Advance Math question and answers for August 20, 2023
- Q Find a basis of U = span {(1,1,2,3), (2,4,1,0), (1,5,-4,-9)}
- Q Given the vectors u1 = (2, ?1, 3) and u2 = (1, 2, 2) find athird vector u3 in R3 such that(a) {u1, u2, u3} spans R3(b) {u1, u2, u3}...
- Q Suppose a dog is chasing a rabbit along the y-axis, and thecoordinate of the rabbit's position at time t is given by (1/3) t^2+4t. The dog's speed is equal to...
- Q A farmer has 150 acres of land suitable for cultivating CropsA and B. The cost of cultivating Crop Ais $40/acre, and the cost of cultivating Crop B is$60/acre. The farmer...
- Q Polynomial and rational functions can be used to model a widevariety of phenomena of science, technology, and everyday life.Choose one of these sectors and give an example of a polynomialor...
- Q Let F be a field and let ? : F ? F be a ring isomorphism. DefineFix ? to be Fix ? = {a ? F | ?(a) = a}....
- Q Fill in the missing algebraic steps in the concreterenormalization calculation for period doubling.Let f(x) = -(1 +mu)x+x^2. Expand p+(n)subn+1 =f^2(p+(n)subnetting) in power of small deviations (n) subn usingthe fact that...
- Q 2. Define a relation R on pairs of real numbers as follows: (a,b)R(c, d) iff either a < c or both a = c and b ? d. Is R...
- Q You wish to retire in 18 years , at which time , you want tohave accumulated enough money to receive an annuity of $500 monthlyfor 20 years of retirement. During...
- Q Find the line y = b + mx of best fit through the data {(.1,.2),(.2, .3),(.3, .7),(.5, .2),(.75, .8)}, using the least squarescriterion.(Use one of the software tools: Excel, SPSS,...
- Q A mass of 1 kg is attached to a spring with constantk = 16 kg/ft.Initially at equilibrium, a periodic external force off(t) =cos(3t)begins to affect the mass fort > 0.Find...
- Q Define a sequence from R as follows. Fix r > 1. Let a1 = 1and define recursively, an+1 = (1/r) (an + r + 1). Show, byinduction, that (an) is...
- Q Please solve the following:ut=uxx, 0<x<1, t>0u(0,t)=0, u(1,t)=A, t>0u(x,0)=cosx, 0<x<1
- Q if s1 and s2 are two simple functions thenprove that the max and minimum of then are also simplefunction.
- Q Khadija Textile Mills produces two types of cottoncloth—Roughand Smooth. Smooth is a heavier grade of cotton cloth and, as such,requires 7.5 kg of raw cotton per meter, whereas Rough requires...
- Q Solve the given differential equation by undeterminedcoefficients. y'' ? 8y' + 20y = 200x2 ? 65xex
- Q 8. (20 pts)a. RSA encryption. Let n = pq = (7)(17) = 119 and e = 5 define a(very modest) RSA public key encryption. Since 25 < 119 <2525, we...
- Q TMA manufactures 37-in. high definition LCD televisions in twoseparate locations, Locations I and II. The output at Location I isat most 6000 televisions/month, whereas the output at Location IIis at...
- Q There are n people who can shake hands with one another (where n> 1). Use pigeonhole principle to show that there is always apair of people who will shake hands...
- Q Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1?y2), if 0?y1?y2?10, otherwise. a) Are Y1 and Y2 independent? Why? b) Find Cov(Y1,Y2). c) Find V(Y1?Y2). d) Find Var(Y1|Y2=y2).
- Q How does Willson, F. (2002). Shapes,Numbers, Patterns, And The Divine Proportion In God's Creation.explain that a Spirals in sunflowers demonstrates the divineproportion?Explain why Willson said…“The onlyrational conclusion is that the...
- Q Asmall grocery store has a single checkout line. On Saturdays,customers arrive at the checkout on an average of one every 8minutes. The cashier takes an average of 6 minutes to...
- Q Group theoryConsider the groupGL2(Zp)of invertible 2X2 matrices with entries in the field Zp, wherep is an odd prime.Zp is an abelian group under addition,the group of unites of Zp is...
- Q Let A and B be two non empty bounded subsets of R:1) Let A +B = { x+y/ x ? A and y ? B} show that sup(A+B)= sup A+...
- Q Consider a set of three standard six-sided dice (labelled withpips). What is the probability that the total number of pips shownon three dice thrown at the same time is 11?...
- Q . Determine whether K4 (the complete graph on 4 verticescontains the following: i) A walk that is not a trail. ii) A trailthat is not closed and is not a...
