Advance Math question and answers for July 20, 2023
- Q olve the linear programming problem by sketching the region andlabeling the vertices, deciding whether a solution exists, and thenfinding it if it does exist. (If an answer does not exist,...
- Q 4(a)Verify that the equationy=lnx-lny is an implicit solution of the IVP,                 ydx=x(y+1)dy                               y(e)=1                                           (b) Consider theIVP, test whether it is exact and solveit.                x(x-y)dy=-(3xy-y^2)dx                                       y(-1)=1                                       (c) Determine the degree of thefollowing homogeneousfunction                                                      (i)f(x,y)=4x^2+2y^4,                                           (ii)f(x,y)=√5x^6-3y^6+4x^2y^4,          Â
- Q Using the power series method solve the given IVP. (The answerwill include the first four nonzero terms.)(x + 1)y'' − (2 − x)y' + y = 0, y(0) = 4,...
- Q 1) Solve the given initial-value problem.(x + y)2 dx + (2xy + x2 − 3) dy =0,   y(1) = 12) Find the general solution of the given differentialequation.x dy/dx + (4x +1)y...
- Q Give a recursive algorithm to compute a list of all permutationsof a given set S. (That is, compute a list of all possibleorderings of the elements of S. For example,...
- Q Solve x′=x−8y, y′=x−3y, x(0)=2, y(0)=1
- Q Disprove by counter-example that (? ∩ ?) ∪ (? ∩ ?) ⊆ ((?∩ ?) ∪ ?) ∩ ?Show by any valid method except Venn diagram that ((? ∪?) ∩ ?)...
- Q Let A be a diagonalizable n × nmatrix and let P be an invertible n × nmatrix such thatB = P−1APis the diagonal form of A. Prove thatAk = PBkP−1,where...
- Q Answer each of the following questions in your submission forthis part of the project:List your 4 variables from the Consensus at School (opens in anew window) and state whether they...
- Q A mass 7kg of stretches a spring 18cm. The mass is acted on byan external force of 5sin(t/2) N and moves in a medium that impartsa viscous force of 4N...
- Q 5. Compute a basis for each eigenspace of matrix A = | 6 3 −4 −1| (a) Diagonalize A. (b) Compute A4 and A−3 . (c) Find a matrix Bsuch...
- Q differential equation12. Newton's law of cooling states that the temperature of anobject changes at a rate pro-portional to the difference betweenits temperature and that of its surroundings. Suppose that thetemperature...
- Q (3) Let m be a positive integer. (a) Prove that Z/mZ is acommutative ring. (b) Prove that if m is composite, then Z/mZ isnot a field.(4) Let m be an...
- Q A tank contains 70 kg of salt and 2000 L of water. Watercontaining 0.4kg/L of salt enters the tank at the rate 16L/min. Thesolution is mixed and drains from the...
- Q Use Heun's method to find the value of x at t=3 (assume thechange in t=3).The ode is:(d^2x)/(dt^2)+(.3dx/dt)-4x=0.And the initial conditions are:x(0)=1, dx/dt (0)=0.
- Q 1) Find the Laplace transform off(t)=−(2u(t−3)+4u(t−5)+u(t−8))F(s)=2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6)F(s)=3) Find the Laplace transform of f(t)=u(t−6)⋅t^2F(s)=
- Q integrating factor and the ED solution y (12 + 8x + 6y ^ 2) dx +x (16 + 8x + 12y ^ 2) dy = 0___Indicate the option that contains...
- Q Find vectors of the Frenet frame of the curve at any point ofthe curve x = a(t − sin t), y = a(1 − cos t), z = 4a cos...
- Q Math201:Directions: Annual Percentage Yield (APV). Find the annualpercentage yield (to the nearest 0.01%) in each case.1.) A bank offers an APR of 3.2% compoundedmonthly.Directions: Continuous Compounding. Use the formula forcontinuous...
- Q Suppose that we are interested I the number of heads showingface up on three tosses of a coin. This is the experiment. Thepossible results are: zero heads, one head, two...
- Q Please justify below questions (its a topology question) withvalid arguments:1. Show that an infinite set is not finite.2. Is there an infinite set which is not countably infinite?Thanks in advance.
- Q Use stars and bars to solve each counting problem. You may leaveyour answers as binomial coefficients.(a) How many collections of 6 (not necessarily distinct) coinscan be made from an infinite...
- Q List examples of equations similar to the Pell's equation, ie.any  Diophantine equation other then Pell's.
