Advance Math question and answers for July 13, 2023
- Q Topology question:Show that a function f : ℠→ ℠is continuous in the ε − δdefinition of continuity if and only if, for every x ∈ ℠and everyopen...
- Q Permutations and combinations.a.)A typesetter has before him 26 trays, one for each letter ofthe alphabet. Each tray contains10 copies of the same letter. In how many ways can he form...
- Q DISCRETE MATHIf x has t elements and y has s elements, how many differentone to one and onto functions are there, and what are they? Showyour work
- Q Find the area of △ABC.Where:A=(3,2), B=(2,4), C=(0,2)Suppose that a×b=〈−1,1,−1〉〉and a⋅b=−4 Assume that θis the angle between aand b.Find:tanθ=θ=Find a nonzero vector orthogonal to botha=〈5,1,5〉, and b=〈2,−4,−1〉Find a nonzero vector orthogonal...
- Q IntegralLet f:[a,b]→R and g:[a,b]→R be two bounded functions.Suppose f≤g on [a,b]. Use the information to provethatL(f)≤L(g)andU(f)≤U(g).Information:g : [0, 1] —> R be defined by ifx=0, g(x)=1; if x=m/n (m and...
- Q **Please show all work and explain** VeryconfusedWe can express insertion sort as a recursive procedure asfollows. In order to sort A[1..n], we recursively sort A[1..n-1]and then insert A[n] into the...
- Q Hi. I wanted to know how to prove this:From the fact that the sum of two continuous functions iscontinuous, prove by induction that the sum of n continuousfunctions is continuous....
- Q (1) Research online an alternative form of measuring angles (forexample: radian or turn) and compare it with the degree measure. Inyour description include, if possible, its origin, applications,benefits or drawbacks.(2)...
- Q Check if each of the following ODEs is an exact. If it is not anexact ï¬nd an integrating factor to make it an exact. Then solveeach of the following ODEs.(e)...
- Q letf(x,y)=x^2y(2-x+y^2)-4x^2(1+x+y)^7+x^3y^2(1-3x-y)^8 find thecoefficient of x^5y^3
- Q green inc. produces A and B it wishes to maximize the profit fromthe two items.the linear program is given as below:Max 4A+2Bs.t 4A + B <_ 16 available in graphics...
- Q The Eiffel Tower is 325 metres tall. Assuming the earth isperfectly spherical, how far can a person with perfect eye-sightcan see from the top of the Eiffel Tower? Again, a...
- Q Graphing equations on a coordinate plane is a simple way tovisually represent the relationship between the input values (x) ofan equation and the output values (y). This visual representationallows us...
- Q Calculate the length of the curve r (t) = (3cost, 5t, 3sint) andcalculate what is indicated belowa) Unit tangent vector T=b) Main Normal Vector N =c) Binormal vector B =d)...
- Q Tom has taken out a loan for college. He started paying off theloan with a first payment of $200. Each month he pays, he wants topay back 1.2 times as...
- Q Problem 3. An isometry between inner-product spaces V and W is alinearoperator L in B (V ,W) that preserves norms and inner-products. Ifx, y in Vand if L is an...
- Q Problem 1. Show that the cross product defined on R^3 by [x1 x2x3] X [y1 y2 y3]= [(x2y3 − x3y2), (x3y1 − x1y3), (x1y2 − x2y1)] makes R^3 into analgebra.We...
- Q If technology is so wonderful, why do i need to understand thebasics of matrix operations? Why cant i just an app on a smartphone?
- Q 5. The cost of heart procedures for a county-run hospital is$125,000, with a fixed cost of $50,000 and a variable cost of$75,000. The hospital completed 250 procedures last year. [A]Assuming...
- Q Consider the solid S with the following properties: • The baseof S is the triangle T with vertices (0, 0),(1, 0), and (0, 1). •When S is sliced perpendicularly to...
- Q Show that the integers have infinite index in the additive groupof rational numbers.
- Q Show that there are only two distinct groups with four elements,as follows. Call the elements of the group e, a. b,c.Let a denote a nonidentity element whose square is the...
- Q Use Bisection method to determine the drage coefficient neededso that an 80-kg bungee jumper has a velocity of 36 m/s after 4 sof free fall. Note: The acceleration of gravity...
