Share
Explore BrainMass

Basic Algebra

Algebraic Equation Problem Solving

I need a suitable way to solve these equations with algebra only, not by charts or diagram. - 42.45= 1516 ln ( R) + 5.307 *10^-3 / R , I want to get R value. T^4 = .564 - .876T , I want to get T value.

Converting a formula based on common logarithms

Question 1: The capacitance between two parallel wires in space is given by the formula C = 1 / {3.6 ln [(d-r)/r] where d is the spacing between wire centers in centimeters, r is the wire radius in centimeters, and C is in picofarads per centimeter of wire length. Find the capacitance per meter of length for two 0.2-cm-rad

Summation Notation: Example Problem

I am taking an advanced math course next semester that will involve using summation notation extensively and am somewhat anxious about it. Could you give me a primer on using Σ single, ΣΣ double, and triple sums with examples?

Mathematical Induction Problem

Use mathematical induction to show that a rectangular checkerboard with an even number of cells and two cells missing, one white and one black, can be covered by dominoes.

Nepper Miliampers Conversion

The attenuation constant of a transmission line, measured in nepers, is defined as the natural logarithm of the ratio of the input current to the line to the output current from the line. If the input current is 240 mA, what is the output current if the line has a 0.35-neper loss? (1) 55 mA (2) 84 mA (3) 169 mA (4) 265 mA

Calculating birth rate

A city reported 49,779 births in a year with a population of about 2.6 million people. City B reported 13,892 births in a year with a population of about 1.3 million people. Assume that there are 365 days in a year. Use this data to answer a & b. A. How many people were born per day in city A? ____(round to nearest integer

Why is order of operations necessary?

Use multiplication, division, addition and subtraction and at least one set of parentheses to write an expression that simplifies to 7, 13, or 17. Do your work step by step and explain each step as you simplify the expression. Demonstrate the consequences of not using the proper order of operations by showing that other orders

Mathematical Induction: Flaws and Inductive Proofs

1. Find the flaw with the following "prof" that a^n = 1 for all non negative integers n, whenever a is a nonzero real number. Basis Step: a^0 = 1 is true by the definition of a^0. Inductive Step: Assume that a^j = 1 for all non negative integers j with j <= k. Then note that a^(k+1) = (a^k*a^k)/(a^k-1) = 1*1/1 = 1

Induction Problem: Covering a Checkerboard

Using mathematical induction, prove or disprove that all checkerboards of these shapes can be completely covered using right triominoes whenever n is a positive integer. a) 3 x 2^n b) 6 x 2^n c) 3^n x 3^n d) 6^n x 6^n

Solving Possibilities

Question: 12 people are choosing a President, Vice President, and Secretary from their ranks. How many ways are there to do this? Hi, I think I'm just over complicating this question in my mind, but I am not sure how to answer it. What I typed above is exactly how it reads word for word)

Bisection method

Consider solving equation x = 3/(1+x^4) using bisection method. a) Find an interval, [a,b], to start the iteration. b) Estimate at least how many iterations are needed to find a solution within an accuracy of 10^-6.

Taylor series expansion problem

Solution to the problem 1(b) only in the attached file, please. Let f(x) = sin x b) Let x_0 = 0. Calculate f(0.1), f(1.0), and f(pi/2) to 3 converging decimal points in each case and compare with the exact answers.

Word Problems - Linear Inequality, Etc.

Can you please assist me with formulas for the following? 1. Formula needed for: A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 52 km/h. How long does it takes the passenger train to catch up to the freight train? 2. Desc

Sophie Germain Primes

Hello, I need help with proving the following statement: "A prime p is said to be a Sophie Germain prime if n = 2p+1 is also prime. Prove that a prime p is a Sophie Germain prime if and only if 2^(n-1) = 1 (mod n)." Thank you for your time.

