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Algebra

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.

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

Aerobics Instructor: Water Consumption Problem

An aerobics instructor says she drinks one cup (8 ounces) of water before she starts her classes and then she drinks 10 ounces every 10 minutes. a. How much water does she drink when she teaches 2 one-hour classes in a row? b. Let W represent ounces of water and N the number of 10-minute intervals the aerobics instructor s

Solving Quadratic Equations With Factoring

Solving Quadratic Equations by Factoring is Chapter 13.7 page 955 1) Quadratic Equation is in STANDARD FORM (ax^2 + bx + c = 0 where a is positive) Factor trinomial: x^2 + bx +c =(X + m)( X +n)=0 ,which :(mn=C),and (m+n=b) (X + m)=0 ---->X = - m , and (X + n)=0----> X= - n 2) Pythagorean Theorem in Right triangle (

Maximal and Principal Ideals

Let delta=sqrt(-3) and R=Z[delta]. This is not the ring of integers in the imaginary quadratic number field Q[delta]. Let A be the ideal (2,1+delta). a) Show that A is a maximal ideal and identify the quotient ring R/A. b) Show that A contains the principal ideal (2) but that A does not divide (2).

Groups and Representations

Please help answer the following algebra questions. Provide step-by-step solutions. (i) Now let G be a group with the presentation G=<a,b|a^7=e,b^3=e,b^(-1) ab=a^2> You are told that |G|=21. Let w=exp(2i*pi/(7)) E C. Prove that there is a representation p:G --> GL(3,C) with p(a)= (w^2, 0, 0; 0, w^4, 0; 0, 0, w) and p(

Forming a linear function from a story

The relation between the cost of a certain gem and its weight is linear. In looking at two gems, we find that one of the gems weighs 0.2 carats and costs $3,548, while the other gem weights 0.5 carats and costs $4,374. Find C(x), the linear function that relates the price of gem to its weight x, treating weight as the independen

Prove the following Proposition

Prove the following Proposition: On Z_n, both * and + are commutative and associative. The identity for Z_n with * is [1] and the identity for + is [0]. Please submit response as either a PDF or MS Word file. Infinite thanks. See attachment.