Advance Math question and answers for July 30, 2023
- Q Find the Laplace transform of d2y/dt2
- Q Is 100202345X a valid ISBN number? If not, what would thecorrect check digit have to be ?Solve the congruence 121x ? 5 mod 350.
- Q 4. Verify that the Cartesian product V × W of two vector spacesV and W over (the same field) F can be endowed with a vector spacestructure over F, namely,...
- Q Please explain why and how the following are true.I. p ?(q?r) is equivalent to (p ?q)?(p ?r)II. Let p(x) and p(x) be defined on an random/arbitrary universeof discourse. Why, in...
- Q Prove that the entropy of a node never increases after splittingit into smaller children nodes.
- Q For which values of ? does the system of equations(? ? 2)x + y = 0x + (? ? 2)y = 0have nontrivial solutions? (That is, solutions other than x...
- Q Let V = R^2×2 be the vector space of 2-by-2 matrices with realentries overthe scalar field R. We can define a function L on V byL : V is sent...
- Q Consider a homogeneous system of linear equations with mequations and n variables.(i) Prove that this system is consistent.(ii) Prove that if m < n then the system has infinitely manysolutions....
- Q solve the SDE dX = ? 1 /?( (X ? µ)dt) + (2D)-1/2 dB.X(t = 0) = ?
- Q 2. Give an example of a linear transformation L : lR^2 arrowlR^2 which has a repeated real eigenvalue, but in which lR^2 doesposses a basis of eigenvectors.
- Q (1 point) A bacteria culture starts with 560 bacteria and growsat a rate proportional to its size. After 3 hours there will be1680 bacteria.(a) Express the population after t hours...
- Q Suppose f : R ? R is measurable and g : R ? R is monotone. Provethat g ? f is measurable
- Q A particular mattress company has three factories (1,2,3), eachof which produces three types of mattresses: (1) spring, (2) foam,and (3) hybrid. In the matrix? = [ 80 50 2545 110...
- Q prove that the set of irrational numbers is uncountable by usingthe Nested Intervals Property
- Q Put a metric ? on all the words in a dictionary by defining thedistance between two distinct words to be 2^?n if the words agreefor the first n letters and...
- Q Show that a monotone sequence converges if and only if it isbounded.
- Q 1)Find the power series solution for the equation y'' ? y =x2)Find the power series solution for the equation y'' + (sinx)y= x; y(0) = 0; y'(0) = 1Provide the...
- Q Explain the outcome of 3^4^5. In particular, what is the order of execution of the two exponentiation operations?Write (5^4^3)?1 as a product of prime numbers.The greatest common divisor of two...
- Q Consider the equation uux + uy = 0 with the initialconditionu(x, 0) = h(x) = ? 0 for x > 0uo for x < 0, withuo< 0.Show that there is a...
- Q 4. (Applying LU and LUP decompositions) In this problem, we'lluse the LU/LUP decomposition to solve a linear system ofequations.a) For A = [12 -8 13 -1 13;14 11 -5 -5...
- Q Show that radical 3, radical 5, radical 7, radical 24, andradical 31 are not rational numbers
- Q Let ? : G1 ? G2 be a group homomorphism. (abstract algebra)(a) Suppose H is a subgroup of G1. Define ?(H) = {?(h) | h ? H}.Prove that ?(H) is...
- Q how do you solve tan(theta)-sin(theta)=.25?
- Q Can you please explain the difference between Eulerian paths andHamilton paths as well as Eulerian circuits and Hamilton circuits.Can you determine if a graph is one of these? Can a...
- Q A body of mass 7 kg is projected vertically upward with aninitial velocity 18 meters per second. The gravitational constantis g=98m/s2. The air resistance is equal to k|v| where kis...
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