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Advanced-Math Questions
f(x) = 3x^4-4x^3-3x^2-x-2 find the rational roots by the rational root test
Consider the non linear system X dot = y + x(x^2 + y^2 - 1) *...
(1) Starting with the simple model of constant acceleration for a falling body is 9.8 m/sec,...
From Beginning Logic by E.J. Lemmon 1.2.1: Find proofs for the following sequents, using only the...
The diagram shows a toy. The shape of the toy is a cone, with radius 4...
Prove the statement For all real numbers x, if x − ⌊x⌋ < 1/2 then ⌊2x⌋...
What can be said about a space curve with constant acceleration?
Show that: There are continuum many pairwise disjoint subsets of R each similar to R.
Except for the first two terms,each term of the sequence 1000,x,1000-x,... is obtained by subtracting the...
What is the relation between a Taylor series approximation and gradient descent algorithm? If we take...
A small store has a single phone line. Calls to the store are well modeled by...
Prove that Z32 with the operations of [+] and [*] as defined below is not an...
Given any integer n, if n > 3, could n, n + 2, and n +...
Give a definition of a linear functional, and at least two examples of the functionals.
Show that a continuous injective map f: (0, 1) to R is an embedding.
Define T : M2×2(R) → M2×2(R) by T(A) = A − A^t . a) Determine the...
Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R4 spanned by...
Let A and B be two sets, with | A | = m, | B |...
Suppose you have 7 full wine bottles, 7 half-full, and 7 empty. You would like to...
find all solutions e^(2z) = -4i
the quantity of newspapers produced daily at a certain press is approximately normally distributed with mean...
Let (V, C) be a finite-dimensional complex inner product space. We recall that a map T...
In a survey of 250 employees of a company regarding their 401(K) investments, the following data...
A treatment plant had a flow of 5.5 mgd and the desired chlorine dosage is 3.5...
Use the formal definition of derivative to prove f(x) = 10|x| is not differentiable at a=0.
Develop an amortization schedule for the loan described. (Round your answers to the nearest cent.) $50,000...
Let f: Z -> Z be a function given by f(x) = ⌈x/2⌉ + 5. Prove...
Find the number of binary strings of length n with at most 5 zeros.
(a) You are given the spot rates s5 = 3% and s10 = 5% . If these are the only...
They choose items that amount to $1,700.00. The store has 2 options for purchasing: I. financing...
Use the intermediate value theorem (only) to prove that any real polynomial of odd degree has...
A function f : A −→ R is uniformly continuous and its domain A ⊂ R...
subtract 5e^0.2i from 6 e^2.3i express the answer in polar form
The following table shows the population in a town in the given year. Year 1960 1970...
INSTRUCTIONS: Use natural deduction to derive the conclusion in each problem. Use conditional proof or indirect...
Use natural deduction to derive the conclusion in each problem. Use conditional proof or indirect proof...
solve the differential equations by laplace theorem A sphere of 3cm in diameter will be cooled...
solve the differential equation y'=y/x+3x^2+x
Build a bijection between N and Q.
If G is an n-vertex r-regular graph, then show that n/(1+r)≤ α(G) ≤n/2.
dx dt = y − 1 dy dt = −3x + 2y x(0) = 0, y(0)...
) In the following problems, let ? be a cycle of length ?, say ? =...
(D + 1)x + (D − 1)y = 4 5x + (D + 4)y = −1...
For integer n ≥ 1, let h(n) be the number of length n words consisting of...
Find the explicit general solution of: (x^5 + 6y^5) - 5xy^5y' = 0
solve the bernqoulli equation dy/dx+xy+xy^2=0
y^4 - y = 0 IVP (Initial Value Problem) y(0) = 0 y'(0) = 1 y''(0)...
find the general solution to y''+4y'+4y=4x^2+6e^x
solve the differential equation (2y^2+2y+4x^2)dx+(2xy+x)dy=0
Suppose u and v are two vertices in a graph G with ecc(u) = m, ecc(v)...
prove that every graph has an even number of odd nodes
Let A ⊆ R uncountable. Prove that A′ ≠ ∅.
Prove the mean value theorem
Prove the folllwing case and use the Contrapositive approach to the proof. If n^2 + 2...
Show that if X is an infinite set, then it is connected in the finite complement...
TOPOLOGY Prove that a subspace of a first countable space is first countable and that countable...
2. Suppose [a, b] is a closed bounded interval. If f : [a, b] → R...
Consider the ring R = Z∞ = {(a1,a2,a3,···) : ai ∈ Z for all i}. It...
For which subspaces S in R^2 is there a 2x2 matrix A for which row(A)=col(A)=S?
suppose 13% of the population are 64 or over, 30% of those 64 or over have...
1 Shaky Party A host and a hostess invited 4 couples to a party and at...
Matrix A= -2 1 0 2 -3 4 5 -6 7 vector u= 1 2 1...
find the power series representation centered at a=0 of a.) f(x) = x/(5+7x) b.) f(x) =...
Let Sb be the standard basis for R^6 . Construct a set S, which is a...
Let G be a graph where every vertex has odd degree, and G has a perfect...
Let φ:G ——H be a group homomorphism and K=ker(φ). Assume that xK=yK. Prove that φ(x)=φ(y)
A computer password consists of: • letters {a, A, 6, B, ...,2,Z}, • digits {0, 1,...,9),...
State the Pythagorean Identity, and (using a diagram) show why it is true. • Explain how...
Use the principle of Mathematics Induction to prove that for all natural numbers 3^(3n)-26n-1 is a...
Let F be a field. It is a general fact that a finite subgroup G of...
Can you please solve this question, Using separation of variables, write down a complete list of...
Lomustine is used in the treatment of brain tumors. The recommended dose is 130 milligrams for...
Which of the following congruences have solutions? a) x2 Congruent 7(mod 53) b) x2 Congruent 14(mod...
Let X be a topological space. Let S and T be topologies on X, where S...
A mass of 3 kg stretches a spring 61.25 cm. Supposing that there is no damping...
Let E be a field of characteristic p, where p is a prime number. Show that...
need asap please - will rate right away! find the image of v and the preimage...
Let C be a normal subgroup of the group A and let D be a normal...
Let H, K be two groups and G = H × K. Let H = {(h,...
1) Let G be a group and N be a normal subgroup. Show that if G...
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