- Q Let K = { s+t * 2^(1/2), such that s, t are Rational}. Show thatK is a Field
- Q Determine if ~w = (−4, 6, 1) is a linear combinationof ~u = (1, 0, −1) and~v = (1, −11, 3) . If so, then express ~w as a linear...
- Q Let G a graph of order 8 with V (G) = {v1, v2, . . . , v8} suchthat deg vi = i for 1 ≤ i ≤ 7. What...
- Q 1). Consider the quadratic equationx^2+ 100 x + 1 = 0(i) Compute approximate roots by solvingx^2 -100 x = 0(ii) Use the quadratic formula to compute the roots ofequation(iii) Repeat...
- Q Brainstorm an exampleof a skewed data distribution relating to something in reallife.For yourexample would the median be a better description of the center ofthe distribution, why or why not? What...
- Q An agricultural products manufacturer's research and developmentdivision is testing a newly developed wheat fertilizer.Wheat is planted in several test areas (plots), which are in acontrolled environment. Each area is randomly...
- Q Use a relative error in pn (relative error=abs(pn-pn-1)/abs(pn)) of 0:0001 to find the root off(x) = x + exp(x) = 0 using both the Bisection method, the FixedPoint method and...
- Q Homework problems: Nested quantifiers(1.9-1.10)Determine the truth value of each expression below ifthe domain is the set of all real numbers.∃x∀y (xy = 0) (If true, give an example.)∀x∀y∃z (z =...
- Q Solve the ordinary differential equation analytically:y''-4y-+3y = 5cos(x) + e^(2x)y(0)=1, y'(0)=0
- Q 20 pairwise distinct positive integers are all smaller than 70.Prove that among their pairwise differences there are at least 4equal numbers
- Q The function f(t) represents water going into a swimming poolwith respect to the number of hours(t) water is flowing in where(t)represents time.f(t)=t squared +8t+9There is a leak in the pool...
- Q By using an example, demonstrate the value of theBox-Jenkins Methodobgy. Please make sure to discuss the impact ofseasonality.Need 400 Words
- Q In 75 words describe the Wire Frame and Platonic Solids The mainidea with this question is to use the power of the internet tobring some of these geometry lessons to...
- Q Consider the following sum (which is in expanded form): 1−4 +7−10 + 13−16 + 19−22 +···±(3n−2).Note that this is slightly different from the previous sum inthat every other term is...
- Q Prove that every sequence in a discrete metric space convergesand is a Cauchy sequence.This is all that was given to me... so I am unsure how I amsupposed to prove...
- Q Consider the function f(x, y) = 3+xy−x−2y. Let D be the closedtriangular region with vertices (1, 4), (5, 0), and (1, 0). Findthe absolute maximum and the absolute minimum of...
- Q Suppose we define a relation ~ on the set of nonzero realnumbers R* = R\{0} by for all a , b E R*, a ~ b if and only ifab>0....
- Q Let G act transitively on Ω and assume G is finite. Define anaction of G on the set Ω × Ω by putting(α,β) · g = (α · g, β...
- Q Write a program to implement the Romberg Algorithm.Input: f(x), an interval [a,b], N (the number of subintervals onthe finest grid on level 0 is 2^N, therefore, N is usualy a...
- Q LetN be a submodule of the R-module M. Prove that there is a bijectionbetween the submodules of M that contain N and the submodules ofM/N.
- Q 1(i) Show, if (X, d) is a metric space, then d∗ : X × X → [0,∞)defined by d∗(x, y) = d(x, y) /1 + d(x, y) is a metric...
- Q find the general solution of the equation using cauchyeuler. show complete solutionx^2 y\" - 3xy' + 3y = 2x^4 e^x
- Q For each of (a)-(d) below, decide whether the statement is Trueor False. If True, explain why. If False, give acounterexample.(a) Two non-parallel planes in R 3 will always meet in...
- Q formatrices, what is the difference between row reduced echelon formand an upper triangular matrix?
- Q Homogenous problem. Change of variable(x-y+3)dx + (x+y-1) dy = 0
- Q Let G be connected, and let e be an edge of G. Prove that e is abridge if and only if it is in every spanning tree of G.
