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Advanced-Math Questions
6. Define S={q∈Q:−√3< q <√3}, where Q denotes the rational numbers. Prove that S can not...
What is the equation of the circle that touches the line g: 3x - 4y +...
1) Find the even and odd components of x(t)=e^(jt) 2) Determine whether x(t)=cost+sin√2 t is a...
PLEASE DON'T USE ANY OTHER PROOFS FROM POOFS BY CASES! USE DEFINITION OF ABSOLUTE VALUE! And...
Ralph has just borrowed 1320 dollars to purchase a new stereo, at a nominal rate of...
What are the equations of the lines that pass through the point P(-3,-2) and the circle...
Given: equation of circle k (x - 3)2 + (y - 2)2 = 36 and equation...
Pricing and demand will be taken as exogenously determined. Your goal in each part of this...
Let B be a group and b is in B. Given that the order of b...
Creat a Cayley Table for U24. (is U24 isomorphic to Z8?)
Let E be the e effective yearly rate, and Ec be the e effective continuous yearly...
Question2: Alice and Bob use the Diffie-Hellman key exchange technique with a common prime q =...
Using either proof by contraposition or proof by contradiction, show that: if n2 + n is...
Write a function of the form function [x1pts,x2pts] = unif_over_rect(a1,b1,a2,b2,n) which provides the coordinates (x1pts(i),x2pts(i)), 1...
Billy is walking from the front door of his house to his bus stop, which is...
Multiplicative Principle (in terms of sets): If X and Y are finite sets, then |X ×Y|...
Prove that C \ {0} is not simply connected.
3. Suppose G = <a> is a cyclic group of order 15 (i.e. a has order...
Given that y=e^x is a solution of the equation (x-1)y''-xy'+y=0, find the general solution to (x-1)y''-xy'+y=1.
Prove that the only ring homomorphism from Q (rational numbers) to Q (rational numbers) is the...
1. (5) The half-life of radium is 1700 years. Assume that the decay rate is proportional...
Prove that for all positive integers n, (1^3) + (2^3) + ... + (n^3) = (1+2+...+n)^2
There are four types of drinks. 15 drinks are served. In how many, the drinks can...
Let A and B be 3x3 matrices with det(A) = 2 and det(B) = -3. Find...
Prove that in a collection of 19integers, there are at least two of them whose difference...
The triangle ABC, which is not drawn to scale, represents a roof space with a span...
A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly...
Provide counterexamples to each statement: a)Suppose a, m, n ∈ N and both m and n...
How to come up with 3x2 linear systems that have infinitely many solutions? How do I...
If p = 2k − 1 is prime, show that k is an odd integer or...
The diagram below shows 6 vectors: a, b, c, d, e and f. Each side of...
The floor of a real number n, writtten ⌊n⌋, is the greatest integer which is ≤...
Let a,b be any two elements of a group. Prove that' (ab)-1 = b-1a-1
Let G be a group and define the center (of G) Z(G) = {a ∈ G...
Let G be a group. Prove that following statements are equivalent. a.) G is commutative b.)...
A number n is divisible by 7 if, when we form an alternating sum of blocks...
4 linear equation Q1: y=5-0.8a Q2: y=10-b Q3=Q1+Q2 Q4:y=0.4c If a+b=c, then which point does Q4...
NON EUCLIDEAN GEOMETRY Prove the following: Claim: Let AD the altitude of a triangle ▵ABC. If...
Prove the following: Claim: Consider a convex quadrilateral □ABCD. If σ(□ABCD) = 360, then σ(▵ABC) =...
Prove why the following statement is true: A determinant is linear as a function of each...
Let a < b, a, b, ∈ R, and let f : [a, b] → R...
Assume A is an invertible matrix 1. prove that 0 is not an eigenvalue of A...
Differential Equation: Determine two linearly independent power series solutions centered at x=0. y” - x^2 y’...
Anthony wants to put solar panels on the top of his house to use to heat...
A relation R is called atransitive if aRb and bRc implies cRa. Show that R is...
Using Fermat’s Little theorem, find the multiplicative inverse of 4 in mod 13. Show your work....
Prove that, if f(x) has a limit as x->a, then the limit is unique. In other...
Discrete Math Most important is c) and e) and f) Statements with nested quantifiers: variables with...
If v1 and v2 are linearly independent vectors in vector space V, and u1, u2, and...
In Problems 14–21, does the function have a global maximum? A global minimum? 14. f(x, y)...
Prove the Basic Principal of Difference of squares: If x2 ≡ y2 (mod n) and x...
solve by separation variable 5, yy'=xe^2+y^2 7, y'=x^2 y/1+x^3 xsiny.y'+cosy
Let T ∈ L(R2) be the linear transformation T(x1, x2) = (3x1 + 2x2, −4x1 −...
(1 point) Consider the DE 7y′′−112y=0 . Check which of the following series functions is a...
prove that a compact set is closed using the Heine - Borel theorem
Discrete Maths ( Please use a concise and clear explanation as well because these I tend...
3. Closure Properties (a) Using that vector spaces are closed under scalar multiplication, explain why if...
What is a subset of pentagon D5 that is a subgroup? Why?, then give an example...
1. From many long years of experience, the weather bureau knows that the temperature on the...
Consider a manufacturing cell in company ABC that repairs defective computers. Computers arrive to the cell...
a) Show that if K = ℤ2 then q = x3 + x + 1 ∈K...
Find the general solution to the given differential equation. 1+(1+ty)e^ty+(1+t^2e^ty) dy/dt=0
Solve the system using the method of eigenvalues and eigenvectors: ? ′ = ( 2 1...
At one point, certain U.S. Treasury bonds were callable. Consider the prices in the following three...
If A is a non singular n × n matrix show that: a) adj(A) is non...
Prove using the definition of truth that for any first-order formula φ, φ is valid iff...
Second-Order Linear Non-homogeneous with Constant Coefficients: Find the general solution to the following differential equation, using...
Show that (Z15, (+)) is a cyclic group. Find all generators of this group. Identify the...
1. The company has agreed on an 8 character password format, comprised of upper case letters...
3) If A = 3 1 and B = 1 7 0 -2 &
For this Pause Problem, pick out a sampling strategy and give me a study idea where...
Instruction: Determine the region area in the first quadrant of the circle of radius 3 and...
can we use fermat's little theorem to prove a number is prime?
Prove the Complement of Difference Lemma: ( A − B )' = A' ∪ B using...
B. Customers arrive at a restaurant according to a Poisson process. On the average, a customer...
Prove that 13 + 23 + 33 + · · · + n 3 = (1...
Prove deductively that for any three consecutive odd integers, one of them is divisible by 3
#mod reset; param T > 0, integer; set IND := 1..T; set END := 0..T+1; param...
Consider the following problem. Maximize Z = 2x1 - x2 + x3, subject to x1...
Prove by mathematical induction that for all odd n ∈ N we have 8|(n2 − 1)....
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