Advance Math question and answers for August 14, 2023
- Q Implement the Lorenz-63 model in MATLAB, and solve numerically(using MATLAB’s ode45 or other built-in solver) for any random,non-zero initial conditions to reproduce, qualitatively, Figures 3and 4. Note that, as usual,...
- Q A toboggan with two people on it weighs 300 lb. It starts fromrest down a slope, 1/4 mile long, from a height 200 ft abovehorizontal level. The coefficient of sliding...
- Q y(4)+18y''+81y=0y(0)=2, y'(0)=8, y''(0)=0, y'''(0)=?108Note; y(4) is the 4th derivative of ySolve the initial value problem y(t)= ?
- Q A parachutist whose mass is 80 kg drops from a helicopterhovering 2000 m above the ground and falls toward the ground underthe influence of gravity. Assume that the force due...
- Q a) verify that y1 and y2 are fundamental solutionsb) find the general solution for the given differentialequationc) find a particular solution that satisfies the specifiedinitial conditions for the given differential...
- Q Let R[x, y] be the set of polynomials in two coefficients. Provethat R[x, y] is a vector space over R. A polynomial f(x, y) iscalled degree d homogenous polynomial if...
- Q Problem #1 :Using separation of variables and the formalism demonstrated inclass, find the general solution to the Helmholtz equation (alsoknown as the time independent wave equation) :?^2 F + k^2...
- Q How is the ratio of outputs to inputs, y x, different from theslope ratio?When a linear graph passes through the origin, why is the ratioof outputs to inputs, y x...
- Q The population of mosquitoes in a certain area increases at arate proportional to the current population, and in the absence ofother factors, the population doubles each week. There are 800,000mosquitoes...
- Q Determine the entropy of the random variable which counts thesum ofthree dice.
- Q 2) A drug lord wishes to optimize the area in which he will growhis coca plants. The area concerned has a river on one side andmust be closed in with...
- Q Quiz 4A manufacturer makes and sales four types ofproducts: Product X, Product Y, Product Z, and ProductW. The resources needed to produce one unit of each product and thesales prices are given...
- Q Prove that ?3 is irrational using contradiction. You can useproblem 4 as a lemma for this.Problem 4, for context isProve that if n2 is divisible by 3, then n isdivisible...
- Q A 2nd order homogeneous linear differential equation hasodd-even parity. Prove that if one of itssolutions is an even function and the other can be constructed asan odd function.
- Q A list of six positive integers, p, q, r, s, t, u satisfies p< q < r < s < t < u. There are exactly 15 pairs ofnumbers that...
- Q 1. You have an order to give Penicillin 150,000 Units (I.M.).You have a vial of Penicillin containing 3,000,000 Units in 10ml.How many ml. will you give?______ 2. The doctor orders...
- Q Apply Newton’s method and the modified method to the equationf(x) = 1?cos(x?5) to approximate the a double root 5. Compare theresults and demonstrate the superiority of the modified method.Numerically identify...
- Q Let (F, <) be an ordered field, let S be a nonempty subset ofF, let c ? F, and for purposes of this problem let cS = {cx | x...
- Q (a) Consider the function f(x)=(ex ?1)/x.Use l’Hˆopital’s rule to show that lim f(x) = 1 when xapproaches 0(b) Check this result empirically by writing a program tocompute f(x) for x...
- Q You can verify that the differential equation:?7x2y???14x(x?1)y?+14(x?1)y=0?7x2y??14x(x?1)y?+14(x?1)y=0,x>0x>0 has solutions y1=3xy1=3x andy2=5xexp(?2x)y2=5xexp?(?2x).Compute the Wronskian WW between y1y1 and yThe solutions y1y1 and y2y2 form a fundamental set of solutionsbecause there is...
- Q Let G be an abelian group.(a) If H = {x ? G| |x| is odd}, prove that H is a subgroup of G.(b) If K = {x ? G| |x|...
- Q Solve each system. Express the solution set using vectors.Identify a particular solution and the solution set of thehomogeneous system.(a) 3x + 6y = 18x + 2y = 6(b) x +...
- Q Use the method of variation of parameters to find the generalsolution of the differential equationy''+6y'+5y = 7e^(2x)
- Q A 60 kg individual needs to work at a MET level of 8 toreach her target heart rate. If the treadmill speed is set at 3.5mph, what grade is needed?...
- Q 5AResearch and share two or more real lifeapplications of radial, rotational, or gradient fields.5BExplain the concept of divergence and provide an example showinghow to calculate the divergence of the vector...