- Q Find the intersection of the line passing through P=(21,21) andQ(−63,168) and the line passing through points R(21,0) and S(0,21)using vectors.
- Q For each of the following simplicial complexes ,X = {[a], [b],[c], [d], [a, b], [c, d]}, and X = {[a], [b], [c], [d], [e], [a,b], [b, c], [c, d], [a,...
- Q A three-phase 60-Hz transmission line is energized with 420 kVat the sending end. This line is lossless and 400 km long with ? =0.001265 rad/km and ?? = 260 Ω....
- Q a.)Find the length of the spiral r=θ for 0 ≤ θ ≤ 2b.)Find the exact length of the polar curve r=3sin(θ), 0 ≤ θ ≤π/3c.)Write each equation in polar coordinates....
- Q Find a study in a professional journal whichuses correlation and/or regression as at least one of thestatistical processes. Write one paragraph aboutthe purpose of the study, another paragraph aboutthe conclusions...
- Q For each of the statements, begin a proof by contraposition anda proof by contradiction. This will include rewriting thestatement, writing the assumptions, and writing what needs to beshown. From there,...
- Q The price of a new car is $16,000. Assume that an individualmakes a down payment of 25% toward the purchase of the car andsecures financing for the balance at the...
- Q Sketch a drawing that matches the values givenDetermine how to begin (Law of Sines/Law of Cosines)Solve for the missing values of the triangle (if possible)a=4.2 in, b=2.5 in, c=5.8 inb=3.9...
- Q Find the Chebyshev interpolation nodes on the interval [4,12]for an interpolating polynomial of degree 5
- Q For the following exercises, evaluate the expressions, writing the result as a simplified complex number.1/i11 – 1/i21
- Q What interest will be earned if $6600 is invested for 8 years at12% compounded monthly? (Round your answer to the nearest cent.)$
- Q Complex Variable Evaluate the following integrals:a) int_c (z^2/((z-3i)^2)) dz; c=lzl=5b) int_c (1/((z^3)(z-4))) dz ; c= lzl =1c) int_c (2(z^2)-z+1)/(((z-1)^2)(z+1)) dz ; c= lzl=3(Details Please)
- Q Find the system of equations to model the problem. Don't solvethe system.A paper company produces high grade, medium grade and low gradepaper. The number of tons of each grade produced...
- Q A large tank containing a mystery liquid is filled to a depth ofL = 35 m. The upper surface of the liquid isexposed to the atmosphere (of density 1.2kg/m3). A...
- Q Purchase of a new homeJohn and Jane had planned to save $60 000 dollars over the nextfive years as a down payment on a house. Jane assured John that ifthey...
- Q Show all work, write legibly, explain indetaily\"-3y'+2y = 8u2(t) , y(0) = 0, y'(0) = 0Solve the following initial value problem using the Laplacetransform
- Q 5.       Solve the followingdifferential equation using the given initial conditions (Useconvolution and set up the integral but do not integrate.)              y'’− 2y’ + 2y =18e−tsin3t;         y(0)= 0, y’(0) = 3
- Q Write a recursive formula that shows how many ways you can tilea 3xn checkboard with 1x3 tiles. Show how the pattern is establishby showing how different value n give their...
- Q Let S be a set of n numbers. Let X bethe set of all subsets of S of size k, and letY be the set of all ordered k-tuples(s1, s2,   ,sk)such...
- Q It is like a class discussion and we're supposed to write adiscussion about Vector spaces, subspaces and basesOverview (what to write on the discussion): So we'resupposed to discuss and explain...
- Q 1. A=Z show if xRy <=> xy>=1 is reflexive, transitiveand transitive.2. A=Z show if nRm <=> nm >= 0 is an equivalencerelation and show the equivalence clases3. A= R (real...
- Q An ice cream company collected data on their ice cream conessales over a month in July in a Chicago suburb, along with dailytemperature and the weather. The company is interested...
- Q A model for the populationP(t)in a suburb of a large city is given by the initial-valueproblemdPdt= P(10−1 −10−7P),    P(0) = 3000,where t is measured in months. What is the limitingvalue of...
- Q PART 2: Instructions: Write threeparagraphs to answer this question:Suppose a sociologist at John Jay College is given a grant tostudy “whether there is a binge drinking problem on the campus...
- Q The centers of two circles are 4 cm apart, with one circlehaving a radius of 3 cm and the other a radius of 2 cm. Find thearea of their intersection.
