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# Basic Algebra

### 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.)

### Computation of the spherical metric via stereographic projection.

Find the induced metric of the sphere S^2 in stereographic projection coordinates (M, N), where M = - x/(z-1), N = -y/(z-1), with x^2+y^2+z^2=1.

### 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

### Give big-O estimate for each of these function

a) Arrange the function (1.5)^n, n^100, (log n)^3, (n^1/2)*log n, 10^n, (n!)^2, n^99 +n98 in a list so that each function is big-O of the next function. b) Give big-O estimate for each of these functions. For the function g in your estimate f(x) is O(g(x)), use a simple function g of smallest order. i) (n^3 + (n^2)*log n) *

### Observational Study or Experiment?

Identify whether the following study is an observational study or an experiment. If its an experiment identify the control group and treatment group and discuss whether a single or double blinding is necessary. If the study is observational state whether it is a case control study and if so identify cases and controls. A do

### Cost analysis: weekly fixed and variable costs of picnic tables

Cost analysis: A small company manufactures picnic tables. The weekly fixed cost is \$1,200 and the variable cost is \$45 per table. Find the total daily cost of producing X picnic tables. How many picnic tables can be produced for a total weekly cost of \$4,800? Please show all work in algebra form.

### Solving Expressions and Equations

Rafael is filling up a 150 gallon tank. He is pouring the water at rate 2.5 gallons per minute. a) Write an expression that represents how many gallons Rafael has poured since he began. b) Write an equation that represents how long it will take for the tank to be 1/2 full. c) Solve the equation in part c and say what your a

### Writing expressions and equations

During a marathon, Kim our champion cyclist is having struggles. At the halfway checkpoint she is behind the leader, Allison by 10 miles. Kim still has a lot of energy left and pacing herself at a constant 15 miles per hour. Allison on the other hand, is getting tired and has slowed down to 11 miles per hour. a) Write an exp

### Exponential multiplication and intercepts

You identified when these functions will grow and when they will decay. However, can you explain why this is true based on our exponential multiplication? Also, what are some of the other characteristics like the x and y intercepts? Thanks.

### Important characteristics of an exponential function

Identify the important characteristics of an exponential function. Explain the difference between the graph of an exponential growth function and an exponential decay function and give an example of each type of function.

### Distinguish between square roots and factoring.

A) 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. 9x^2-12x+4=27

### Square Roots, Factoring, and Example

A) 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 as an example. 25(y-10)^2 = 36

### Intermediate Algebra and Website Example

Using the internet, locate a web site that has additional examples on intermediate algebra that interest you. Use the search words "'rational expressions applications."

### Rational Exponents and Radical Expressions

What is a rational exponent? How are rational exponents related to radicals? Give an example of how an expression with a rational exponent can be rewritten as a radical, using the following as an example: (-25)^13

### Glacier on this peak covered 5 acres.

By 2004 this glacier had melted to only 1 acre. (a) Assume that this glacier melted at a constant rate each year. Find the yearly rate. (b) Use your answer from part (a) to write a linear equation that gives the acreage A of this glacier t years past 1920. The yearly rate of change is ___ acres/year. (type an integer

### Simplifying a rational expression: Example problem

In regards to the example that I included, can we cancel out the x's? I guess the big question here is how to we identify whether we are dealing with factors or with terms? Answer: When simplifying the rational expression, it is improper to cancel out the x's in general. For instance, (x^2-x)/(x^2+x+1). We cannot cancel x

### Simplifying the Rational Expression: Canceling Out the X's

When simplifying the rational expression, explain why it is improper to cancel out the x's? State a general rule for canceling factors in a rational expression and give an example of how this rule would be used. Use the following: 3a^2+5ab-2b^2/3a^2+8ab-3b^2.

### When is it necessary to find the least common denominator?

When is it necessary to find the least common denominator (LCD) of two rational expressions? Describe, in your own words, the process for finding the LCD of two rational expressions. How is factoring related to this process? Give an example use the following to explain. p/p^2-3p+2+4/p-1

### When is it necessary to find the least common denominator of two rational expressions?

When is it necessary to find the least common denominator (LCD) of two rational expressions? Describe, in your own words, the process for finding the LCD of two rational expressions. How is factoring related to this process? Give an example. use the following. 4x-5/x-4+1-3x/4-x

### Algebra 2 revised

A2. Inverse Function The correct inverse for the function f(x)=2x is not x/2. A3. Domain and Range Please revise the domain and range for the function and its inverse after identifying the correct inverse for the function f(x)=2x. A4. Graph A graph for the functions f(x)=2x and f-1=x/2 has been provided but the corre

### In 1990, the life expectancy of females was 78.8 years

In 1990, the life expectancy of females was 78.8 years. In 1997, it was 79.5 years. Let E(t) represent the life expectancy, and let t represent the number of years since 1990. a) Find a linear function that fits the data: ________________________________________ b) Use the function to predict the life expectancy of female

### Analytical solution of parametric equation

A projectile is fired with an initial velocity of 230 feet per second at an angle of 45 degrees with the horizontal. The parametric equations describing its motions are x = 115 - SQR(2)*t y = 115- SQR(2)*t-16t². Find the time when the projectile hits the ground, and the range of the projective (the horizontal distanc

### Set Up and Solve the Equations for Word Problems

1. Anthony leaving Kingston at 2:00pm and drives to Queensville, 160 mi distant, at 45mi/h. At 2:15pm Helen leaves Queensville and drives to Kingston at 40mi/h. At what time do they pass each other? 2. The hypotenuse of a right triangle has a length of 20cm. The sum of the lengths of the other two sides is 28cm. Find the

### What is Binomial Factoring?

What is a binomial factor? In your own words, describe the process of factoring by grouping. Explain how the distributive property is used in this process. Give a detailed example of this process. Example: 15xy-9yz+20xz-12z^2