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QUESTIONS

Newest Featured Answered Unanswered Pro Bono
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$25.00

answered


[LINEAR ALGEBRA] DIAGONALIZABLE OPERATOR AND SPECTRUM

$25.00
answered

See attached image. Exercise from my Advanced Linear Algebra class.Working from
Hoffman/Kunze LinearAlgebra and Roman Advanced Linear Algebra.Any questions
about notation, just let me know.*Just an ad...

Linear Algebra Vector Spaces Eigenvalues & Eigenvectors
Matchmaticians Alumnus
$20.00

answered


EVALUATE ∫0Π2SIN⁡XSIN⁡X+COS⁡XDX\INT_0^{\FRAC{\PI}{2}}\FRAC{\SQRT{\SIN
X}}{\SQRT{\SIN X}+\SQRT{\COS X}} DX∫02Π SINX +COSX SINX DX

$20.00
answered

Evaluate \int_0^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}
dx.Hint: First show that for any function f(x)f(x)f(x) the following formula
holds 

Calculus Algebra Trigonometry
Malindad
$45.00

answered


DERIVE THE SOLUTION
U(X,T)=X4Π∫0T1(T−S)3/2E−X24(T−S)G(S) DSU(X,T)=\FRAC{X}{\SQRT{4 \PI}}
\INT_{0}^{T} \FRAC{1}{(T-S)^{3/2}}E^{\FRAC{-X^2}{4(T-S)}}G(S) \, DSU(X,T)=4Π X
∫0T (T−S)3/21 E4(T−S)−X2 G(S)DS FOR THE HEAT EQUATION

$45.00
answered

Given g:[0,∞)→Rg: [0,\infty) \rightarrow \Rg:[0,∞)→R, with g(0)=0g(0)=0g(0)=0,
derive the formula for a solutions of the initial/boundary-value problem (Hint:
Let v(x,t):=u(x,t)−g(t)v(x,t) := u(x,t) - g(t)v(x,t):=u(x,t)−g(t)  and extend
vvv to {x<0}\{x<0\}{x<0} by...

Partial Differential Equations Heat Equation Parabolic PDEs
Daniel
$10.00

answered


WHY DOES ∑N=1∞22N×(N!)2N(2N+1)(2N)!=2 \SUM\LIMITS_{N=1}^{\INFTY } 2^{2N} \TIMES
\FRAC{(N!)^2}{N(2N+1)(2N)!} =2 N=1∑∞ 22N×N(2N+1)(2N)!(N!)2 =2 ?

$10.00
answered

In my Calculus class, we were solving an integration by parts problem two
different ways. One way gave an answer pretty easily, the other led to an
infinite series that stumped us. After playing aroun...

Calculus Sequences and Series Convergence
Wmorrison49
$3.00

answered


PROVE THAT 1+12+⋯+1N≤2N−11+\FRAC{1}{\SQRT{2}}+\DOTS+\FRAC{1}{\SQRT{N}} \LEQ 2
\SQRT{N}-11+2 1 +⋯+N 1 ≤2N −1

$3.00
answered

Use induction to prove that
1+12+⋯+1n≤2n−1,1+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{n}} \leq 2
\sqrt{n}-1,1+2 1 +⋯+n 1 ≤2n −1,
for all n≥1n\geq 1n≥1.

Algebra Calculus Sequences and Series
Xander G
$5.00

answered


[MODULES] SHOW THAT Q/Z IS INJECTIVE AND NOT PROJECTIVE

$5.00
answered

Consider the set of all rational numbers Q as a Z-module, Z as a submodule of Q
and M:=Q/Z the quotient. Show that M is an injective module, but not a
projective module.

Abstract Algebra
Matchmaticians Alumnus
$25.00

answered


PROBABILITY MAXIMUM VALUE OF SAMPLES FROM DIFFERENT DISTRIBUTIONS

$25.00
answered

Assume you are sampling values at random from two normal distributions,
Distribution A and Distribution B. Both distributions have the same standard
deviation σ but slightly different means μAμ_AμA and μBμ_BμB , where
μA>μBμ_A>μ_BμA >μB . Let δμ=μA−μB\delta_\mu = μ_A-μ_Bδμ =μA −μB .

