Advance Math question and answers for August 18, 2023
- Q Show that the map Q[X] ? Q[X],sum^{n}{i=0}(a_nX^i) ? sum^{n}{i=0}(a_n(2X + 3)^i) , is anautomorphism of Q[X],
- Q Boise Lumber has decided to enter the lucrative prefabricatedhousing business. Initially, it plans to offer three models:standard, deluxe, and luxury. Each house is prefabricated andpartially assembled in the factory, and...
- Q A spring with a spring constant 4 N/m is loaded with a 2 kgmassand allowed to reach equilibrium. It is then displaced 1 meterdownward and released. Suppose the mass experiences...
- Q Let [x]B be the coordinate vector of a vector x ? Vwith respect to the basis B for V . Showthat x is nonzero if and only if [x]B is...
- Q Let D8 be the group of symmetries of the square.(a) Show that D8 can be generated by the rotation through 90?and any one of the four reflections.(b) Show that D8...
- Q 10. SHALL WE SCREAM?What mathematics is involved in the design of roller coasters?How does one make them safe but still scary?
- Q 4) Find the volume of the solid formed by the region bounded bythe graphs of y= x3 , y=x for x=0 and x=1-Sketch the region bounded by the graphs of...
- Q A binary string is a “word” in which each “letter” can only be 0or 1Prove that there are 2^n different binary strings of lengthn.Note:Your goal is to produce a properly...
- Q Solve the following using Polya’s four-step problem-solvingprocess. Use the strategy “Direct Reasoning” to solve the problem.Show all work and clearly describe your thought process.julia, william, kelly, and mary each entered...
- Q The commanding officer (CO) plans to move a part of hisbattalion toanother location. There are two types of vehicle available to him,a Fordvehicle that can carry 25 m3 plus 5...
- Q Consider the IVP t2y''?(t2 + 2)y' + (t +2)y = t3 with y(1) = 0 and y'(1) = 0.• One function in the fundamental set of solutions isy1(t) = t....
- Q 15. Let r be a positive real number. The equation for a circleof radius r whose center is the origin is (x^2)+(y^2)= r^2 .(a) Use implicit differentiation to determine dy/dx...
- Q A company manufactures Products A, B, andC. Each product is processed in three departments: I, II,and III. The total available labor-hours per week for DepartmentsI, II, and III are 900,...
- Q Determine the number of permutations of {1,2,3,...,n-1,n} wheren is any positive integer and no even integer is in its naturalposition.
- Q Define the following order on the set Z × Z: (a, b) < (c, d)if either a < c or a = c and b < d. This is referred...
- Q A certain college graduate borrows $8,937 to buy a car. Thelender charges interest at an annual rate of 16% . Assuming thatinterest is compounded continuously and that the borrower makespayments...
- Q Consider a 5x5 chessboard. Prove that no matter how the 25 cellsare colored in red and blue (each cell is either red or blue),there exist 4 cells of the same...
- Q Suppose that ? ? R n is bounded, and path-connected, and u ?C2 (?) ? C(??) satisfies ( ??u = 0 in ?, u = g on ??.Prove that if...
- Q An experiment is given together with an event. Find the(modeled) probability of each event, assuming that the coins aredistinguishable and fair, and that what is observed are the facesuppermost.Three coins...
- Q Solve by separation variables (2x-5y-2)dx+(5x-y-5)dy=0
- Q A researcher believes that female stray cats are more cautiouswhen approaching people than male cats. He knows that the stray catpopulation is 50% male and 50% female. In order to...
- Q 6. Let V be the vector space above. Consider the maps T : V ? VAnd S : V ? Vdefined by T(a1,a2,a3,...) = (a2,a3,a4,...) and S(a1,a2,a3,...)= (0,a1,a2,...).(a) [optional] Show...
- Q solve the differential equationa) ? ?? ? ? ? = 1 1 + ? ??b) ? ?? + 3? ? + 2? = cos(?x )c) 10) ? ?? ? 2?...
- Q Lamia's House of Software (LHS) wants to prepare a cash budgetfor months ofSeptember through Dêcember. Using the followinginformation,Sales were $50,000 in June and $60,000 in July. Sales havebeenforecasted to be...
- Q Boise Lumber has decided to enter the lucrative prefabricatedhousing business. Initially, it plans to offer three models:standard, deluxe, and luxury. Each house is prefabricated andpartially assembled in the factory, and...