- Q Write notes on omitted variable bias. define what the issue isexplain whether, or under what circumstances, it causes aproblem for inference in OLS regressionexplain how it can be detected (if itcan) state...
- Q PLEASE EXPLAIN WHY YOU CHOOSE EACH ANSWER1). How many distinct ways can a President, Vice President,Secretary and Treasurer be selected from a group of 10 people if noone can hold...
- Q letS in Rn be convex set.show that u point in S is extreme point of S if and only if uis not convex combination of other points of S.
- Q A semi trailer of 9.0% wb moisture soybeans sits outsideovernight without a tarp and it rains 1.5 in. The trailer had beenlevel, filled to a depth of 4.5 feet. Assume...
- Q Prove the case involving ?E(or elimination) of the inductivestep of the (strong) soundness theorem for natural deduction inclassical propositional logic. Hint: you need to simultaneouslyconsider 3 di?erent instances of entailment,...
- Q Find the maximum and minimum values, and at what point theyoccur.A. F(x,y)= 25-16x-2x2+8y+4y2 over theregion bounded by x=5, y= -2, and y=xB. F(x,y)= x2y+3xy-4y+15x over the region bound byx=0, x=3,...
- Q For each of the following equations, find the generalsolution:(x^2)y??+xy?+ 4y= sin(lnx) + sin(2 lnx)y??+y=tcostThank you!
- Q Answer the following questions: (a) Show that the following is atautology by using truth table and using list of equivalences.(This problem should be solved using 2 different methods mentionedabove). ((¬p...
- Q Discuss a relationship between two quantities associated withyour major (business finance). Include your major and describe therelationship 1) in words, 2) graphically, 3) and as an equation.Define the terms in...
- Q Find all local extreme values of the given function and identifyeach as a local maximum, local minimum, or saddle point of the nextfunctions.1) f(x, y) = e-(x2 + y2 -...
- Q A fluid has velocity components of u=(8t2)m/s and v=(8y+3x)m/s,where x and y are in meters and t is in seconds.Part ADetermine the magnitude of the velocity of a particle passingthrough...
- Q This is a problem from Jeff ’s notes - reproduced here for ease.The d-dimensional hypercube is the graph defined as follows. Thereare 2d vertices, each labeled with a different string...
- Q Write an 8-10 sentence paragrpah describing Galois Theory.
- Q a, The vectors v1 = < 0, 2, 1 >, v2 = < 1, 1, 1 > ,v3 = < 1, 2, 3 > , v4 = < -2, -4,...
- Q In parts a, b, and c, determine if the vectors form a basis forthe given vector space. Show all algebraic steps to explain youranswer.a. < 1, 2, 3 > ,...
- Q LetA, Bbe sets andf:A?Bandg:B?C. Characterize wheng?f:A?Cis a bijection.
- Q Let f: X-->Y and g: Y-->Z be arbitrary maps of sets(a) Show that if f and g are injective then so is thecomposition g o f(b) Show that if f...
- Q Find all unlabeled trees on 2,3,4 and 5 nodes. How many labeledtrees do you get fromeach? Use this to find the number of labeled trees on 2,3,4 and5 nodes.
- Q Show the conversion of the following numbers with the standardconversion procedure.1. (AD)H = ( ?)2 = ( ? )102. (24)7 = ( ?)10 = ( ? )23. ( 10011001)2 ...
- Q Your remodeled home will have an open floor plan with the diningarea, living area, and kitchen in one large room. You will have afireplace along one of the walls, and...
- Q 3. Given is the function f : Df ? R with F(x1, x2, x3) = x 2 1 +2x 2 2 + x 3 3 + x1 x3 ? x2...
- Q Describe the ring obtained from the product ring R×R byinverting the element (2,0).and we already know that the ring R x R is isomorphic toR[x]/(x^2-1)
- Q A spring with a spring constant ? k of 100 pounds per foot isloaded with 1-pound weight and brought to equilibrium. It is thenstretched an additional 1 inch and released....
- Q Required: Formulate and solve the LP Relaxation of the problem.Solve it graphically, and round down to find a feasiblesolution.Explain/show what excel parameters and cells should beentered into the excel to...
- Q Determine if each of the following statements is true or false.If it’s true, explain why. If it’s false explain why not, or simplygive an example demonstrating why it’s false. (A...
