = 6) Find...
- Q Let f(x) = sin(x) for -pi < x < pi and be ZERO outsidethis intervala. Find the Fourier Transformation. Plot on Desmos.b. Find the Fourier Integral representation of f(x). Plot...
- Q 4. At age 35 you start saving for retirement. Your investmentplan pays 6% APR compounded monthly and you want to have $2,000,000when you retire at age 65.       a) How much...
- Q 2. Describe the image of the circle |z − 3| = 1 under the M̈obius transformation w = f(z) = (z − i)/(z − 4). Be sure toexplain why your...
- Q You are standing at a base of a Ferris Wheel which is 4 m aboveground while your friend is riding. The Ferris Wheel is 8m indiameter. Describe how the shape...
- Q Evaluate the surface integral  SF · dSfor the given vector field F and the orientedsurface S. In other words, find the flux ofF across S. For closed surfaces, use thepositive (outward)...
- Q Suppose A is an n × n matrix with the property that the equationAx = b has at least one solution for each b in R n . Explain whyeach...
- Q Use a triple integral to determine the volume of the solidbounded by paraboloid x2+y2=z and the plane z=4y. Round your answerto two decimal places.
- Q maclaurin series for x=.5, 1.5 radians f(x)= (tanx - sinx -2.75)to the third derivative
- Q Solve the initial value problem using systems of LinearDifferential Equations. Please try to use computer typingx’ – 4y = 3x + y’ = 2IVP: x(0) = 0, y(0) = 1
- Q The half-life of carbon-14 is 5730 years. Assume that the decayrate is proportional to the amount. Find the age of a sample inwhich 10% of C-14 originally present have decayed.Select...
- Q a) State Mellin’s inverse Laplace transform formula.b) State Cauchy’s residue theorem.iii. Use (a) and (b) to prove that the inverse Laplace transform ofF(s)=1/(s+a) is equal to f(t)= e^(-at),t>0
- Q True or False.1. If the set {v1,v2} is a basis of R^2, then the set {v1,v1+v2}is also a basis of R^2.2.If W be a vector space and V1,V2 are subspaces...
- Q Find the six nonisomorphic trees on 6 vertices, andfor each compute the number of distinct spanning trees in K6isomorphicto it.
- Q Howmany of the 6^4=1296 secret codes in the game of Mastermind (6colors, 4 positions) use:a.) 4 different colorsb.) 2 of one color and 2 of anotherc.) 2 of one color...
- Q If T : R 3 → R 3 is projection onto a line through the origin,describe geometrically the eigenvalues and eigenvectors of T.
- Q Let A = {a+b*sqrt14: a,b∈Z}. Prove that A ∩ Q = Z. Explain isset A countable?
- Q how does gender impact the workplace and the home for both menand women? (300-500 words)
- Q 2. For the curve y = 3x / x^2-1 determine each of the followingand use all of the information to draw its graphand notate the information on it.(a) Find the...
- Q Differential Equations22. Solve each of the following systems of equations.(c) (D-2)x=0; -3x+(D+2)y=0; -2y+(D-3)z=0I got x=c1e2t, y= 3/4C1e2t + C2e-2t by usingdiffieq method d/dx(ye2t) =3C1e2t....., but the right answer isx=4c1e2t, y=...
- Q What is an example of a vector space besides Rn?What are the three properties of a vector subspace?
- Q (e) When newspapers were printed by lithograph, the newsprinthad to run over three rollers, illustrated in the diagram below bythree circles. The centres A, B and C of the three...
- Q Please explain how to determine the bounds for the tripleintegral in order to solve the following:Find the volume of the solid B whereB={(x,y,z)|x2+y2≤z2≤3x2+3y2}is bounded by the hemispherex2+y2+z2=9 with z≥0 and...
- Q Find the solution to the linear system of differential equations{x′ = 8x+5y and  y' = −10x−7y } satisfying the initialconditions x(0)=3 and y(0)=−4y.
- Q Construct a generator matrix and a parity check matrix for aternary Hamming code Ham(2, 3).Assume a codeword x from for the ternary Hamming code Ham(2, 3)$was sent and the word...
- Q a. Consider d on R, the real line, to be d(x,y) =|x2 – y2|. Show that d is NOT a metric on R.  b.Consider d on R, the real line,...
- Q Let B = {u1,u2} whereu1 = 1 and u2 = 0   0 1andB' ={ v1 v2] wherev1= 2 v2= -31 4be bases for R2find1.the transition matrix from B′ to B2....
- Q Determine if the following sets are real vector spaces with theindicated operations.(a) The set V of all ordered pairs (x, y) of real numbers withthe addition defined by (x1, y1)...
- Q Q5a) A leading company in Delhi is planning to renthouses and open spaces.The houses are in three categories namely, having three bedrooms,two bed-rooms and single bedroom homes. A market survey...
- Q Let Un×n be an upper triangular matrix of rank n. If anyarithmetic operation takes 1µ second on a computing resource,compute the time taken to solve the system Ux = b,...
- Q Two dentists, Lydia Russell and Jerry Carlton, are planning toestablish practices in a newly developed community. Both haveallocated approximately the same total budget for advertising inthe local newspaper and for...
- Q 1. 17 years ago, I purchased 124 shares of a stock worth $12.67per share. There was a 3:1 split, a 3:1 split, and a 5:1 splitduring that time period. Today...
- Q Let T = (V,E) be a tree, and letr, r′ ∈ V be any two nodes.Prove that the height of the rooted tree (T, r) is at most twicethe height...
- Q Q2a) Consider a transformation T : R2×2 → R2×2such that T(M) = MT.This is infact a linear transformation. Based on this, justify ifthe followingstatements are true or not. (2)a) T...
- Q Ralph's Electronics purchased 75 sound bars from themanufacturer for $250 each less discounts of 25% and 12%. Theregular markup on the sound bar is 60% of the regular sellingprice, and...
- Q A hotel rental service needs to have clean towels for each dayof a three-day period. Some of the clean towels may be purchasednew and some may be dirty towels from...
- Q 1a) Theasymptotes for the graphs of tangent, cotangent, secant,and cosecant are difficult to remember, especially if there is achange in the period. Discuss how to find the asymptotes from theequation...
- Q An eccentric Computing Science Professor decides to hide theirhoard of NSERC funded money, 100 identical gold coins, in 20 uniquelocations hidden across campus. It is assumed that multiple coinsor even...
- Q Find the best quadratic approximation to f(x,y) =e5ycos(-4x)about the origin (0,0) and estimate the value when thisapproximation is used to calculate f(0.1,0.1).Donot do the error approximation. Also, find the extremevalues...
- Q 1.Identify the open intervals on which the function isincreasing or decreasing. (Enter your answers using intervalnotation.) f(x) = sin(x) + 5 0 < x < 2Ï€ increasingdecreasing2. Identify the open...
- Q What are the connected components and the path components of theproduct space R x Rl where R has the standard topologyand Rl has the lower limit topology?
- Q 1) Suppose that a function f(x) is defined forall real values of x, except x =xo. Can anything be said about lim x → x 0 f (x ) ?Give...
- Q 1. Use a Laplace transform to solve the initial value problem:9y\" + y = f(t), y(0) = 1, y'(0) = 22. Use a Laplace transform to solve the initial value...
- Q a loan of 17000 is to be repaid by 4 equal paymentsdue in 2,5,6and 9 years respectively. determine the size of theequal payments if the loan was granted at 12%...
- Q Let x,y ∈ R3 such that x =(x1,x2,x3) and y =(y1,y2,y3) determine if<x,y>=x1y1+2x2y2+3x3y3  is an inner product
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