- Q Undetermined Coefficients:a) y'' + y' - 2y = x^2b) y'' + 4y = e^3xc) y'' + y' - 2y = sin xd) y" - 4y = xe^x + cos 2xe)...
- Q Use the simplex method to solve the linear programmingproblem.MaximizeP = 3x + 2ysubject to3x+4y?33x+y?92x+y?13x ? 0, y ? 0 ?The maximum is P = at(x, y)
- Q Find y as a function of x if y????16y??+63y?=144ex, y(0)=16,y?(0)=11, y??(0)=15. y(x)=
- Q graph theoryhow many 4-regular graphs of order 7 are there? justify youranswer.
- Q A farmer owned a square field measuring exactly 2261 yards oneach side. 1898 yards from one corner and 1009 yards from anadjacent corner stood a beech tree. A neighbor offered...
- Q Supply proofs for the following miscellaneous propositions fromthe course in a metric space context:(1) A compact set (you may use either definition) is closed andbounded.(2) An epsilon-neighborhood is an open...
- Q The current population of Tanzania is 49.3 million with apopulation growth rate of 2.53% per year. The average annualagricultural yield in Tanzania is 8950 kg/ha (where "ha" meanshectare, which you...
- Q 1. For each permutation? of {1,2,··· ,6} write the permutationmatrix M(?) and compute the determinant |m(?)|, which equalssgn(?).(a) The permutation given by 1 ? 2, 2 ? 4, 3 ?...
- Q Please find f(x') and f(x") for all:1) f(x) = 3(x2 -2x)3/4(7 -5x2)62) f(x) = (y - x)4(y2 - x)33) f(x) = x7/3 + 16x3 + x4) = f(x) = (x2...
- Q Newton's Law of Cooling is based on the principle that the rateof change of temperature y'(t) of a body in an environment withambient temperature A is proportional to the difference...
- Q 2.) By Theorem 3.23 of the text, the linear diophantine equationof the form ax + by = c has no integral solutions if c is notdivisible by (a, b), the...
- Q Use the method of Undetermined Coefficients to find the solutionof the initial value value problem:y'' + 8y' + 20y = 9cos(2t) - 18e-4t, y(0) = 5. y'(0)= 0
- Q Solvex^3 -3x^2 +27 = 0(mod1125)
- Q show that the power set of N and R have the same cardinality
- Q letx:=7show that x is the least upper bound of [3,7]show that x is the least upper bound of (3,7)
- Q A mass-spring-dashpot system is described bymy?? + cy? + ky = Fo cos ?t,see §3.6 Eq. (17). This second-order differential equation has beenused in simulations, such as thisone at the...
- Q What is the general solution to xy''+y'+k^2xy=0
- Q Using the epsilon-delta definition proveLim of x^2 =4 when x approaches 2
- Q Problem 1: Consider the following Initial Value Problem (IVP)where ? is the dependent variable and ? is the independentvariable: ??=sin(?)?(1??) with ?(0)=?0 and ??0Note: the analytic solution for this IVP...
- Q in parts a and b use gaussian elimination to solve the system oflinear equations. show all algebraic steps.a. x1 + x2 + x3 = 2x1 - x3 = -22x2 +...
- Q Find y as a function of x ify''''?4y'''+4y''=?128e^{-2x}y(0)=2, y?(0)=9, y?(0)=?4, y?(0)=16.y(x)=?
- Q Find the order of each of the following elements.( 3 , 4 ) in Z 4 × Z 6 ;( 6 , 15 , 4 ) in Z 30 ×...
- Q a) Show that 6, 28, 496, 8128, and 33550336 are perfect numbers(recall, according to the note: n is said to be perfect if ?(n) =2n).b) Recall that prime numbers of...
- Q For the following functions, determine if they are injective,surjective, bijective, or none and explain the reason. Recall thatR: is the set of real numbers, Z: the set of Integers, and...
- Q An urn contains 8 white balls and 5 green balls. A ball is drawnat random, its color is noted, andreplaced together with 2 more of the same color. Then theselection...
- Q In this question, we are going to call a function, f : R ? R,type A, if ?x ? R, ?y ? R such that y ? x and |f(y)|...
