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Advanced-Math Questions
Solve by using a matrix exponential x' = x - 2y + 2e-t y' = 2x-3y
Events A1, A2, and A3 form a partiton of sample space S with Pr(A1)=27, Pr(A2)=47, and...
Prove the division algorithm for R[x]. Where R[x] is the set of real polynomials.
1-Assume that f is a homomorphism from (G, ∗) to (H, ⊗). a) If a∈G, why...
What is the relationship between the vector fields given as x ̇ = Ax y x...
A lathe to make a single pass on a 2.000 in. diameter (diameter before the cut),...
True or False 1. A subset H of Rn must be a sub space of Rn...
so we have a matrix: assume [[row]. [row]], dx/dt = [[6, -2], [20, -6]]x. which is...
Consider the differential equation: y'' = y' + y a) derive the characteristic polynomial for the...
A partially solved PERT problem is detailed in the table below. Times are given in weeks....
Solve the following initial value problem. y'''-4y''+5y'=100e^5x;y''(0)=-34,y'(0)=-6,y(0)=7
How to find laplace of .... L [t3 sint] ? usually I don't know how to...
Let the edges of K7 be colored with the colors red and blue. Show that there...
Assume that all the eigenvalues of A have a negative real part. Show that the linear...
Show that the n-cube Qn has 2 to the power n vertices and n2 to the...
7. (Problem 3 on page 341 from Rosen) Let P(n) be the statement that a postage...
Let A, B be n × n matrices. The following are two incorrect proofs that ABhas...
Use the Mean Value Theorem and the fact that for f(x) = cos(x), f′(x) = −sin(x),...
Let X be the vector space of all ordered pairs of complex numbers. Can we obtain...
Show that if a and d are positive integers, then (-a) div d= -a div d...
Find the exact length of the curve. x = 8 + 9t2, y = 3 +...
Randomized Leader Election A group of n people sit together and each one chooses a uniformly...
Random pigeonholing 100 pigeons p1,…,p100 fly into 500 labelled holes h1,…,h500. Each pigeon picks a hole...
True or False: An infinite group must have an element of infinite order. I know that...
Prove that if E is a finite field with characteristic p, then the number of elements...
Determine if vectors are linearly dependent or independent: 1. (1,-2,1,1),(3,0,2,-2),(0,4,-1,-1),(5,0,3,-1) 2. (1.-1.2),(4,0,0),(-2,3,5),(7,1,2)
Determine if vectors are linearly dependent or independent: 1. (1,2), (-1,-3) 2. (2,-1,4),(4,-2,7),(1,5,8) 3. (-3,4,2),(7,-1,3),(1.1.8)
Determine if the following subsets are subspaces: 1. The set of differentiable functions such that f´...
Let f : R → R be a continuous function which is periodic. Show that f...
y’ – y = 2x -1 y(0) = 1 , 0 ≤ x ≤ 0.2 ...
Prove that if G is a graph in which any two nodes are connected by a...
Trigonometry – The cosine function Determine all roots on ?=−8 ???(−6?−?/3)+1 Smallest positive root? spacing between...
Let X be the vector space of all ordered pairs of complex numbers. Can we obtain...
✓For Pi as defined below, show that {P1, P2, P3} is an orthogonal subset of R4....
Use the Miller–Rabin test on each of the following numbers. In each case, either provide a...
Show the vectors [x y z] where xyz=0 is a subspace V of R^3. is it...
using theorem 11.10 (First Isomorphism Theorem), Show that G1xG2/G1x{e _G2} is iso to G2 Theorem 11.10...
Jazelle Momba wants to visit her family in zimbabwe in 2025, which is 6 years from...
Find a subset of the given vectors that form a basis for the space spanned by...
Determine all real numbers a for which the vectors v1 = (1,−1,1,a,2) v2 = (−1,0,0,1,0) v3...
1.) Suppose that on January 1 you have a balance of$4200 on a credit card whose...
After graduating from High School Peter works for four years. During this time he deposits each...
Half life of radium is 1700 years, assuming that the decay rate is proportional to the...
engineering mathematics solve (3y2+2x+1)dx+(2xy+2y)dy=0 Find an integrating factor and solve the ode,tks.
Prove that if p does not equal 5 is an odd prime number, then either p^2-1...
Use the power method to determine the highest eigenvalue and corresponding eigenvector for [ (2-λ) 8...
Suppose U is m×n. Explain why if U has orthonormal columns, then we must have m...
Prove that there is no integral domain with exactly 6 elements. Can your argument be adapted...
A physician orders a 5.4-g vial of a drug to be added to D5W for a...
consider the following mode for simple harmonic motion in a mass spring sysyem 4x"(t)+12x(t)=0 x(0)=1 x'(0)=1...
In Exercises 11–15 find a power series solution to (1+2x^2)y''+(2-3x)y'+4y
Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in...
Let H <| G. If H is abelian and G/H is also abelian, prove or disprove...
Let G be a finite group and let H, K be normal subgroups of G. If...
You wish to take out $375,000 mortgage. The yearly interest rate on the loan is 3%...
Apply the Gram-Schmidt orthonormalization process to transform the given basis for ℝ4 into an orthonormal basis....
Prove: If the sides of a right triangle have integer lengths and the area of the...
1105 = 5 × 13 × 17. Find three different ways of writing 1105 as the...
Prove: If (a,b,c) is a primitive Pythagorean triple, then either a or b is divisible by...
Discuss the properties of polynomials
A businesswoman wants to invest a certain sum of money at the end of each year...
y'+(x+1)y=e^(x^2)*y^3,y(0)=0.25
Let W be the subspace of R4 spanned by the vectors a = 3e1 − 4e2...
Find the Möbius transformation that falls on the right half plane of the disk "| ?...
A simple random sample of 55 adults’ measurements of their red blood cell count (in cells...
1) if 3200 is invested for 6 years at 8% compunded quarterly, how much will be...
Let a and b be vectors. Show that (a.b) = 1/4 (||a +b||^2 − ||a −b||^2...
Prove that {5k | k ∈ Z} ∩ {7l | l ∈ Z} = {35m |...
1. Prove that every quadratic polynomial has two complex solutions 2.Use properties of addition and multiplication...
suppose A is a 6 x 4 matrix and b is a 4 x 6 matrix....
Use triple integrals to calculate the average value of F(x,y,z) over the given region: F(x,y,z) =...
Paula is considering the purchase of a new car. She has narrowed her search to two...
Given △ABC, extend sides AB and AC to rays AB and AC forming exterior angles. Let...
How to convert Scholes Black equation to heat equation (I need explanation of the method of...
The town recluse has invited you to dinner at his lavish century-old Victorian mansion outside of...
Let T be the half-open interval topology for R, defined in Exercise 4.6. Show that (R,T)...
Let G be a finite group and let H be a subgroup of order n. Suppose...
Discrete Math There are 10 distinct books on a table. 2 are biology books, 2 are...
Calculate integral s FndA for F = [x ^ 2, y ^ 2, z ^ 2],...
Let S denote the set of all possible finite binary strings, i.e. strings of finite length...
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