Recall the following definition: For X a topological space, and for A ⊆ X, we define the closure of A as cl(A) = ⋂{B ⊆ X : B is closed in X and A ⊆ B}. Let x ∈ X. Prove that x ∈ cl(A) if and only if every neighborhood of x contains a point from A. You may not use any definitions of cl(A) other than the one given.
In: Advanced Math
1. Find absolute max and min of f(x,y)= x^2- xy + y^2 +1 on the closed triangular plate in the first quadrant x=0, y=4, y=x
2. Given position of a particle by π (t)= Cos2ti + 3 sin2ti, Find the particle velocity and acceleration at t=0
In: Math
At a certain temperature, the ?p for the decomposition of H2S is 0.844. H2S(g)↽−−⇀H2(g)+S(g) H 2 S ( g ) ↽ − − ⇀ H 2 ( g ) + S ( g ) Initially, only H2S H 2 S is present at a pressure of 0.168 atm 0.168 atm in a closed container. What is the total pressure in the container at equilibrium?
In: Chemistry
Develop two examples each of closed-ended questions and open-ended questions. Ask both questions to at least five of your friends and document the responses. Which type of question was easier to control? Why? Which type of question provided more information? Why? How might you use both types of questions in a sales presentation?
In: Operations Management
ECO 252 - Macroeconomics
In a closed economy (in equilibrium), assume that real GDP is $15 trillion, government purchases are $1.3 trillion, public saving is $0.5 trillion, and national saving is $2.2 trillion. Calculate the following:
a. Taxes
b. Consumption
c. Investment
d. Private saving
e. The government budget deficit or surplus.Precise which one.
In: Economics
How to calculate suitable spring rate for oscillating forced closed cam and follower having simple harmonic motion so that it will always in contact with cam.Also at which speed it will loss contact with cam and how much distance it will lift-off from cam.Please explain in detail with example using SHM equations and cam follower drawing with resolve forces.
In: Mechanical Engineering
Calculate the expected life of N (# of cycles) in a compression spring with the specifications.
Material: 302 Stainless Steel
End type: closed
Overall Length: 2"
OD: 0.5"
ID: 0.406"
Wire Diameter: 0.047"
Wire Shape: Round
Compressed Lenght: 1.35"
Maximum Load: 3.8 lbs
Rate: 5.85 lbs/in
RoHS: Compliant
In: Mechanical Engineering
The Law of Biot-Savart shows that the magnetic field of an infinitesimal current element decreases as 1/r^2. Is there anyway you could put together a complete circuit (any closed path of current-carrying wire) whose field exhibits this same 1/r^2 decrease in magnetic field strength? Explain your reasoning.
In: Physics
4. Other things equal, what effect will each of the following changes independently have on the equilibrium level of real GDP in the private closed economy? 1. A decline in the real interest rate. 2. An overall decrease in the expected rate of return on investment. 3. A sizable, sustained increase in stock prices. (answer in your own words)
In: Economics
] Consider the following dynamic equations: ?1̇ = −2?1 + 6?2 ?2̇ = −4?1 + ?(?) ?(?) = ?1 The control is obtained through state feedback with ?(?) = −?1?1 − ?2?2 + ?(?), where ?(?) is reference input. Find the ?1 and ?2 if the closed-loop system has a natural undamped frequency of 10 rad/sec and a damping ratio of 0.707.
In: Physics