Advance Math question and answers for August 05, 2023
- Q Show that a set is convex if and only if its intersection withany line is convex. Show that a set is affine if and only if itsintersection with any line...
- Q Jack has two children. What is the probability that both areboys. In addition, what is the probability the oldest is a boy, atleast one is a boy, at least oen...
- Q Show that (0, 1) and (?1, 1) have the same cardinality.
- Q If a set K that is a subset of the real numbers is closed andbounded, then it is compact.
- Q Factor the following polynomials as a product of irreducible inthe given polynomial ring.A. p(x)=2x^2+3x-2 in Q[x]B. p(x)=x^4-9 in Q[x]C. p(x)=x^4-9in R[x]D. p(x)=x^4-9in C[x]E. f(x)=x^2+x+1 in R[x]F. f(x)=x^2+x+1in C[x]
- Q If an undamped spring-mass system with a mass that weighs 6 lband a spring constant 9 lb/in is suddenly set in motion at t=0 byan external force of 99cos(20t) lb,...
- Q Suppose I is an interval in R. Prove from the definition ofouter Lebesgue measure that m^? (I) = I.
- Q 1) What permutation group is pentagon D5 a subgroup of ?why?2) What is a generating set of pentagon D5? Why? Is it a minimalgenerating set?Why or why not?3) What is...
- Q Write a procedure that implements the Fermat factorizationmethod done in Mathematica.
- Q Let V be a vector space of dimension 1 over a field k and choosea fixed nonzero element voe V, which is therefore a basis. Let W beany vector space...
- Q (a) Give an example of a collection of closed sets whose unionis not closed.(b) Give an example of a collection of open sets whose infiniteintersection is not open.Thank you!
- Q Explain the process of using Laplace transforms for solving adifference equation with an initial condition. You may illustratewith an example, but you don’t have to solve the whole thingout.
- Q Find all the subgroups of the group of symmetries of a cube.Show all steps.Hint: Label the diagonals as 1, 2, 3, and 4 then consider therotations to get the subgroups.
- Q For each pair a, b with a ? R ? {0} and b ? R, define a functionfa,b : R ? R by fa,b(x) = ax + b for each...
- Q Find the solution of the following differential equations(x(x-1))dy-(xy+2x3-x2-2y)dx=0
- Q A soccer ball has 32 faces, each of which is a regular pentagonor hexagon. Because of the angles involved, exactly three facesmeet at each corner. Without looking at the ball,...
- Q Recall that the set {0,1}? is the set of all finite-lengthbinary strings. Let f:{0,1}??{0,1}? to be f(x1x2…xk)=x2x3…xkx1.That is, f takes the first bit of a string x and moves it...
- Q 1.Prove the following statements:.(a) If bn is recursively defined by bn =bn?1+3 for all integersn?1 and b0 =2,then bn =3n+2 for all n?0..(b) If cn is recursively defined by cn...
- Q if L1(x) = x is a solution to the ODE:(1-x)L'' - 2xL' +2L = 0a.) Show that L1(x) = x is a solution to the ODE2.) Use reduction of order...
- Q Prove that all parallel lines have the same vanishing point.
- Q Find the local maximum and minimum values and saddle point(s) ofthe function. If you have three-dimensional graphing software,graph the function with a domain and viewpoint that reveal all theimportant aspects...
- Q Use induction to proveLet f(x) be a polynomial of degree n in Pn(R). Prove that forany g(x)?Pn(R) there exist scalars c0, c1, ...., cn such thatg(x)=c0f(x)+c1f?(x)+c2f??(x)+?+cnf(n)(x), where f(n)(x)denotes thenth derivative...
- Q Solve y''-y=e^t(2cos(t)-sin(t)) with initial conditiony(0)=y'(0)=0
- Q Solve the initial value problem Utt = c^2Uxx,u(0,x)= e^-x^2 , Ut(0,x) = sin x(PDE)
- Q Two people are on a city block. Person A is on the northeastcorner and Person B is on the southwest corner. Person A startswalking towards the southeast corner at a...
