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Algebra

Seismographs and Half-Life

Question 1: A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.9 x 10^2 µm. Find this earthquake's magnitude on the Richter scale. Question 2: An artifact was found and tested for its carbon-14 content. If 81% of the original carbon-14 was still present, what is its probable age

Cartesian Coordinates and Graphs

Please evaluate the following expressions: 92-7(8) 6(32-17) 6(32)-17 Please use the function f(x) = -3x+5 when f (2), (-1) ,(.5) , (-3) and plot the following on Cartesian coordinates: (2,3) (4,-1) (-.5,3.5) (-1.5,-4) (-5,3)

Square Root Property and Its Form

What is the square root property and what is it used for? In what form should an equation be in order to use the square root property? When should the square root property be used instead of factoring? Use the following to explain. (3t-2)^2=108

Square Root versus Factoring

What is the square root property and what is it used for? In what form should an equation be, in order to use the square root property? When should the square root property be used instead of factoring? Use the following to explain. 10-4p^2=21

Classification of Positive Integers

The positive integers are classified into two types, A and B; a number is A if and only if it is the sum of two (distincts) A numbers, or the sum of two (distincts) B numbers. a) Classify the numbers 1,2, 3 as A and B. b) Prove that if n, n+1, n+2 are A numbers, then every integer >= n is an A number. c) Find the smalle

Fahrenheit to Celsius conversion

26. The formula for converting Fahrenheit temperature, F, to Celsius, C, is C = 5(F-32)/9. If Celsius temperature ranges from -6 degree C to 15 degree C, inclusive, what is the range for the Fahrenheit temperature? 27. Find the solution(s) for the equation. |4x - 8| + 11 = 23

Writing an Equation of a Relationship

I need help with the following problem: Write an equation that expresses the relationship. Then solve the equation for m. b varies directly as the cube of u and inversely as m. b=? (use k as the constant of variation) m=?

A person invested $7200 for 1 year, part at 4%, part at 10%, and the remainder at 15%. The total annual income from these investments was $863. The amount of money invested at 15% was $1400 more than the amounts invested at 4% and 10% combined. Find the amount invested at each rate.

A person invested $7200 for 1 year, part at 4%, part at 10%, and the remainder at 15%. The total annual income from these investments was $863. The amount of money invested at 15% was $1400 more than the amounts invested at 4% and 10% combined. Find the amount invested at each rate. The person invested $__ at 4%, $__ at 10%,

Synthetic Division

How would you explain the performance of synthetic division to someone else? Use the problem (2x3 - 3x2 - 11x + 7)/(x + 3) to support your explanation.

Finding Slope from the Equation of a Line

Please help with the following algebra problems. Provide step by step calculations as well as explanations. If possible, provide an additional example. The equation of a line is given below. Find the slope of a line that is: a. Parallel to the line with the given equation. b. Perpendicular to the line with the given equa

Linear Equation Example Question

Begin by solving the linear equation for Y. This will put the equation in slope-intercept form. Then, find the slope and the y-intercept of the line with this equation: 2y=x (this must stay in fraction format).

Computing the balance in the account

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A 19,000 deposit in an account with an APR of 2.5%. The balance in the account after 1 year is approximately $ (Round to the nearest cent as needed.) The balance in the account

Operator R(theta) for matrix representation

Assume the operator R(theta) transforms a vector v (in two-dimensional real space) by swinging it around counterclockwise through an angle theta. How can I show that the operator R(theta) has the matrix representation cos(theta) -sin(theta) sin(theta) cos(theta) That is supposed to be a matrix.

Traveling Salesman Problem

Provide an example of when the traveling salesman problem can be used to find the best solution to a problem pertaining to grocery stores.

