Advance Math question and answers for July 22, 2023
- Q Use the Euler method to solve the following differentialequation for the domain [2,2.5]. Use the step-size ℎ = 0.1.?′=?ln?/? ;?(2)=?1b) Use the third order Taylor series method to find ?(0.1)...
- Q a building supply store prices all products to give aone third (33.33%)margin.a.what rate of markup do they use?b.if the company had profits of$500,000 what was their cost ofgoods sold?c.if operating...
- Q In general, what do you need to show to prove the following?:(For example: to prove something is a group you'd show closure,associative, identity, and invertibility)a. Ringb. Subringc. Automorphism of ringsd....
- Q Let f be an irreducible polynomial of degree n over K,and let Σ be the splitting field for f over K. Show that[Σ : K] divides n!.
- Q A number is a Universal Product Code (UPC) if its last digitagrees with the following computations:• The sum of the odd position digits (not including the last) isM. That is...
- Q You are shipwrecked on a tropical island and you builtyourself a hut at the edge of the beach. At high tide the waterlineis 10feet from your hut. At low tide...
- Q (a) A bank’s safe has 5 dials each of which can be set to anumber from 0 to 36 (so each dial has 37 possible settings).i. How many different ways...
- Q Prove that if f, g are integrable, then the function (f(x) +cos(x)g(x))2is integrable.
- Q Find the general solution of the given differential equation,and use it to determine how solutions behave as t→∞.9y′+y=5t2
- Q Consider the differential equation:y'(x)+3xy+y^2=0.    y(1)=0.   h=0.1Solve the differential equation to determine y(1.3)using:a. Euler Methodb. Second order Taylor series methodc. Second order Runge Kutta methodd. Fourth order Runge-Kutta methode. Heun’s predictor corrector...
- Q From a shipment of 75 transistors, 5 of which are defective, asample of 6 transistors is selected at random.(a) In how many different ways can the sample be selected?(b) How...
- Q Calculate the Euler method approximation to the solution of theinitial value problem at the given x-values. Compare your resultsto the exact solution at these x-values.y' = y+y^2; y(1) = -1,...
- Q Determine the reasonable form of the particular solution foreach non homogeneous differential equation. Do not solve it.a) y''-y'-2y= e^-x+xcos2x+e^xsin2x.b) D^2[y] +4y =1+x^2+xsin2x.
- Q Let a and b be integers and consider (a) and (b) the ideals theygenerate. Describe the intersection of (a) and (b), the product of(a) and (b), the sum of (a)...
- Q Solve SVM for a data set with 3 data instances in 2 dimensions:(1,1,+), (-1,1,-),(0,-1,-). Here the first 2 number are the2-dimension coordinates. ‘ +’ in 3rd place is positive class....
- Q How many ways are there to choose three different numbers eachbetween one and ahundred so that their sum is even? Explain
- Q For p = 5 , find a number x such that x^2 is congurent to -1 modp. here x is denoted by sqrt(-1). Determine if sqrt(-1) exists modp for p...
- Q 2.31. Show that for each of the following values of a and b,there exists x, y in Z satisfying ax + by = 11. (i) a = 11, b =...
- Q Coding: Use MATLAB to figure out the following problem,if you do not know how to use MATLAB then please do not answer.Coding is required for the exercise.For f(x) = arctan(x),...
- Q Karon went to the post office and spent $31.57 on 84 stamps. Shebought 27¢ stamps for all the postcards, 42¢ stamps for each letteraddressed to friends in the U.S., and...
- Q [Note that, in thisexample, the mesh sizes in x and y are identical (h); strictlyspeaking, this need not be true. In some applications, we may needmore resolution along the x-...
- Q find missing sides, angles and area of spherical triangle. if youcannot indicate that it cant be done.general spherical triangle with a= 1, b = 1.5 and gamma =pi/6
- Q Show that the number of solution to x2 -y2 ≡ a (p) is p-1 if p not divides a and 2p -1if p divides a, Use u = x+y and...
- Q Example 10.5: Verify the divergence theorem for the vector ï¬eldF = 2xzi + yzj +z2k and V is the volume enclosed by the upperhemisphere x2 + y2 + z2 =...
- Q Show by induction that for all n natural numbers 0+1+4+9+16+...+n^2 = n(n+1)(2n+1)/6.