Statistics Probability Integrals
Cpcpcp
$20.00

answered


PROBABILITY THAT THE DISTANCE BETWEEN TWO POINTS ON THE SIDES OF A SQUARE IS
LARGER THAN THE LENGTH OF THE SIDES

$20.00
answered

Two points lie at random position on the border of a square of side length LLL.
What is the probability that the distance DDD between them is larger than
LLL? Plese see the attached image below. I nee...

Probability Statistics Geometry
Equationmaestro
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1 Answer


GAMBLER'S RUIN - CHANCE OF WINNING INCREASES BY DOUBLING THE STAKES

Pro Bono
1 Answer

A coin is tossed repeatedly, heads appearing on each toss with probability ppp.
A gambler starts with initial fortune k (where 0<k<N0 < k < N0<k<N); he wins one
point for each head and loses one point f...

Probability Statistics
Crashbandicoot
Pro Bono

2 Answers


MAXIMUM TRANSVERSE TIME FOR A PARTCILE MOVING ALONG A STRAIGHT LINE

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2 Answers

A particle is moving on a straight line, starts from rest, and attains a
velocity vvv after traveling a distance ddd. If the motion is such that the
acceleration was never increasing, find the maximum...

Calculus Word Problem Mathematical Physics
Bradz
$2.00

answered


COMPOUND INTEREST WITH MONTHLY ADDED CAPITAL

$2.00
answered

The thing is: I really don't like not being able to use only one formula to
deduct a monthly compound interest with and addition of ×$ every month.Usually,
I would be solving it by using the interest...

Math Finance Probability Algebraic Geometry
Narukisus
$10.00

accepted


DEMONSTRATING STRICT INEQUALITY IN FATOU'S LEMMA WITH SEQUENCES OF FUNCTIONS

$10.00
accepted

a) Use the sequence of functions (fn)(f_{n})(fn ) to establish that the
inequality in Fatou's lemma can be strict.b) Use the sequence of functions
(fn)(f_{n})(fn ) to establish that the motto of Fatou is false in g...

Measure Theory
Brandon 1212
$5.00

answered


GAME THEORY 100 VOTERS

$5.00
answered

a. Why is it not a Nash equilibrium for everybody to vote?b. Why is it not a
Nash equilibrium for nobody to vote?c. Find all the pure strategy Nash
equilibria in this game?

Game Theory
Bruhmoment
Pro Bono

1 Answer


UNIVERSITY LEVEL GEOMETRY QUESTION 

Pro Bono
1 Answer

Show that for any triangle ABC, the following inequality is truea^2 + b^2 + c^2
> (3)^1/2 max [ | a^2 - b^2 |, | b^2 - c^2 |, | c^2 - a^2 | ] Where a,b,c are
the sides of the triangle in the usual...

Geometry
Aaru
$15.00

answered


THE NONLINEAR SHOOTING METHOD FOR A PROBLEM WITH "MIXED" BOUNDARY CONDITIONS

$15.00
answered

See attached image.I don't necessarily need a worked solution - If someone could
explain how I would modify the shooting method to solve a nonlinear problem with
BC's of this type (ie the right hand B...

Numerical Analysis
Throwaway3
$4.00

answered


EVALUATE ∫C(2X3−Y3)DX+(X3+Y3)DY\INT_C (2X^3-Y^3)DX+(X^3+Y^3)DY∫C
(2X3−Y3)DX+(X3+Y3)DY, WHERE CCC IS THE UNIT CIRCLE.

$4.00
answered

Evaluate where CCC in the unit circle.Please show work. 

Calculus Multivariable Calculus Integrals
Elviegem
$8.00

answered


PROVE THAT (N2)2N−2=∑K=2N(NK)(K2){N\CHOOSE
2}2^{N-2}=\SUM\LIMITS_{K=2}^{N}{N\CHOOSE K}{K\CHOOSE 2}(2N )2N−2=K=2∑N (KN )(2K
)  FOR ALL N≥2N\GEQ 2N≥2

$8.00
answered

Use a combinatorial argument to show that                                      
                (n2)2n−2=∑k=2n(nk)(k2){n\choose
2}2^{n-2}=\sum\limits_{k=2}^{n}{n\choose k}{k\choose 2}(2n )2n−2=k=2∑n (kn )(2k
) for all n≥2.n\geq 2.n≥2.

