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Basic Algebra

Creation of Quadratic Equations

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c

Algebra Basics, Equations, and Mathematical Models

Need comparison. 1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imagina

Sturm-Liouville Problems : Eigenvalues, Eigenfunctions and Square Norm

Please help with the following problems. 1. Find the eigenvalues and eigenfunctions of the boundary- value problem y''+lambay = 0 , y(0) = 0 , y(pi/4) = 0 ( n = pi) 2. Find the eigenvalues and eigenfunctions of the boundary- value problem y''+(lamba+1) y = 0 , y'(0) = 0 , y'(1) = 0 3. Find the square norm

Quadratic equations

1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i). Questi

Ellipses and Parabolas

See the attached file. 1. Find the equation of the parabola with vertex at the origin, that passes through the point (-6,4) and opens upward. X=1/9y^2 Y=-1/9x^2 X=-1/9y^2 Y=1/9x^2 2. Find the equation for the parabola with the given vertex that passes through the given point: vertex: (-5,5) point: (-3,17)

Applications of Logarithmic Equations : Earthquakes and the Richter Scale

The intentisty level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weaket possible tremor. Research how earthquakes are measured. What is the formula for measuring earthquakes? ? Why is a 7.0 earthquake ten times stronger than

Radical and Rational Exponent

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

Rational Expressions Applications Word Problem

In a cancer research lab, you are observing the growth of cancer cells in two specimens, A & B. Specimen A presently has 2160 cells and specimen B has 1200 cells. After recording data for several days, you later determine that the number of cells in specimen A, N(A), is growing ny the formula: N(A) = 24t^2 + 588t + 2160 w

You have recently published a research article on the impact of air friction on falling bodies. In your article, you have noted that the deceleration due to friction is a function of the ratio of the volume of the object to the total surface area of that object.

You have recently published a research article on the impact of air friction on falling bodies. In your article, you have noted that the deceleration due to friction is a function of the ratio of the volume of the object to the total surface area of that object. a. Express this ratio for a rectangular prism of length L, widt

Radicals and Rational Exponents

Radical and rational exponent notation are two ways to show the same process. ? Explain the similarities between radicals and rational exponent notation. ? Provide at least two other examples of mathematical notation or wording denoting the same process.

Algebra : Solving Equations and Inequalities

1) What is the solution for x (7x+1)/11=(10x-12)/6 2) What it the solution for x 2<1-4x greater or = to 8 3) Completely factored form 6x^2+21x-12 4) What it the solution for x X^2+4x-12=0 5) What it the solution for x 6x^2+8x=-1 6) What is the slope of the line between these two points (8,1) (-2,5) 7) Fi

Radical and Rational Exponent Notation

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

Product of Two Infinite Exponential Series

Prove the following product explicitly using infinite series expressions: Here inf = infinity ( Sum_{k=0}^inf u^k/k! ) ( Sum_{l=0}^inf v^l/l! ) = Sum_{m=0}^inf (u+v)^m/m! Please see the attached file for the fully formatted problems.

College Algebra : Application Ratio and Proportion Word Problems

The weight of an object varies inversely as the square of its distance from the center of the earth. If an object 8,000 miles from the center of the earth weighs 90 pounds, find its weight when it is 12,000 miles from the center of the earth. Please see the attached file for the fully formatted problems.

Logarithmic functions on word problems

This problem set is comprised of 8 questions involving logarithmic functions. Complete description of the problem can be found in the attached pdf file. 1. Question involves log to the base of 10 2. Question involves log to the base of 2 3. Question involves finding Decibel Levels 4. Word problem on Earthquake Intensity

Quadratic Equations: Discriminants and Imaginary (Complex) Numbers

When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminate is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value

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?

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.

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