- Q Estimates of the number of cells in the human body vary overan order of magnitude. Indeed, the precise number varies from oneindividual to another and depends on whether you count...
- Q Show that if (x,y,z) is a primitive Pythagorean triple, then X andY cannot both be even and cannot both be odd. Hint: for the oddcase, assume that there exists a...
- Q A metropolitan area is facing a serious problem with disposingof its waste. Its current landfill is almost full and it is lookingfor other sites that can fulfill its likely future...
- Q In the study of population dynamics one of the most famousmodels for a growing but bounded population is the logisticequation dP/dt = P(a − bP), where a and b are...
- Q Use eulers Method with step size h=.01 to approximate thesolution to the initial value problem y'=2x-y^2, y(6)=0 at thepoints x=6.1, 6.2, 6.3, 6.4, 6.5
- Q Use the Laplace transform to solve the problem withinitial valuesy''+2y'-2y=0y(0)=2y'(0)=0
- Q A tank initially contains 150 gal of brine in which 20lb of saltare dissolved. A brine containing 3 ​lb/gal of salt runs into thetank at the rate of 4 gal/min.The...
- Q Let A =| 0.4 −0.3 || 0.4 1.2 |Analyze the long-term behavior of Ak , i.e., lim k→+∞ Ak .
- Q How can Singular Value Decomposition be used on imagecompression and its limitation?
- Q Show that {a + b√3 | a, b ∈ Q} is a field (a subfield of thefield R), but {a + b√3 | a, b ∈ Z} is not a...
- Q Prove that {f(x) ∈ F(R, R) : f(0) = 0} is a subspace of F(R, R).Explain why {f(x) : f(0) = 1} is not.
- Q 7.(Please, if you are not willing to answer the questioncompletely, please leave the question to someone who is!)a. At the time of his daughter's birth, a man deposited $ 1,000in...
- Q Each time draw 6 different numbers from 1 ~ 45 randomlyLet M denote the times you have to draw such that all the numberfrom 1~45 has been drawnWhat's the expected...
- Q Adirondack Savings Bank (ASB) has $1 million in new funds thatmust be allocated to home loans, personal loans, and automobileloans. The annual rates of return for the three types of...
- Q Let S be a non-empty set (finite or otherwise) and Σ the groupof permutations on S. Suppose ∼ is an equivalence relation on S.Prove (a) {Ï âˆˆ Σ : x...
- Q Nepal and Tibet can both produce butter [B] or tea [T].       If Nepal allocatesall resources to butter, it can produce a maximum of 500 units ayear. If all its       resources...
- Q A) Solve the initial value problem:8x−4y√(x^2+1) * dy/dx=0y(0)=−8y(x)=B)  Find the function y=y(x) (for x>0 ) whichsatisfies the separable differential equationdy/dx=(10+16x)/xy^2 ; x>0with the initial condition y(1)=2y=C) Find the solution to the...
- Q These questions are about math cryptography1) Encrypt the plaintext \"this is a secret message\" using theaffine functionf(x) = 5x + 7 mod 26.2) Determine the number of divisors of 2n,...
- Q You manage an ice cream factory that makes two flavors: CreamyVanilla and Continental Mocha. Into each quart of Creamy Vanilla go2 eggs and 3 cups of cream. Into each quart...
- Q The resistance of blood flowing through an artery isR = CLr4where L and r are the length and radius of theartery and C is a positive constant. Both L andr...
- Q You are the owner of a lawn service company (LawnCo) whichprovides grounds and maintenance services to a range of corporatecustomers. Customers are expected to pay on the first of eachmonth,...
- Q 2- Develop a simulink model for natural PWM inverter connectedto a dc source of 100 V and an output frequency of 60 Hz. The loadis a series RL load with...
- Q Assignment 7: Congressional Vote TrackingDatabaseDescriptionDesign an Extended E-R schema diagram for keeping track ofinformation about votes taken in the U.S. House of Representativesand Senate during the current two-year congressionalsession.  The database...
- Q Let G be a group with the binary operation of juxtaposition andidentity e. Let H be a subgroup of G.(a) (4 points) Prove that a binary relation on G defined...
- Q A restaurant has the following table of values for some of itsburrito sales during January from the previous 10 yearsYears200720092010201120132015Price10.50910.75111312.25Sales110165105987580a. Find a cubic model for the price demand functions. What...