- Q Solve the ODEy"+3y'+2y=(cosx)+(x^2)+(e^-1)
- Q Suppose u(t,x)solves the initial value problem Utt = 4Uxx +sin(wt) cos(x),u(0,x)= 0 , Ut(0,x) = 0. Is h(t) = u(t,0) a periodicfunction?(PDE)
- Q The Janie Gioffre Drapery Company makes three types of draperiesat two different locations. At location I, it can make 10 pairs ofdeluxe drapes, 20 pairs of better drapes, and 13...
- Q construct a subgroup Lattice of Z 36 & 60
- Q Show that the integral ( over a volume) of the curl of thevector A is equal to the integral over a closedsurface (containing the volume) of A x da
- Q Let x ? Rn be any nonzero vector. Let W ?Rnxnconsist of all matrices A such that Ax = 0. Show that W is asubspace and find its dimension.
- Q Find the particular integral of the following differentialequations.(Explain each step clearly)(a) d2y/dx2 + y = (x + 1) sin x. show thatthe answer is yp(x) = ? 1/8 [ (2x2...
- Q 2. (a.) Consider [3]12 in Z12. Is[3]12 a zero divisor of Z12 and does[3] have a multiplicative inverse in Z12?Justify your answer.(b.) Prove that [3]10 has a multiplicative inverse inZ10...
- Q How many permutations of the letters ABCDEFGHIJKLM do notcontain the strings “BAD” or “DIG” or “CLAM” consecutively? (Hint:Inclusion-exclusion and subtraction).**I KNOW THE ANSWER IS NOT 13! - 11! - 11!...
- Q 1)a. Which of the following sets are the emptyset?i. { x | x is a real number and x2 – 1 = 0 }ii. { x | x is a...
- Q Consider the subgroup of S(4) and the group of symmetries of therectangle discussed after Theorem 5.3.1. There we defined oneisomorphism between these groups but this is not the only one....
- Q A zip code is a string of five digits (0,1,2,3,4,5,6,7,8,9). Howmany zip codes are there subject to the followingrestrictions?(1) Only even digits are allowed.(2) The first digital is even and...
- Q Give a real-world example of the inclusion/exclusion principlethat involves at least two finite sets. Specify values for three ofthe following four values, the size of the first set, the set...
- Q Prove that isomorphism is an equivalent relation on the set ofall groups.
- Q A least squares adjustment is computedtwice on a data set. When the data is minimally constrained with 20degrees of freedom, a reference variance of 0.69 is obtained. Inthe second run,...
- Q A power shovel with a dipper of two cubic yard capacity has astandard operating cycle time of 80 seconds. The excavated materialwhich has a swell factor of 05 will be...
- Q Solve the following problem using the simplex method. If theproblem is two dimensional, graph the feasible region, and outlinethe progress of the algorithm.Max Z = 5X1 + 3X2 +2X3Subject to 4X1...
- Q Give Examples (this is complex analysis):(a.) First characterize open and closed sets in terms of theirboundary points. Then give two examples of sets satisfying thegiven condition: one set that is...
- Q Let X be a set with infinite cardinality. Define Tx ={U ? X : U = Ø or X U is finite}. Prove that Tx is atopology on X. (Tx...
- Q How many elements of order 2 are there in S5 and in S6? How manyelements of order 2 are there in Sn? (abstract algebra)
- Q Use Euclid’s algorithm to find integers x, y and d for which3936 x + 1293 y = d is the smallest possible positive integer.Using your answers to this as your...
- Q Describe the inverse properties of real numbers andprovide examples. What is useful about the inverse properties ofreal numbers?Start with definitions for identity elements and then defineadditive and multiplicative inverses. Discuss...
- Q Solve the following problems using the concepts and notation ofset theory and vector spaces:What is a Cartesian vector?What is a real vector space?Does the rational numbers fulfill the definition of...
- Q 1. I am trying to determine the level of measurement of my datatype?I am looking for advice on Nominal, Ordinal, Interval, andRatio2. Does the data set have any categorical variables?I...
- Q If R is a division ring, show that cent R forms a field.
- Q Find the general power series solution for the differentialequation2x^2y''-xy'+(x^2 +1) y =0 about x=0(Answer should be given to the x^4+r term)
- Q A tank initially contains 10 liters of clean water (with no saltin it). Every minute, a solution containing one liter of water andone gram of salt is added to the...