Formula for Word Problems

1. During a road trip, Tonya drove one-third the distance that Lana drove. Mark drove 15 miles more than Lana. The total distance they drove on the trip was 491. How many miles did each person drive? 2. A business wholesaler wants to create a new punch. He will mix fruit juice worth 2.00 per gallon and rum worth 7.00 per gall

Fibonacci Numbers and Golden Rule

Show that |(frac{f_(n+1)}{f_n}) - phi| = frac{1}{(f_n)(phi^{n+1})} and lim_{n --> infty} frac{f_{n+1}}{f_n} = phi, where phi is the Golden Ration and is the unique positive root of phi^2 - phi - 1 = 0. For some discussion on this question, see http://math.stackexchange.com/questions/106049/another-way-to-go-about-provin

Polynomial Functions and Validity

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counter example. 1. Every polynomial function of odd degree is one-to-one. 2. The graph of a one-to-one function intersects each vertical line exactly once. 3. The inverse of f(x) = x^2 is g(x) = sqrt of x

Half life formula

Radium 226 gives half-life exponentially quantity of a metal with a half life of 1600 years, If you start with one kilogram of Radium how much will you have in 1000 years? How much after 10,000 years?

Approximation doubling

Use the approximation doubling formula (rule of 70) and discuss rather the formula is valid for the following case; "If oil consumption is increasing at a rate of 2.2 per year what is its doubling time? By what factor will oil consumption increase in a decade?"

Exponential growth of a small town

Please assess this statement. A small town that grows exponentially can become a large city in just a few decades. Option 1) Does not make sense because exponential growth leads to repeated halvings, making the population decrease rapidly. Option 2) Does not make sense because growth cannot continue indefinitely so the

Using growth rate to predict population

Use a growth rate of 1.5% to predict the population in 2073 of a country that in the year 2006 had a population of 300 million. Use the approximate doubling time formula. (Round the final answer to the nearest whole number as needed. Round the doubling time to the nearest year as needed.)

Multiplication Equations, Division Equations, Etc.

1. Using only whole numbers, write as many multiplications equations as possible with 12 as the product. 2. Chance wrote four division equations with 6 as the quotient. What could have been the four division equations that he wrote? 3. For the next two problems tell what kind of situation is described, then write an equ

Toxic Chemical Decay - Sensical Statement or Not

Analyze the following statement and decide whether it makes sense or not: A toxic chemical decays with a half life of 7 years, so half of it will be gone 7 years from now and the other half seven years after that. Will the toxic chemical decay with a factor of 2, .25, or .5?

Algebra: Geometric Progression and Acceleration

1. a) Transpose the following formula to make v the subject: f = uv/(u + v) b) Solve the folowing equation to find the value of x: (3.4)^2x+3 = 8.5 c) In the formula theta = Ve^(-Rt/L), the value of theta = 58, V = 255, R = 0.1 and L = 0.5. Find the corresponding value of t.

The value of critical thinking to your personal and professional development

Problem solving and critical thinking is indispensable to every area of our lives. There was a great deal of critical thinking and problem solving presented this term involving working Algebra problems and their applications to everyday life. How will you take these critical thinking skills to the real world and become a mo

Filling a Tank with Water.

Can you help? Water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second hour, 550 litres during the third hour and so on. Find the number of hours necessary to fill a rectangular tank 16m x 9m x 9m.

Mathematics and Log Functions

To illustrate: b^xT - b^xA [approximately equal to] (log b)b^xT (x_T - x_A) Rel(b^xA) [approximately equal to] (log b)x_T Rel(x_A)(*) k = (log b)x_T (**) [Please see the attachment for the formatted question] Compare pi^100 to pi^100.1. Calculate these directly as accurately as you can. Then calculate Rel(pi^100.1)

Evaluations with Order of Operations

Use each of these numbers exactly one time to write an expression equal to 9. You may go through many steps to arrive at a solution, but use what you know about order of operations to write your answer as a single expression. Then find at least one more way to do it with the same numbers, again writing your answers as just a s