- Q Prove that a continuous function for sections(subrectangles) isintegrable in R^N
- Q Show that, for each value of n, the graph associated with thealcohol CnH2n+1OH is a tree (the oxygenvertex has degree 2). Draw the tree corresponding to the moleculeC2H5OH.
- Q How is truth found in philosophy and how is that different thanin science?How is truth found in math and how is that different than inscience?Please include the ideas of experimentally...
- Q In the proof of bolzano-weierstrass theorem in R^n on page 56 of"Mathematical Analysis" by Apostol, should the inequality bea/2^(m-2) < r/sqrt(n) or something related to n? a/2^(m-2) <r/2 seems not...
- Q This is considering the Phi function (The Euler PhiFunction)(a) Explain why ?(m) is always even when m ?3.(b) ?(m) is rarely a prime number. Find all numbers m so that?(m)...
- Q Do the following numbers have a finite binary expansion ornot:0.5, 0.125, 0.015625, 0.0125, 0.05
- Q Explain the difference between the actual definition of aRiemann Integral of function f on the interval [a,b] and theconclusion of the FTOC Part 2.(Fundamental Theorem of Calculus Part2)
- Q A farmer has a mixing tank of capacity 1200 liters which shehalf-filled with pure, fresh water. She pumps into the tank aconcentrated liquid fertilizer (CLF) at rate 3 liters/minute,containing 1/3...
- Q use euclidean algorithm to find integers m,n such that1693m+2019n=1
- Q A girl who has two siblings is chosen at random and the number Xof her sisters is counted. Describe how to simulate an observationon X based on U ? unif[0,...
- Q Suppose there are two lakes located on a stream. Clean waterflows into the firstlake, then the water from the first lake flows into the secondlake, and then water from the...
- Q This problem is an example of critically damped harmonic motion. A mass m=6kg is attached to both a spring with spring constant k=96N/m and a dash-pot with damping constant c=48N?s/m...
- Q Check whether the following families of functions of t arelinearly independent or not(a) t^2 + 1, 2t, 4(t + 1)^2(b) sin(t) cos(t), sin(2t) + cos(2t), cos(2t)(c) e^2t , e^-2t ,...
- Q Suppose a hospital has 100 winen who are tested postive for HPVvirus. Select a simple random sample of size three (SRS of n=3)from the hospital population of women who are...
- Q Suppose A is an mxn matrix of real numbers andx in an nx1 column vector.a.) suppose Ax=0. Show thatATAx=0.b.)Suppose ATAx=0.show Ax=0.c.) by part a and b, we can conclude that...
- Q i) A set of 4 6-tuples (“sextuplets”) is linearly independent:(always), (never), (sometimes). ii) A set of 6 4-tuples(“quadruplets”) is linearly independent: (always), (never),(sometimes). iii) A set of 4 equations with...
- Q Let (Z, N, +, ·) be an ordered integral domain. Let {x1, x2, . .. , xn} be a subset of Z. Prove there exists an i, 1 ? i...
- Q For a 2 by 2 invertible matrix A, define the condition number tobe cond(A) = ||A|| ? ||A||-1. Assume that the matrixnorm is defined using the Euclidean vector norm.(a) Find...
- Q Use Laplace Tranform in solving the ff.:After cooking for 45 minutes, when a cake is removedfrom an oven, its temperature is measured at 300°F. 3 minuteslater, its temperature is 200°F....
- Q The more compounding periods per year, the lower the effectiverate of return. T or FThe stated interest rate is the real or true rate of return onan investment T or...
- Q use Laplace transform 2dy/dt + y = sin3t; initial conditionsy(0)= 0
- Q prove every cauchy sequence converges
- Q Compute growth function and VC dimensionH ={h: R -> {-1, +1} | h(x) = 1D(x) where D is afinite set of R}
- Q (6) In each part below, find a basis for R4 CONTAINED IN thegiven set, or explain why that is not possible: Do not usedimension(a) {(1,1,0,0),(1,0,1,0),(0,1,1,0)}(b) {(1,?1,0,0),(1,0,?1,0),(0,1,?1,0),(0,0,0,1)}(c) {(1,1,0,0),(1,?1,0,0),(0,1,?1,0),(0,0,1,?1)}(d) {(1,1,1,1),(1,2,3,4),(1,4,9,16),(1,8,27,64),(1,16,81,256)}
- Q Problem 1a) Bernard operates a chocolate shop in Paris. The annual demandfor chocolatecovered cherries is 2,500 units. The setup cost is $15per order and the unit cost is $0.6. The...
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