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# Basic Algebra

### Cobb-Douglas Economics

1. Let Y=L^αK^1-α, 0<α<1; let y=lnY, l=lnL, k=lnK. a.Show that this production function is linear in its natural logarithms. b.Show that the instantaneous percentage change in out put is the weighted sum of the instantaneous change in L and K, with weights α and (1-α) 2. Suppose that the production function in Questio

### Integral Calculus : Inverse function of limited quadratic equation.

F(x) = 2x^2 - 8x, where x = or > 2 Even though I know that this particular quadratic equation does have an inverse since the domain is limited, I don't know how to figure out the formula for the inverse for a quadratic equation. I don't know how to solve for x, since there are two different x's. Thank you!

### Calculate the discriminant

5. For a quadratic equation of the form, ax2 + bx + c = 0, how do you calculate the discriminant? What information about the equation can we learn by calculating the discriminant?

### Exponential and Logarithmic Functions Word Problem

Use the formula R=6e^(12.77x), where x is the blood alcohol concentration and R, given as a percent, is the risk of having a car accident. What blood alcohol concentration corresponds to a 50% risk of a car accident?

### Contrast and Discuss Asymptotes and a Real-Life Example of an Exponential Function

One of the archaeologists you interviewed for your article is graphing asymptotes to illustrate the data generated through carbon dating the half-life of fossil specimens. Help him with his work by solving these problems: 1. Explain and contrast the types of asymptotes considered for rational functions. 2. B

### Exponential and Logarithmic Equations and Word Problem

1. Write the equation in its equivalent logarithmic form. 10^2 =y 2. Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. log5 (x+4) - log5 (x+1) 3. Solve the equation. Give an exact

### Routh Stability Criterion

Consider the following characteristic equations: (a) s^3 + 2s^2 + s +2 = 0 (b) s^5 + 2s^4 + 24s^3 + 48s^2 - 25s - 50 = 0 Using Routh stability criterion, determine whether the above systems are stable or unstable.

### Algebra : Percent Increase and Decrease, Slope, Y-intercept, Trends and Trendlines

1. Evaluate the following: e = &#61629;-2.7&#61629;= 40 = LN 2 = (1.01)365 = (-8)2/3 = 5-3/2+1 = 2. A stock price went down by 10%, and subsequently went up by 10%. If the final price was \$20, what was the original price? (Please show your thinking here.) 3. In a p

### Intermediate Algebra : Solving Equations and Inequalities and Maximum Area of a Rectangle Given Perimeter

Solve the equation by the method of your choice. Simplify solution, if possible. 1. (3x + 5)2 = 6 Solve the following problems. 2. You have 188 feet of fencing to enclose a rectangular region. What is the maximum area? 3. An object is propelled vertically upward from the top of a 112-foot building. The quadrat

### Intermediate Algebra problems

Intermediate Algebra problems in radicals, radical functions, and rational exponents. (See attached file for full problem description) These algebra problems all relate to radicals, radical functions, and rational exponents. Simplify the expression. Include absolute value bars where necessary. 4&#8730;t4

### Working with Logarithms

Explanation and breakdown of Logs (See attached file for full problem description with proper equations) --- Logarithms: a) Using a calculator, find log 10000 where log means log to the base of 10. Answer: b) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In comput

### C program to find the roots of a quadratic equation

This program is written is C, not C++. File should have a .c extension. Make broad use of comments so that I can understand the program. This program should be written with the use of "if" statements, not loops. I have a similar assignment to turn in, so the instructions must be thoroughly followed. Details about what to

### Poverty, Income Inequality, and Discrimination

I need assistance attempting to solve my study questions. --- Study question: In 1987, there seemed to be bipartisan agreement that Aid to Families with Dependent Children should be transformed into a vehicle for education, training, and work. In what sense is work the solution to dependency? Can training and job placemen

### Two Problems

8. A mother is four times as old as her duaghter. IN 20 years, she will be twice as old as her daughter. How old are mother and duaghter now? 9. Find the equation of the line that is perpendicular to the line 4x-3y = 15 AND has the same y intercept as the line that is parallel to 4x-3y =15 and passes through the point (24

### Solve the equation by any means

Solve the equation by any means. Find the exact solutions when possible and approximate ones otherwise. 45. 2sinx = 1 55. 2 sin²x - 3 sin x = 2 56. cos 2x = cos x Hint first use an identity 57. sec²x + 3 tan²x = 13 58. sec² = 4 tan x - 2 59. 2 sin²x + sin x - 2 = 0

