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# Algebra

### Finding the equation of a line.

Given a line containing the points (1,4), (2,7), and (3,10) determine the slope-intercept form of the equation, and graph the function. Give the domain and range as defined by the points, and also the domain and range of the entire function.

### Finding the nth term and Sum of a Geometric Series

Use the geometric sequence of numbers 1,1/2,1/4,1/8,.... to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.

### Arithmetic Sequences

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula

### Logarithmic scale and sound

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to ( a ratio of) the weakest sound the ear can hear. A. The formula for measuring sound. B. Pick a specific sound, give the decibels of the sound, and explain what this measurement means.

### Problem Set

(See attached file for full problem description with proper symbols) --- 1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56. 2. If y = x , calculate the value of p given that y = 2.65 and x = 0.745. 3. If x = (1 + 1nr), evaluate r when x =0.34, P = 1.08 and

### Formula for Measuring Sound and the Loudness of Sound

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear. Using web resources, and other course material, research how sound is measured. Include the following items in your posting: The formula for measuring sound.

### Scatter Plot

Question 6: House cat owners invest a lot of time and expense to find just the right cat food for their finicky, spoiled and pampered pets. Some house cat owners believe that the reaction of the house cat, in terms of how much time passes between the serving of the food and the point at which the finicky, spoiled and pampered

### Please solve these equations related to arithmetic sequence and geometric sequence:

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the

### Fundamental Theorem of Arithmetic

Please show complete solution so that I may understand the reasoning behind each step. I will need a thorough understanding to complete future assignments. See attached file for full problem description.

### Exponential Growth Rates

Consider the following disaggregation of carbon emissions: Carbon emissions(kg C/yr)= Population x (Energy(kJ/yr)/Person) x (Carbon (kgC)/Energy(kJ)) Using the following estimates for the United States and assuming that growth rates remain constant, Population (kJ/yr)/Per

### Please solve these equations related to arithmetic sequence and geometric sequence

1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the

### Word problem

In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive? (Please show steps) I'm trying to figure out what the steps would be to come to this conclusion. The problem says "220 more votes". I understand that (I think) to be +200, but

### Description of a Geometric Series

3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27... to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 7 significant figures. c) Using the for

### Geometric sequence

2) Use the geometric sequence of numbers 1, 3, 9, 27, ... to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the nth term of a geometric sequence, what is the 10th term? c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?

### Arithmetic series

1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? d)

### Vectors, Subspaces and Dimensions

2 a) Find a base for the subspace W of spanned by What is the dimension of W? b) Let 1) Show that W is a subspace of 2) Find a base for W 3) Determine the dimension of W c) Let 1) Determine whether Y is a base for , the vector space of all 2 x 2 matrices. d) Find the two values of a for

### Mathematics of the Richter Scale

The intensity 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 weakest possible tremor. Include the following items in your posing: What is the formula for measuring earthquakes? Why is a 7.0 earthquake ten times stronger th

### Interest and the Time Value of Money : Continuously Compounding Interest

3) The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following: A=P(1+R/N)rt A is the amount of returned P is the principal amount deposited r is the annual interest rate (expressed as a decimal) n is the compound period t is t

### Given information in attachment, please sketch the graph

(See attached file for full problem description with proper equations) --- Given information in attachment, please sketch the graph. For the rational function f(x) = (x2 - 1) / (x2 - 9), give the intercepts and asymptotes and sketch the graph. Let f(x)=0, we get x=1 or x=-1. So, the x-intercepts: x=1 or x=-1. Let x=

### Rational function

For the rational function (see attached file) a.) determine the equation of the oblique asymptote b.) determine the x-intercepts c.) determine the y-intercepts d.) determine the equation of the vertical asymptote e.) sketch the graph

### A computer is infected with the Sasser virus.

A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?

### Synthetic Division, Intermediate Value Theorem and Asymptotes

21) Use synthetic division to find: f(?2) f(x)=2x3?3x2+7x?12 21) 22) For the function f(x) = ?x3 + 8x2 ? 40 Show how to use synthetic division to find out if -1 is a zero. 22) 23) One of the zeros of the function f(x) = ? 7x2 + 17x ?15 is 2-i. Find all the other zeros. 23) ____________________ 24) Use the intermediate val

### Negative Number Sums

12. The second of three negative numbers is 6 less than the first negative number. The third negative number is 3 times the second number. Find the set of all possible third numbers given that twice the sum of the first two numbers is greater than the third number. 13. A woman can row 11 miles downstream in the same ti

### Three times one number equals one-fourth of another number.

8. Three times one number equals one-fourth of another number. If the sum of four times the first number and twelve equals three times the second number, then what are the two numbers? 11. Mrs. Montero invested \$10,000, part at 9% and the remainder at 10% per year. If at the end of 5 years the two investments had earned \$4,80

### Measurement problems strategies

1) 1 mile is about equal to 1 1/3 kilometers. How many kilometers long is 26-mile race? 2) two numbers have a product of 3 1/5 and the sum of 3 3/5. One of the numbers is a whole number. Find the numbers. 3) Theo's bedroom measures 12 3/4ft by 9 2/3ft. What is the difference between the length and width of the room? 4)

### Word Problem

How many quarts of 60% alcohol solution must be added to 20 gallons of 20% alcohol solution to obtain a mixture that is 30% alcohol?

### Solve for x

(See attached file for full problem description)

### The answer to Geometric sequence

Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8, ......to find the following: a. What is r, the ratio between 2 consecutive terms? b. Using the formula for the sum of the first n terms of a geometric series. What is the sum of the first 10 terms? Please round your answer to 4 decimals. c. Using the formula f

### Arithmetic Sequence Differences

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9, ..... to find the following: a. What is d, the difference between any 2 terms b. Using the formula for the nth term of an arithmetic sequence, what is 101st term? c. Using the formula for the sum of an arithmetic series, what is the sum of the first 20 term? d.

### Geometric sequence

The classic problem - put a penny on first square of a checkerboard, and then double the amount on each succeeding square. How much money would be put on the 32nd square? How much money would you recieve if there only 32 squares? How much money is needed to fill all 64 squares of the checkboard? Thank you!