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# Basic Algebra

### Quadratic formula - error analysis

Improving the Quadratic Formula. Show that these roots can be calculated with the equivalent formulas... (See attachment for full question including Hint)

### Manipulating the Quadratic Formula

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. 12. Improving the quadratic formula... Please see attached.

### Taylor polynomial

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Find the Taylor polynomial of degree n=4 for each function expanded about the given value... Please see attached.

### Taylor series

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Consider the function... a. Expand f(x) in a Taylor series about the point x=0 b. Find an expression for the remainder... Please see attached.

### GED practice - LCM, GCF, number patterns

Write the next two terms in the pattern 6,250 1,250 250 50 Find the GCF 140, 180 Find the LCM 7, 11, AND 21

### Equations and word problems

1- suppose you have 45 muffins. how many muffins are left after you give a friend 1/5 of them? 2- a baker at rod's bakery misread the directions and used 5 3/4 cups of flour in a recipe. it was 1 3/4 times too much flour. how much flour should the baker have used? 3- solve the equation. check the solution: x/3=

### Factor the Expressions

(r+6)^3-216 then 7(3k-1)^2+26(3k-1)-8.

### Basic Algebra Review

4. By choosing specific nonzero values of z1 and z2, show that ... is not always valid when log is replaced by Log. Please see the attached file for the completely formatted problems. Others are attached.

### Roots of a Quadratic Equation: Sinx and Cosx

If sinx and cosx are the roots of the equation ax^2 + bx + c = 0 then prove that a^2 - b^2 + 2ac = 0.

### Sequences of Transformations and Finding Domains

I need a sequence of transformations that will transform the graph of 'f' into the graph of 'g' where f(x)=x[squared]+1 and g(x)=(x+3)[squared]-4. m(x)= [the sqare root of] (4x+12) [divided by] (2x[squared]-7x+5). (I need to find the domain of m, using interval notation).

### Superincreasing Sequence and Prove that Expression is Prime

1) Let S= {b ,b ,...........b } satisfies b j+1 >2b j for all j =1,2,3,.......n-1. Prove that S is a superincreasing sequence. ≡ 2) Prove that n E N with n ≥ 3 is prime if and only if there exists an integer m such that m^(n-1) ≡ 1 (mod n)^((n-1)/q) but m is not ≡ ( mod n) for any prime q| (n-1)

### Use of Calculator : Log Function

Please explain how I make this work via my TI-30 (or any calculator for that matter). I dont understand how to "punch" it in. 10 Log 1.9X10^-4 / 1X10^-12 the answer is 82.8 Thank you for helping me get to this answer.

### Algebra Application Word Problem : Relative Rates, Speed and Time

Bonnie drove 540 miles in three times the time it took Buffy to travel 135 miles. Buffy's speed was slower than Bonnie's by 15 miles per hour. Find the rate and time of each.

### A Basis for an Eigenspace

Without computing the characteristic polynomial, explain why the matrix A below has 0 as eigenvalue; then find a basis for the corresponding eigenspace. A = 1 -1 1 -1 1 -1 1 -1 1.

### Growth Rate of Functions

Function A Function B ------------ ----------- n^1/3 6 log(n) is A=O(B) ? Yes/No is A=o(B) ? Yes/No is A=Big Omega(B) ? Yes/No is A=Small Omega(B) ? Yes/No is A=Theta(b) ? Yes/No Also the same for the following pai

### Polynomial division

Please walk me through this. 6x^4 + 9x^3 + 2x^2 - 8x + 7 / 3x^2 - 2

### Simplifying Various Algebraic Expressions

Please simplify the attached expressions.

### Simplify the Expression: {(a-2/3a^4)/(5a-10/27a)}

Please solve: {(a-2/3a^4)/(5a-10/27a)}. See the attached file.

### Arithmetic Sequences General Law

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

### Two distinct integers in A whose sum is 104

Let A be any set of twenty integers chosen from the arithmetic progression 1, 4, 7, ...,100. Prove that there must be two distinct integers in A whose sum is 104.

### Energy Methods Motion

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...

### Word Problems, Simplify, Area, LCM, Solve for X and Hypotenuse

Divide (12a squared - 25a -7 divided by (3a-7) (x cubed - 6x squared + 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

### Derivatives and Integrals of Exponential and Logarithmic Functions (24 Problems)

1. Find the derivatives for the following functions ("^" means "to the power of", sorry I can't do double exponents on my keyboard) : a. f(X) = 100e10X b. f(X) = e(10X-5) c. f(X) = e^X3 d. f(X) = 2X2e^(1- X2) e. f(X) = 5Xe(12- 2X) f. f(X) = 100e^(X3 + X4) g. f(X) = e^(200X - X2 + X100) 2. Fi

### Functions : Graphs, Limits, Continuity, Equation of Line from Two Points, Equation of Line from Slope and a Point and Linearity (15 Problems)

1. Take the function f(X) = (X-1)/X a. What does this function equal when X = 0, X = 1, and X =2 ? b. How about when X =100, X = 1000, and X = 10,000? c. Describe in words what a graph of this function would look like. d. What would you say the limit of this function is as X approaches infinity? You can use logic or

### Equation Given Two of the Complex Conjugate Roots

The equation x^4 - 18x^3 + 121x^2 - 368x + 420=0 has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of : x^4

### Solve using the quadratic equation.

1) -2X^2 - 1 = 0 2) &#8730;X + 4 = 0

### Prove using Mathematical Induction

If x > 1 is a given real number, then for every integer n > or equal to 2, (1 + x)^n > 1 + nx.

### 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