- Q How important is the use of an appropriate system of symbols tothe development of a branch of mathematics?
- Q usethe method of undetermined coefficients to find one solution ofy'' + 3y' - 14y = 8exp(3t)y(t)=
- Q This question illustrates how bidding dishonestly can end uphurting the cheater. Four partners are dividing a million-dollarproperty using the lone-divider method. Using a map, Danny dividesthe property into four parcels...
- Q Solve the following optimization problem (Be sure to include thestatement of the optimization problem and a graph of the feasiblein your solution):Jamie has joined a building contest. A dog shape...
- Q For each of the following data sets, write a system of equationsto determine the coefficients of the natural cubic spline passingthrough the given points.x| 3 Â Â 4 6------------------y| 10 15...
- Q Given a second order ode m y’’  + c y’ + k y = 0with  m, c and k all positive.  (like amassâ€spring system with damping) Argue that the solution willalways be damped;...
- Q Solve the initial value problemy′=(2cos(2x))/(3+2y), y(0)=−1and determine where the solution attains its maximum value (for0≤x≤1.697).Enclose arguments of functions in parentheses. For example,sin(2x).Y(x)=?x=?
- Q M r. and Mrs. Fox have each contributed $1235.00 per year forthe last eight years intoRRSP accounts earning 4.3% compoundedannually. Suppose they leave theiraccumulated contributions foranother five years in the...
- Q Find ? as a function of ? if 81?″−90?′+29?=0, ?(3)=8,?′(3)=1y=?
- Q a. Let A be a square matrix with integer entries.Prove that if lambda is a rational eigenvalue of A then in factlambda is an integer.b. Prove that the characteristic polynomial...
- Q Let G = Z3 × Z6 × Z2.(a) What is the order of (2, 3, 1) in G?(b) Find all the possible orders of elements of G. Is the groupG...
- Q 3. Solve the following linear programming problem. You must usethe dual. First write down the dual maximization LP problem, solvethat, then state the solution to the original minimizationproblem.(a) Minimize w...
- Q 1. Consider the following second-order differential equation.d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into afirst-order system in terms of x and v, where...
- Q a. Assuming a low-informative prior probability distribution,find the posterior distribution of left-handed students in thepopulation. Summarize your results with an estimation of the mean,median, mode, and a 95% credible interval....
- Q 3. True or false? All vectors below are in Rn forsome n. If your answer is “Trueâ€, explain why. If your answer is“Falseâ€, give a counterexample. Please specify for all...
- Q Please explain in the most simple way possible what Bipolarcoordinates are and what each coordinate represent in them comparedto cartesian coordinates. A reference book would be great too.
- Q If I is an ideal of the ring R, show how to make the quotientring R/I into a left R-module, and also show how to make R/I into aright R-module.
- Q 1.critical analisys of the movie Donald in mathmatic land2what is the central idea of the movie Donald in mathmaticland?3.conclusion of the movie Donald in mathmatic land4.history of the pictogram
- Q Two sets are separated if the intersection of the closure of oneof the sets with the other is empty.a) Prove that two closed and disjoint sets of some metric spaceare...
- Q Using Kurosch's subgroup theorem for free proucts,prove thatevery finite subgroup of the free product of finite groups isisomorphic to a subgroup of some free factor.
- Q solve for x:[x * sqrt(1+x2)]+ ln[x +sqrt(1+x2)] = 25
- Q Question 2 Materials Requirements Planning An MRP exercise isbeing implemented over an 8-week period and the following relevantinformation is provided: One (1) unit of A is made of two (2)...
- Q For Exercises 1-4 below, (a) verify that y1 and y2 satisfy thegiven second-order equation, and (b) find the solution satisfyingthe given initial conditions (I.C.).2. y′′−3y′+2y=0; y1(x)=e^x,y2(x)=e^2x. I.C.y(0)=0,y′(0)=−1.3. y′′−2y′+y=0; y1(x)=e^x,y2(x)=xe^x. I.C.y(0)=1,y′(0)=3.
- Q What is the difference between multiplying a matrix times avector and multiplying two matrices?
- Q The post office uses a multiple channel queue (M/M/C), wherecustomers wait in a single line in front of two service providersfor the first available window. If the average service time...
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