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Consider the R²-R function f defined by f(x,y)=x²+2y²-x²y.


Show that f has two saddle points

Prove that a ring with one consists only of zero if and only if 1 = 0


Consider the R²-R function f defined by f(x,y)=e^xIn(1+y).


Find the third order Taylor polynomial of f about the point (0,0)

Present a theorical explanation for pyromania as motitive for arson

6. Nitrous oxide, NO, is sometimes used in dentistry. It is produced when

ammonium nitrate(NH,NOg) decomposes in the reaction below.

(NHANO3) - N20 + 2H20

a. How many moles of NH,NO; are required to produce 5.6 moles of Ng0?

b. How many grams of NO is that?


5. How many moles of CO, (carbon dioxide) are produced when 5.5 moles of Oz

(oxygen) is used in the reaction below?

26gH18 + 2502 - 16CO2+ 18H20

B. How many grams of oxygen is that?


4. How many moles of Feliron)are produced with 3.45 moles of Mg(magnesium)?

3Mg + FezO - 2Fe + 3MgO

b. How many grams of Mg is that?


2. How many moles of Na2O (sodium oxide) are produced if 1.5 mol of Fe(iron) is

produced in the following reaction:

6Na + Fe2O3 - 3Na,O + 2Fe

3. If 4.3 moles of CaC2 (calcium carbonide) are used up in the reaction below, how

many grams of HO(water) are needed?

CaC2 + H20 - CaH2 +Ca(OH)?


1. Hydrogen gas can be produced through the following reaction

Mg + 2HCI - MgCl2 + H,

a. How many grams of HC|(hydrochloric acid) are used by the reaction of 3.50

moles of Mg (magnesium)?


Describe if the following reaction is spontaneous or non-spontaneous based on enthalpy, entropy and Gibbs energy:


H = 8457J/mol,


S = 546J/K*mol, and


G = 432J at room temperature


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