- Q Research a mathematician of your choice and write an essay abouthim/her (atleast 2 pages long, double spaced) You are expected toresearch the topic and write a clear, well-organized essay. Themathematician...
- Q If G={e, a, b, c, ...}. The set Inn (G)={phi e, phi a,phi b, phi c, ...} is called the set of inner automorphisms. Provethat Inn(G) is a group under...
- Q Find the minimal generating set of G-- G = Z2 × Z3-- G = Z2 × Z2-- G = Z × Z
- Q BUSINESS TRAVEL EXPENSES An executive of Trident Communicationsrecently traveled to London, Paris, and Rome. She paid$280, $330, and $260 per night for lodging in London, Paris, andRome, respectively, and his hotel...
- Q Are the groups D2 × A3 and Z/6Z × S2 isomorphic?
- Q Consider the system of equations5x+5z=04ax-y+4az=0bx+10y+az=6cFind conditions on a, b, and c such that the systems has(a) no solutions(b) infinetly many solutions, and provide a formula forsolutions in this case(c) exactly...
- Q Find the solution ofy?+8y?=1024sin(8t)+640cos(8t)y(0)=4 and y'(0)=3y=?
- Q Recall the group Hom(G, A) (especially the group Hom(G, C ? )whose elements are called characters of G) and the group µn of n-throots of unity.(i) Let n be a...
- Q Q1: A new cream that advertises that it can reduce wrinkles andimprove skin was subject to a recent study. A sample of 56 womenover the age of 50 used the...
- Q Let X ? L(U, V ) and Y ? L(V, W). You may assume that V isfinite-dimensional.1)Prove that dim(range Y) ? min(dim V, dim W). Explain thecorresponding result for matrices...
- Q Let f be a continuous function on [a, b] which is differentiableon (a,b). Then f is non-decreasing on [a,b] if and only if f?(x) ?0 for all x ? (a,b),...
- Q 1. Let ??(F), ??(F) and ??(F) denote the spaces of strictlyupper triangular, diagonal,and strictly lower triangular ?×? matrices over F,respectively. Show that ??(F) = ??(F)???(F)???(F). Compute thedimensions of these spaces...
- Q Let??(?)=?(?0cos?)?,?12??2+(?0sin?)??r?(t)=?(v0cos??)t,?12gt2+(v0sin??)t?on the time interval [0,2?0sin??][0,2v0sin??g], where ?>0g>0;physically, this represents projectile motion with initial speed?0v0 and angle of elevation ?? (and ??9.81m/s2g?9.81m/s2).Find speed as a function of time ?t, and find...
- Q Exercise 4. Let P (n) be the statement that a postage of ncents can be formed using just 4-cent stamps and 7-centstamps.The parts of this exercise outline a strong induction...
- Q In Exercises 7–29 use variation of parameters to find aparticular solution, given the solutions y1, y2 of thecomplementary equation.1.) 4xy'' + 2y' + y = sin sqrt(x); y1 = cos...
- Q please explain the multiplication rule as it appliesto the Rules of Probability in at least 400 words
- Q A car rental agency in a major city has a total of 4500 carsthat it rents from three locations: Metropolis Airport, downtown,and the smaller City Airport. Some weekly rental and...
- Q 1. Consider the group Zp for a prime p with multiplicationmultiplication mod p). Show that (p ? 1)2 = 1 (mod p)2. Is the above true for any number (not...
- Q List ONLY positive relationships between two variables. (Pleaselist as many as possible, the more the better.)
- Q Consider an ecological niche with three species A, B and C.Their dynamics are given by their population rates shown belowdA/dt=A+B-C … (2a)dB/dt=-A+2B … (2b)dC/dt=C-A-B … (2c)Initially, the niche is in...
- Q Find the positive root of the equation x^3-×-11 usinginspection method.
- Q MATLAB questionThe range of a projectile launched at velocity V and angle qis R=2 V2 sin(q) cos(q)Find the range if V=20m/s and q=30 degrees (5 pts)If the uncertainty in the...
- Q 1. How many 12-bit strings (that is, bit strings of length 14)start with the sub-string 011?2. You break your piggy bank to discover lots of pennies andnickels.You start arranging them...
- Q Let sn = 21/n+ n sin(n?/2), n ? N.(a) List all subsequential limits of (sn).(b) Give a formula for nk such that (snk) is an unboundedincreasing subsequence of (sn).(c) Give...
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