Combinatorics Algebra Calculus
Ava Smith
$50.00

answered


PROVE THAT EVERY COMPACT HAUSDORFF SPACE IS NORMAL 

$50.00
answered

A topological space XXX is normal if every singleton is closed and for any
disjoint closed subsets A,B⊆XA, B \subseteq XA,B⊆X there are disjoint open
subsets U,VU,VU,V with A⊆UA \subseteq UA⊆U, B⊆VB \subseteq VB⊆V.Prove...

Real Analysis Functional Analysis
Theresa Lee
$47.00

answered


ABSTRACT ALGEBRA : COMMUTATIVITY AND ABELIAN PROPERTY IN GROUPS AND RINGS 

$47.00
answered

We have a Group  (G, ·) and Ring (R, +, ·) on the  set
R[G]:={(αg)g∈G∣αg∈R ∀g∈G  and  αg=0R  for  all  finitely  many  g∈G}R[G] :=
\left \{ (\alpha_{g})_{g\in G}| \alpha_{g} \in R  \forall g \in G \; and\;
\alpha_{g} = 0_{R}\; for \;all\; finitely\; many\; g \in G \right \} R[G]:={(αg
)g∈G ∣αg ∈R ∀g∈Gandαg =0R forallfinitelymanyg∈G}

Algebra Abstract Algebra
Darius
$10.00

answered


PROVE THAT P2−1P^2-1P2−1 IS DIVISIBLE BY 24 FOR ANY PRIME NUMBER P>3P > 3P>3.

$10.00
answered

Prove that p2−1p^2-1p2−1 is divisible by 24 for any prime number p>3p > 3p>3.
Can this be proved with an elementary argument? 

Number Theory
Mark W
$2.00

answered


TRYING TO FIGURE OUT PROBABILITY PROBLEM FOR A SERIES

$2.00
answered

So essentially I would have 10 items/figures, each with the option of being
either A or B (for simplicity).Each of the 10 figures has a set pre-determined
probability that A or B will happen, for exam...

Probability
Indgoat1
$15.00

answered


SHOW THAT ∫0Π2XTAN⁡XDX=Π2LN⁡2\INT_0^{\FRAC{\PI}{2}}\FRAC{ X}{ \TAN
X}DX=\FRAC{\PI}{2} \LN 2∫02Π TANXX DX=2Π LN2

$15.00
answered

I would like to prove that ∫0π2xtan⁡xdx=π2ln⁡2.\int_0^{\frac{\pi}{2}}\frac{ x}{
\tan x}dx=\frac{\pi}{2} \ln 2.∫02π tanxx dx=2π ln2. None of the integration
techniques seems to work.

Calculus Integrals Real Analysis
Sarah M
$40.00

answered


WEEK SOLUTION OF THE EQUATION UT+U2UX=F(X,T)U_T + U^2U_X = F(X,T)UT +U2UX
=F(X,T)

$40.00
answered

Derive the weak formulation of the partial differential equationwith the initial
value u(x,0)=u0(x)u(x,0)=u_0(x)u(x,0)=u0 (x).Please provide a detailed ans easy
to follow solution. 

Partial Differential Equations Differential Equations Elliptic PDEs
Theresa Lee
$7.00

answered


FIND XXX SO THAT (10C0A−B−1AXX2)\BEGIN{PMATRIX} 1 & 0 & C \\ 0 & A & -B \\
-\FRAC{1}{A} & X & X^2 \END{PMATRIX} 10−A1 0AX C−BX2 IS INVERTIBLE

$7.00
answered

Find xxx so that the matrix is invertible. Please show your work. 

Linear Algebra Matrices Algebra
Lilian00
$15.00

answered


A QUESTION IN PROBABILITY THEORY

$15.00
answered

If (Ω,A,P)(\Omega, \mathcal{A}, P)(Ω,A,P) is a probability space without atoms,
then for every a∈[0,1]a \in[0,1]a∈[0,1] there exists at least one set A∈AA \in
\mathcal{A}A∈A of probability P(A)=aP(A)=aP(A)=a. The question comes with a
hin...

Probability Measure Theory
Dannyboy990
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