- Q Prove or disprove: In a hyperbolic geometry, if any righttriangle has its hypoteneuse and one leg congruent (respectively)to the hypoteneuse and one leg of another right triangle, then thetwo right...
- Q Find and solve a recurrence relation for the number of ways to stack n pokerchips using red, white and blue chips such that no two red chips are together.Use your...
- Q for unit quaternions used to represent rotations for 3D provethat :a) quaternion conjugate corresponds to rotation inverse (Approach 1: negate the angle in the formula for converting from theaxis-angle form...
- Q Find a basis for the subspace of R4 spanned by (1,0,-2,1),(2,-1,2,1), (1,1,1,1), (0,1,0,1), (0,1,1,0) containing the firstand fifth vectors
- Q Prove Proposition 6.10 (Let f : X ? Y and g : Y ? Z be oneto one and onto functions. Then g ? f : X ? Z is...
- Q Which of the following is not an assumption of the one-wayANOVA?A. Group means are equalB. Group variances are equalC. data between and within groups are independentD. Observations are normally distributed...
- Q Show that id D is dense metric space of X and if all cauchysequences Yn from a sense set D converge in D then X iscomplete.
- Q Show that if (1) F1 andF2 are connected sets, and (2)F1 ? F2 is not empty,then F1 ? F2 isconnected.alsoSuppose that F is connected. Show that F¯ (the closure of F)...
- Q police car is traveling south towards the intersection that arobber’s car has just crossed traveling east. The robber’s car iscurrently traveling 55 mph. The police car’s speed is currently 63mph....
- Q subject:engineering mathematicssolve [cos(x+y)-sin(x+y)]dx-sin(x+y)dy=0,is the ODE exact?Findan integrating factor and solve the ODE.
- Q A 25-year-old male presents to clinic complaining about eye painand itching in his eyes. Upon examination the ophthalmologist foundredness and some discharge of yellow pus. He looked into the retinato...
- Q Let G be a cyclic group generated by an element a.a) Prove that if an = e for some n ? Z, then G isfinite.b) Prove that if G is...
- Q Problem 3. Let F ? E be a field extension.(i) Suppose ? ? E is algebraic of odd degree over F. Prove thatF(?) = F(?^2 ). Hints: look at the...
- Q You have just started a new job that offers a retirement savingsaccount. You have two options: You can invest 5% of your monthlywages at 2% OR You can invest 4%...
- Q Prove If C is a binary self-dual code, show thatevery codeword has even weight. Furthermore, prove if each row ofthe generator matrix of C has weightdivisible by 4, then so does...
- Q B. Five bowls are labeled 1,2,3,4,5. Bowl i contains i white and5 ? i black ping pong balls, for i = 1,2,3,4,5. A bowl is randomlyselected, and 2 ping pong...
- Q B. Five bowls are labeled 1,2,3,4,5. Bowl i contains i white and5 ? i black ping pong balls, for i = 1,2,3,4,5. A bowl is randomlyselected, and 2 ping pong...
- Q Prove that the minimum distance of a linear code is the minimumweight of any nonzero codeword.
- Q Find either a linear or an exponential function that models thedata in the table.x?3?2?101y1286432168?f(x)=?(Use integers or fractions for any numbers in the?expression.)Note: Please show how to solve using TI-84 Plus...
- Q Determine if the column vectors [2,1,3,4]' [1,1,1,1]' and[5,3,7,9]' are linearly independent
- Q Answer the following:145 mod 20712 mod 17Determine whether the following pair of numbers are relativelyprime. If the answer is not, please give a reason.34, 1181, 15Determine the followingGCD(35, 10)GCD(100, 70)
- Q (DRUG DOSAGE PROBLEM) A drug company wantsto know how to calculate a suitable dose and time between doses tomaintain a safe but effective concentration of a drug in the blood.To be...
- Q Let G be a nonabelian group of order 253=23(11), let P<G be aSylow 23-subgroup and Q<G a Sylow 11-subgroup.a. What are the orders of P and Q. (Explain and include...
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
- Unlimited Question Access with detailed Answers
- Zin AI - 3 Million Words
- 10 Dall-E 3 Images
- 20 Plot Generations
- Conversation with Dialogue Memory
- No Ads, Ever!
- Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!