### Logarithms and Composite Functions

Pick best answer: For the given pair of functions 1.) f= 5x-1 and g=x^2, find fog(2) a. 81 b. 19 c. 5x^2-1 d. (5x-1)^2 2.) f= 2x^2 and g=x+1, find gof(x) a. gof(x) = 2(x+1)^2 b. gof(x) = 2x^2 +1 c. gof(x) =2x^2 +x +1 d. gof(x) = not given 3.) Simplify: 10^log(1000) a. 3 b. 1,000 c. -3 d. 1,000,000

### Solve the inequality and write the solution set in interval notation: (3/5)x + (2/3)(x - 5) < x

Solve the inequality and write the solution set in interval notation: (3/5)x + (2/3)(x - 5) < x

### Story problem

This is a intermediate algebra problem: A company that manufactures hospital beds has fixed monthly costs of \$225,000. The average cost per bed, C, for the company to manufacture x beds per month is modeled by the formula C = 550x + 225,000 ------------------- x How many hospital beds can be m

### Solving Rational Equations - Intermediate Algebra Problem

Solving rational equations, this is a intermediate algebra problem. x = -2x + 2x-3 ------ ------- -------- 2x+2 4x+4 x+1.

### Index Numbers, Ratios and Price Index

In 1990, a price index based on 1980 = 100 had a value of z. During 1990, it was rebased at 1990 = 100, and in 1998 the new index stood at 112. If the total price movement between 1980 and 1998 was an increase of 40%, was was the value of z in 1990, that is, before rebasing? The answer given was, Using ratios, 1.12 x

### Group Theory : If H is a subgroup of G, let N(H) = {g belongs to G|gHg^-1 = H}. Prove that H is normal in G if and only if N(H) = G.

Modern Algebra Group Theory (XLVIII) Normal Subgroups of a Group

### Normalizer of a Subgroup of a Group: If H is a subgroup of G, let N(H) = {g belongs to G|gHg^-1 = H}. Prove that N(H) is a subgroup of G.

Modern Algebra Group Theory (XLV) Normalizer of a Subgroup of a Group

### Intersection of a Subgroup and the Normal Subgroup of a Group

Please address the following question: If H is a subgroup of G and N is a normal subgroup of G, show that H intersection N is a normal subgroup of H.

### Solve Equations, Factor Monomials & Find Greatest Common Factor

Solve each equation by performing the same inverse operations to both sides and show steps. 1- 42+7x=0 2- -13r-92=77 3- 757=25n+132 4- x/4-13 =15 5- -13m-348=-23 6- t/13-56=-72 7- 47=-18+ y/8.2 8- -21+a/4=3.4 9- 240=-2.1-6h 10- 3(x+1)=9 11-17-k=-99 12- 6{1/3+m}

### Solving Equations and Writing Equations from Word Problems

Solve the equations: 1- 3.14 = Z/-3.7 2- -4.7t = 12.22 3- m+2.7 = -9.3 4- -38=z minus 20.5 Write an algebraic equation and solve. 1- Years of stress from his BLA students have reduced the number of hair on Mr. Sit's head to 7560 strands. if he lost 963 strands during his time at BLA, how much hair did Mr

### Write Expressions with only Positive Exponents, Number Lines

1- Write the expressions with only positive exponents. 1-p to the power of negative 4 time q to the power of negative 7 time p to the power of 3 2-27a to the power of negative 3 b to the power of negative 11/9 a to the power of 6 b to the power of two c 2- Use a number line to order the integers from least to greatest.

### Factoring Monomials, Greatest Common Factor, Lowest Common

1-Factor the monomial into its smallest factors. a-14xy to the power of 2 z b-40n to the power of 3 m to the power of two 2-Find the GCF and the LCM 1-24c to the power of two d to the power of two, 48c to the power of 3d 3- Simplify each fraction a- 13ab/26a b- 42xyz to the power of 4/36y to the power of tw

### Group Theory : Show that the intersection of two normal subgroups of G is a normal subgroup of G.

Modern Algebra Group Theory (XXXVIII) Subgroups of a Group Normal

### College Algebra : 'Together and Alone' Word Problems, Simplifying Complex Expressions (5 Problems)

30. Assume that Joe take 6 hours working alone and Sam takes 8 hours working alone, how long does it take the, to do it together? 54. (1 +3i) (2-5i) 64. i(3-4i) (6+4i) 84. 14 + 5i divided by 3 +2i 94. 5 divided by 9i

### Solve: Normal Subgroups of a Group

Modern Algebra Group Theory (XXXVII) Subgroups of a Group Normal Subgroups of a Group If N is a normal subgroup of G and H is any subgroup of G, prove that NH is a subgroup of G.