- Q Consider the curve traced out by the parametric equations: { x =1 + cos(t) y = t + sin(t) for 0 ≤ t ≤ 4π.1. Show that that dy dx...
- Q Information theoryConsider a random variable representing cointhrows (Bernoulli Variable with Σ = {0,1} ). Let the trueprobability distribution be p(0) = r, p(1) = 1-r.Someone guesses a different distribution q(0)...
- Q Given y 1 ( t ) = t2 and y2 ( t ) = t ^− 1 satisfy thecorresponding homogeneous equation oft^2 y ' ' − 2 y = −...
- Q You want to be able to withdraw the specified amountperiodically from a payout annuity with the given terms. Find outhow much the account needs to hold to make this possible....
- Q Show that the indicial roots of the singularity x=0 differ by aninteger. Use the method of Frobenius to obtain the first four termsof at least one series solutions of the...
- Q Discrete StructuresUse a proof by contraposition to show if x3 + 3x isan irrational number then so is x, for any real number x.
- Q A tank originally contains 120 gal of fresh water. Then watercontaining 1/2 lb of salt per gallon is poured into the tank at arate of 2 gal/min, and the mixture...
- Q 4) Laplace Transform and Solving second order LinearDifferential Equations with Applications The Laplace transform of afunction, transform of a derivative, transform of the secondderivative, transform of an integral, table of...
- Q Suppose V and V0 are ï¬nitely-generated vector spaces and T : V →V0 is a linear transformation with ker(T) = {~ 0}. Is it possiblethat dim(V ) > dim(V0)? If...
- Q a) How many integers in between 1 and 106 have aneven number of divisors?Show work proving your answer.Express your answer in prime factorized form.b) With proof, determine all integer solutions...
- Q Demand for rug-cleaning machines at Clyde’s U-Rent-It is shownin the following table. Machines are rented by the day only. Profiton the rug cleaners is $19 per day. Clyde has 3...
- Q An object with mass 40.5 kg is given an initial downwardvelocity -3ms in a medium that exerts a resistive force withmagnitude proportional to the square of the speed. The resistanceis...
- Q A furniture store manufactures 2 products; tables (X) and chairs(Y): the production process for each require a certain number oflabor hours in the carpentry department and a certain number oflabor...
- Q the physicians in problem 3-36 have been ap-proached by a marketresearch firm that offers to perform a study of the market at a feeof $5,000. the market researchers claim their...
- Q A new drug has been developed to treat a particular condition,and it is alleged to be more effective than traditional treatment.An experiment will be conducted to test whether the statement...
- Q Find the slope of the tangent line to the graph of thefunction at the given point.f(x) = 4/3x at (1,4/3)Determine an equation of the tangent line.y =i need belp determing...
- Q 1. Consider the problem of two polluting sources in the region,each of which generated 10 units of pollution for a total of 20units released into the environment. The government determined...
- Q ï¬nd the solution of the given initial value problem1.   y''+4y=t2+3et, y(0) =0,y'(0) =22. y''−2y'+y=tet +4, y(0) =1, y'(0) =1
- Q find the projection vector of the vector v = (2,3,5) onto theplane z = 2x + 3y -1
- Q ï¬nd the general solution of the given differential equation1. y''+2y'=3+4sin2t2. 2y''+3y'+y=t2 +3sint
- Q What purpose does Medea find for myth (= story telling) in theMedea of Euripides?
- Q 1. For an m x n matrix A, the Column Space of A is a subspace ofwhat vector space?2. For an m x n matrix A, the Null Space of...
- Q Second order Differential equation:Find the general solution to [ y'' + 6y' +8y = 3e^(-2x) + 2x ]using annihilators method and undetermined coeficients.
- Q Given the curve −→r (t) = <sin3 (t),cos3 (t),sin2 (t)> for 0 ≤ t ≤ π/2 findthe unit tangent vector, unit normal vector, and the curvature.
- Q Use the method of undetermined coefficients to find the completesolutions of the following differential equations.d2y/dx2 − 3 dy/dx + 2y = 2x2 +ex + 2xex + 4e3x .
- Q Another model for a growth function for a limited population isgiven by the Gompertz function, which is asolution to the differential equationdP/dt=cln(K/P)Pwhere c is a constant and K is the...
- Q Solve the following linear equations with constant coefficients,using characteristic equations and undetermined coefficients asneeded.y''+4y'-12y=x+e^2x y(0)=1,y'(0)=2
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