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Basic Algebra

Arithmetic Sequence

I am trying to determine and prove the general law for the following sequence: I would like to express it in notation. 1+2=3 4+5+6=7+8 9+10+11+12=13+14+15 16+17+18+19+20=21+22+23+24

Energy Methods

Select and justify the use of energy methods to molve motion problems.. Please see attached.

Simplify Seven Trigonometric Expressions

1. [sin(x+b) + cos(x+b)]/[cos(x+b)-sin(x+b)]= 2. cos^2(x+b)-cos^2(x-b)= 3. tan x + cot 2x = 4. tan (45 + x) -tan (45 -x)= 5. tanx - cotx + cot 2x = Plus two more...

24 Problems : Word Problems, Simplify, Area, LCM, Solve for X and Hypotenuse

Divide (12a squared - 25a -7 divided by (3a-7) (x cubed - 6x sqyared + 7x -2 divided by (x-1) A circle has a radius of 10 inches. Find the increase in area that occurs when the radius is increased by 2 in. Round to the nearest hundredth. An object is released from the top of an building 320 ft high. The initial velocity

Quadratic equation and equilibrium concentration

The Quadratic Equation. Consider the reaction N2O4(g) = 2 NO2(g) at 25 C in a 5.00-L container. Use the quadratic equation to determine the equilibrium concentrations of the N2O4 and NO2 if the initial amounts are 0.100 mol N2O4 and 0.00 mol NO2. The value of the equilibrium constant for the reaction is 4.63 x 10-3 at 25 C

Using a Quadratic Equation

The Quadratic Equation. Question: Consider the reaction 2 COF2(g) = CO2(g) + CF4(g) at 1000 degrees Celsius in a 5.00-L container. Use the quadratic equation to determine the equilibrium concentrations of all reactants and products if the initial amounts are 0.105 mol COF2, 0.220 mol CO2, and 0.055 mol CF4. The value

Congruences : Primes, Inverse Modulo, GCD and Wilson's theorem

Please assist me with the attached congruence problems (hint: use Wilson's Theorem) a)Prove if a,b,c Z, N and gcd (c, ) = , then ac bc(mod ) if and only if a b (mod ). b) Let a Z, N, and p > 2 be a prime. Prove that a is its own inverse modulo p if and only if a 1 (mod p ). C) Let a,b Z, N .prove that ax

Metric Conversions : km^2 to mm^2

I need the step by step answer to how to come to the answer given in the practice test. Thanks. Problem (also attached): 36 km² to mm² = ?

Solve: Formula Weight

Question: Determine the formula weight of K3PO4. a. 134.1 amu b. 185.1 amu c. 212.3 amu d. 173.2 amu e. 228.3 amu

Simplify the expressions.

Please solve the attached expressions. Please see the attached file for the fully formatted problems.

Simplified Radical Expression

I received your response to my problem the square root of 12 times the square root of 2 minus the square root of 7. I did not indicate that the square root of 2 minus the square root of 7 was in parenthesis. I am having difficulty understanding this concept, and my final exam is tomorrow.

Convert Equation into given form (numerator dependent on s)

[(Kp * s + Ki)/s] * (K * Km) / [s[(Ls+R)(Js+b) + K^2m)]] I want to get the above into the form of d / [s^3 + a s^2 + b s + c] Please give complete solution. I want the numerator dependent on s. All the other values are given other than s. I just need it into that form.

Quadratic function

Questions (also attached): Graph each equation and state its domain and range. 27) g(x)= x 2 + 2 28) f(x)= x 2 - 4 32) y= 2x 2 + 3 Graph each square root and state its domain and range. __ 34) g(x) = √ x - 1 _____ 36) f(x) = √x + 1

Modern algebra - Extension field

Please see attachment. P/S: To show subfield please show a) closed under addition, and multiplication b) additive identity and additive inverse c) closed under reciprocal

Instabilities

Please work on question A1 from this practice exam. A thin layer of water thickness d=0.5cm is heated from below. The bottom of the layer is held at temperature... Please see attached.

Word Problem : How much will each party pay?

The Gooch family, the McCoy family, a bachelor and a couple without children have decided to buy a summer home together. They will divide the purchase price according to the size of each family. The house costs $264,000. The smaller of the two families- the McCoys - have 2 children and will carry one third of the cost. The large

Algebra

( 3 x - 5) ( x +1) ( x - 6) = 0 ( 3x - 6) (3x - ½ ) = 0 Please see attached for full question.