Quadratic Function Model

Annual profit in thousands of dollars is given by the function, P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ? 0. Describe the meaning of the number -.1 in the formula, in terms of its meaning in relation to the profit. Describe the meaning of the number -300 in the formula, in terms of its meaning in rel

Recipe Word Problems

1. You are doubling a receipe that calls for 3/4 of a cup of milk. How much milk will you need? 2. Write a number using the following instructions: put a 5 in the hundreds place divide 24/8 and put the result in the tenths place put the number in the hundreds place also in the ones place subtract 3 from the numbe in the t

Finding the Value of a Variable Based on Equations

You are choosing between two health clubs. Club A offers membership for a fee of $50 plus a monthly fee of $25. Club B offers a membership fee of $25 plus a monthly fee of $30. a. Using variables of your choice, set-up an equation for each club's membership cost. Make sure your variables are defined clearly. b. After how ma

Quadratic Function: Word Problem

1. Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone else? Provide a detailed example. You may use the Internet for help/ideas. Cite your source if it is not an original idea. 2. Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where

arithmetic sequence for depreciation

Depreciation: For tax purposes, businesses frequently depreciate equipment. Two methods of depreciation are straight-line depreciation and sum-of-the-years'-digits. Suppose that a college student buys a $3000 computer to start a business that provides Internet services. This student estimates the life of the computer at 4 years,

Telescoping Series Proofs

Prove telescoping series: Let a_n from n=0 to infinity be a sequence of real numbers which converge to 0, i.e. lim n-->infinity a_n=0. Then the series of the sum from n=0 to infinity of (a_n - a_n+1) converges to a_0. Hint: first work out what the partial sums of the sum from n=0 to N of (a_n - a_n+1) should be, and prove yo

Series and Infinite Series

Is the series sum from n=1 to infinity of (-1)^n convergent or divergent? Justify your answer. Can you now resolve the difficulty of the following: Divergent series: S=1+1/2+1/4+1/8+1/16+... You have probably seen the following trick to sum this series: if we call the above sum S, then if we multiply by 2, we obtain: 2S=2

Key Components of Functions and Graph Verbally

The height h(t) in feet above the ground of a golf ball depends on the time, t (in seconds) it has been in the air. Ed hits a shot off the tee that has a height modeled by the velocity function h(t) = 0.5at^2 + vt + s where a is -32 ft/sec^2, v is the initial velocity, and s is the initial height. 1. Write a function that mod

Network Models

Minfly Golf Company manufactures golf balls at Philadelphia, Chicago, and Denver. Cases of golf balls are shipped to warehouses in Orlando, Dallas, and Los Angeles. The following table provides the weekly capacities of the factories and the minimum weekly requirements of the warehouses along with the cost per case to ship betwee

Fence material and needs to enclose an area

Jim has 400 ft of fence material and needs to enclose an area of 10,000 square feet for his garden as the diagram depicts. (The length of the house is 62 ft, and the fence extends the same distance on either side of the house.) What must the dimensions of the rectangular enclosed region be? That is, what are the values of x and

Scalar projection

Please see the attached file for the full problem. How can I use a scalar projection to show that the distance from a point? P[1](x[1], y[1]) to the line 3*x-4*y+5 = 0 is > abs(a*x[1]+b*y[1]+c)/sqrt(a^2+b^2);

Surface area of a cone

1. Solve by factoring: 6t^2 - t - 1 = 0 2. Solve the attached equation. 3. Solve each formula for the indicated letter. Assume that all variables represent nonnegative numbers. A = pr^2 + prs, for r

In solving the equation (x + 1)(x - 2) = 4

1.) In solving the equation (x + 1)(x - 2) = 4, Eric stated that the solution would be x + 1 = 4 => x = 3 or (x - 2) = 4 => x = 6. However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain

Fields - Cardinality and Splitting Fields.

We know that F_2[x]/(x^2 + x + 1) is a field of cardinality 4; call it F_4. Find an irreducible quadratic f(y) [element of] F_4[y]. What is the cardinality of the finite field F_4[y]/(f(y))? This field is isomorphic to the splitting field for x^2^n - x over F_2[x]. What is the appropriate n in this case? Show that x^4 + x

Proof of two Legendre Symbol identities

1) Use that (Z/pZ)* is cyclic to directly prove that (-3/p) = 1 when p = 1 (mod 3). 2) If p = 1 (mod 5), directly prove that (5/p) = 1. I know that with exercise 1, we show that there is an element c in (Z/pZ)* of order 3, and that (2c+1) ^2 = -3. Similarly for exercise 2, there is a c in (Z/pZ)* of order 5, and [(c + c