- Q Real Mathematical Analysis, Pugh, 5.29 : Prove Corollary18 thatrth-order di?erentiability implies symmetry ofDrf, r ? 3. Use induction to show that(Drf)p(v1,.....,vr) is symmetric with respect topermutations of v1,...,vr?1 and ofv2,...,vr....
- Q Two chemicals A and B are combined to form a chemical C. Therate of the reaction is proportional to the product of theinstantaneous amounts of A and B not converted...
- Q Let A ? R ^ (nxn) with autovalue ? associated with the vectorV_? ? R ^ (n), determine the shape of the eigenvalues andeigenvectors ofa) 8A + Ib) A^(2) +...
- Q What is a vector space? Provide an example of afinite-dimensional vectors space and an infinite- dimensionalvector space.
- Q Consider a vibrating system described by the initial valueproblem. (A computer algebra system is recommended.) u'' + 1/4u' +2u = 2 cos ?t, u(0) = 0, u'(0) = 6(a) Determine...
- Q Q1what is the definition of knapsack problem ?Q2 what is the main difference between salesman travellingproblem and stagecoach problem ?please give short answer
- Q Based upon market research, the Hawthorne Company has determinedthat consumers are willing to purchase 132 units of their portablemedia player each week when the price is set at $132.00 per...
- Q Co-planar test is an important step in continuous collisiondetection. Let p0= [0,0,0], p1= [1,0,1], p2= [0,1,1], p3= [1,1,0]be four points and v0= [0,0,0], v1= [1,0,0], v2= [0,1,0], v3=[0,1,1] be their...
- Q Name and sketch two ways in which an open method for rootfinding can fail to locate a root even when a root exists.
- Q In this problem we prove that the Strong Induction Principle andInduction Principle are essentially equiv-alent via Well-Ordering Principle.(a) Assume that (i) there is no positive integer less than 1, (ii)if...
- Q Find the general solution to the differential equation below.y?? ? 6y? + 9y = 24t?5e3Calculate the inverse Laplace transform of ((3s-2)e^(-5s))/(s^2+4s+53)Calculate the Laplace transform of y = cosh(at) using theintegral...
- Q Show that, in n-dimensional space, any n + 1 vectors arelinearly dependent.HINT: Given n+1 vectors, where each vector has n components,write out the equations that determine whether these vectors arelinearly...
- Q (a) Let a > 1 be an integer. Prove that any composite divisorof a ? 1 is a pseudoprime of base a.(b) Suppose, for some m, than n divides a^(m...
- Q Use Classic Runge-Kutta method with h = 1 to solve thesystem y” - y’ - 6y = 0, y(0) = 2, y’(0) = 3 on [0,1]
- Q Consider a square matrix A such that Ker(A2 ) = Ker(A3 ). IsKer(A3 ) = Ker(A4 ). Explain your reasoning.
- Q Find a general solution of the inhomogeneous equation y?? + 2y?+ 5y = f(x) forthe following cases: (i) f(x) = 1 (ii) f(x) = x2 (iii) f(x) = e?xsin2x (iv)...
- Q Let f be a continuous function on the closed interval [0,1] witha range also contained in [0,1]. Prove that f that there exists anx in [0,1] such that f(x)=x. Is...
- Q 1) Elipse. Calculate 5 pixels, if Rx= 4, Ry= 7, Xc= 0, Yc= 02) Circle line. Calculate 6 pixels, if R= 14, Xc= 1, Yc= -9I just need matematical solunations
- Q Let (X,d) be a metric space. The graph of f : X ? R is the set{(x, y) E X X Rly = f(x)}. If X is connected and f...
- Q Use laplace transform in solving the ff.:After cooking for 45 minutes, when a cake is removedfrom an oven its temperature is measured at 300°F. 3 minutes laterits temperature is 200°F....
- Q 9.2.6 Exercise. Let R = Z and let I be the ideal 12Z of R.(i) List explicitly all the ideals A of R with I ? A.(ii) Write out all...
- Q Find the solution of the following initial value problem.y''' + y'' + y' + y = e^-t + 4cost ; y(0)= 0, y'(0)= -1, y''(0)=0
- Q Every teacher at a high school is given a n-digit code, e.g.530...297 (n digits in total).(1) How many different codes are there?(2) How many codes read the same backward and...
- Q Use the Euclidean algorithm to find the GCD of 3 +9i and 7-i
- Q K-TAB, a slow-release potassium chloride tablet, contains 750 mgof potassium chloride [KCl; MW = 74.5] in a wax/polymer matrix. Howmany milliequivalents of potassium chloride (round to the nearestwhole number) are...