- Q (a) Prove the following claim: in every simple graph G on atleast two vertices, we can always ï¬nd two distinct vertices v,wsuch that deg(v) = deg(w).(b) Prove the following claim:...
- Q Show that if a function f(z) is analytic in a domain D then ithas derivatives of all orders in D.
- Q Sketch the direction field of the equationdy/dx=y-4y^3. Sketch the phase portrait. Find the equilibriumsolutions and classify each equilibrium as stable, unstable orsemi-stable. Sketch typical solutions of the equation.
- Q 3) Laplace Transform and Solving first order Linear DifferentialEquations with Applications The Laplace transform of a function,transform of a derivative, transform of the second derivative,transform of an integral, table of...
- Q Suppose R and R0 are 2 ⇥ 3 row-reduced echelon matrices and thatthe systems RX = 0andR’X = 0 have exactly the same solutions. Prove that R = R’.
- Q Suppose f : X → S and F ⊆ P(S). Show, f −1 (∪A∈F A) = ∪A∈F f −1(A) f −1 (∩A∈F A) = ∩A∈F f −1 (A)Show, if A,...
- Q show that 43 is the largest integer that cant be written in theform of 6a+9b+20c
- Q Let f : X → Y and g : Y → Z be functions. We can deï¬ne thecomposition of f and g to be the function gâ—¦ f : X...
- Q Many elderly people have purchased medigap insurance policies tocover a growing Medicare copayment. These polices cover some or allof the medical costs not covered by Medicare. use economic theoryto explain...
- Q For this Variation of parameter problem, consider the followingmethod of solving the general linear equation of first ordery' + p(t)y= g(t)(a) If g(t) = 0 for all t, show that...
- Q Consider the equation: ?̇ +2? = ?(?) with initial condition x(0)= 2(a) If u(t) = 0, find the solution ?(?). What is ?(?) as t ->∞?(b) If u(t) = 4+t,...
- Q Let x,y ∈ R satisfyx < y. Prove that there exists a q ∈Q such that x < q <y.Strategy for solving the problemShow that there exists an n ∈N+...
- Q Consider the following 3-person encryption scheme based on RSA.L (can be trusted in this case) generates two large primes p and q,calculates both n and φ(n). L also chooses k1,...
- Q 1. This exercise is based on one in Hartman (2007). Apharmaceutical company needs to use a supercomputer to runsimulation models as part of its research on cures for AIDS,cancer, and...
- Q A school has a principal, many students, and many teachers. Eachof these persons has a name, birthdate, and may borrow and returnbooks. Teachers and the principal are both paid a...
- Q let f be the function on [0,1] given by f(x) = 1 if x isdifferent of 1/2 and 2 if x is equal to 1/2Prove that f is Riemann integrable...
- Q With regard to multi variable calculus can some explainDivergence Theorem and applications in detail. Thank you. Providean example problem and solve too thanks!
- Q The demand equation for a computer desk is p =−4x + 290,  and the supply equation isp = 3x + 80.(b) Find the equilibrium quantity x and pricep. (Round your answers...
- Q Solve the given differential equation by using an appropriatesubstitution. The DE is homogeneous.dydx=y − xy + x
- Q 1) A loan of RM10,000 at 12% compounded monthly is to beamortized by 36 monthly payments.a) Calculate the monthly payment.b) Construct an amortization schedule.2) Sarimah invests RM300 every 3 months...
- Q If p is prime, then Z*p is a group undermultiplication. Â
- Q Unless otherwise noted, all sets in this module are finite.Prove the following statements...1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A...
- Q A donut shop has 10 types of donuts including chocolate. (a) Howmany ways are there to choose 6 donuts? (b) How many ways are thereto choose 6 donuts, where at...
- Q If P = (1,4) in the elliptic curve E13(1, 1) , then 4P is????PLEASE SHOW ALL STEPS IN DETAIL AND EXPLAIN EACH STEP...
- Q State and prove the Weighted Mean Value Theorem forintegrals.
- Q Prove uniqueness of (a) LU-factorisation, (b) ofLDU-factorisation of a square matrix.
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