- Q Find the first four nonzero terms in a power series expansionabout x = 0 for a general solution to the given differentialequationw'' - 6x2 w' + w = 0
- Q Suppose you draw a card from a well- shuffled deck of 52 cards.Determine the following probabilities .a. drawing a 9b.drawing a 3 or kingc.drawing a spaded.drawing a black carde. DRAWING...
- Q Calculus w/ analytical geometry:please be concise- Fubini's Theorem: if a function iscontinuous on the domain R, then the tripleintegral can be evaluated in any order thatdescribes R.(a) Explain the significance...
- Q 3) We have notforgotten Halmos Pal. In class I asked you what’s wrong with this“proof” of Halmos’ that all horses are the same color? It’s time totell me what you...
- Q Solve the questionSuppose C and D are two matrices where CD is defineda) fill in the blank: Each column vector of CD is a linearcombination of ___________ and each column...
- Q u(t?c) =uc(t) ={0, 0?t<c,1, t?c.}USE Laplace Transform to solvey??+ 2y?+ 2y=?(t?5)e^tcost, y(0) = 1, y?(0) = 2, where?(t)is theDirac delta. Does the solution show aresonance?
- Q How do you solve this?Find the general solution of the given differential equationShow all stepsy''-5y'-6y=10tsin(3t)
- Q Prove that there is only one possible multiplication table forG if G has exactly 1, 2, or 3 elements. Analyze the possiblemultiplication tables for groups with exactly 4 elements, and...
- Q The Company manufactures paring knives and pocket knives. Eachparing knife requires 3? labor-hours, 7 units of? steel, and 4units of wood. Each pocket knife requires 6? labor-hours, 5 unitsof? steel,...
- Q Determine whether the given differential equation is exact. Ifit is exact, solve it.i) (x 3 + y 3 )dx + 3xy2 dy = 0, Ans. x 4 + 4y 3x...
- Q Find the solution of the given initial value problem:y???+y?=sec(t), y(0)=6, y?(0)=7, y??(0)=?3
- Q Introduction:Panoramio is an application that enables digital photographersto geo-locate, store and organize their photographs–and to viewthose photographs in Google Earth and Google Maps. This applicationwhere users can upload and geo-locate...
- Q Find the Dual of the following LPmax z = 4x1 ? x2 + 2x3x1 + x2 ? 52x1 + x2 ? 72x2 + x3 ? 6x1 + x3 = 4x1...
- Q Let G be a group and K ? G be a normal subgroup. Let H ? G be asubgroup of G such that K ? H Suppose that H is...
- Q 1. If you wanted to find the difference in Elementary Statisticsgrades between students who transferred to CSULB from a communitycollege and students who entered CSULB straight out of high school,what...
- Q 1. Let Q1=y(1.1), Q2=y(1.2), Q3=y(1.3) where y=y(x) solvesy???2y?+ 5y= 0, y(0) = 1, y?(0) = 2.2. Let Q1=y(1.1), Q2=y(1.2) , Q3=y(1.3) where y=y(x) solvesy???2y?+ 5y=e^x cos(2x) , y(0) = 1,...
- Q Hi. I have two questions about the linear algebra.1. Consider the following sets:(a) The set f all diagonal 3*3 matrices(b) The set of all vectors in R^4 whose entries sum...
- Q Find the constants a, b, and c such that the functionf(z)=ax^2-bxy+2y^2+i(x^2+cxy+dy^2) is entire?fleft(zight)=ax^2-bxy+2y^2+ileft(x^2+cxy+dy^2ight)
- Q please tell me how to write proofs for diophantineequation
- Q Write out the first 4 terms of y1 and y2:( x+2 ) y" - 3y' + 2xy = 0 ; x0 = 3
- Q The line k goes through the point Q(-3,5) and is perpendicularto the line g: x - 3y - 22 = 0. Where do the angle bisectors oflines g and k...
- Q NOL Carryback and Carryforward, Valuation Account versus NoValuation Account)(LO 3) Spamela Hamderson Inc. reports the following pretaxincome (loss) for both financial reporting purposes and taxpurposes. (Assume the carryback provision is...
- Q The management of Cal Supermarkets has determined that thequantity demanded per week of their 90% lean ground sirloin, x, andthe quantity demanded per week of their 80% ground beef, y...
- Q Formulate the situation as a system of inequalities. (Let xrepresent the number of goats the farmer can raise and y representthe number of llamas.) A rancher raises goats and llamas...
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