Category: Algebra

Test 40 questions I need at least 90 percent. It’s a test so you can stop and continue later, there is 4 hours total to do the test once you click start. Will tip 15 dollars for 95 and above

Test 40 questions I need at least 90 percent. It’s a test so you can stop and continue later, there is 4 hours total to do the test once you click start. Will tip 15 dollars for 95 and above

Test 40 questions I need at least 90 percent. It’s a test so you can stop and continue later, there is 4 hours total to do the test once you click start. Will tip 15 dollars for 95 and above

Solution: Rearranging terms, we have:
12m2 – 4m2 + 5m – 9m – 7m + 10
= (12 – 4) m2 + (5 – 9 – 7) m + 10
= 8m2 + (– 4 – 7) m + 10
= 8m2 + (–11) m + 10
= 8m2 –11 m + 10

Solution: Rearranging terms, we have:
12m2 – 4m2 + 5m – 9m – 7m + 10
= (12 – 4) m2 + (5 – 9 – 7) m + 10
= 8m2 + (– 4 – 7) m + 10
= 8m2 + (–11) m + 10
= 8m2 –11 m + 10

In a company of CE, ME and EE, the sum of their ages is 2160 and ave is 36. The average age of CE and ME is 39, of CE and EE is 110/3 and EE &ME is 360/11. If the ages of CE is increased by 1 of ME is increased by 6, and of EE increased by 7, the average of all their ages increased by 5. How many CE are there?

In your own words, write two arguments , one that is valid and one that is not valid. Make sure not to specify which is argument is valid.
EXAMPLE:
Hi Class,
I wanted to share how we write arguments using symbols, and how it can be made clear when an argument is valid or not.
Here’s an example:
Cats don’t like swimming. Tom does not like swimming. Therefore, Tom is a cat.
To write the argument using logic symbols:
Let c = being a cat
s = like to swim
T = being Tom
So, the argument “Cats don’t like swimming. Tom does not like swimming. Therefore, Tom is a cat” would be written:
?⟶∼? (If you’re a cat, then you don’t like swimming.
?⟶∼? (If you’re Tom, then you don’t like swimming.)
____________
∴T⟶? (Therefore, if you’re Tom, then you are a cat.)
So, we know only 1 thing about Tom, that Tom doesn’t like swimming.
And, we know only 1 thing about cats, that cats don’t like swimming.
We have not proven that Tom is a cat! It is possible that some people (and dogs and pigs, etc.) don’t like swimming…

Please use the assignment to submit your first project.
If your project was done in class, please submit an explanation.
Please detail what sections in the book your project covered and what you learned by working on your project.
Description
Projects can take various forms, such as Zines, lecture videos, exams with solutions manuals/grading rubrics, and more. These projects allow you to demonstrate your mastery of the material in ways that suit your learning style.
Zines: Create a visually engaging zine that explains key concepts from a selected section. Use illustrations, diagrams, and concise explanations to convey the material.
Lecture Videos: Develop a series of short lecture videos covering specific topics within a section. Explain concepts, provide examples, and guide viewers through problem-solving. (Most strongly recommended)
Exams with Solutions Manuals and Grading Rubrics: Design a comprehensive exam that tests understanding of a particular section. Include a solutions manual with detailed explanations and a grading rubric for self-assessment. (Strongly recommended)
Interactive Online Modules: Create interactive online modules using platforms like HTML, CSS, or JavaScript. Include animations, quizzes, and simulations to illustrate concepts from various sections.
Graphical Representations: Develop graphical representations, such as infographics or posters, to visually explain the relationships and applications of concepts within a section.
Educational Board Games: Create an educational board game centered around calculus concepts. Include rules, game pieces, and questions that reinforce learning through play. (Strongly recommended)
Peer Teaching Sessions: Organize and lead a peer teaching session on a specific topic. Prepare materials, examples, and engage your classmates in the learning process. (Strongly recommended)
Mathematical Modeling Project: Develop a mathematical model for a real-world problem, applying the principles of calculus. Present your model, assumptions, and conclusions. (Strongly recommended)
Data Analysis Project: Collect and analyze data, applying calculus concepts to draw conclusions. Present your findings and explain how calculus contributes to the interpretation of data.
Artistic Expression: Express calculus concepts through art, whether it’s through paintings, sculptures, or digital art. Use creativity to convey mathematical ideas.
Programming Project: Develop a computer program or script that simulates a calculus concept. Showcase your coding skills in solving mathematical problems. (Strongly recommended)
Effort
An individual project should take you about 1 day of work (3-6 hours). If a project takes more work, please let me know and we can consider counting it for more.
Sharing
Your project will require a presentation unless it is a video. Also, all projects will be shared with the class.
Examples
Here is a great video explaining one of the more interesting topics later in the semester.

Second, here is a more fun and creative project.

This assignment serves as an opportunity to assess your ability to identify exponential and logarithmic functions. Among the various functions you’ve studied, exponential and logarithmic functions hold particular significance when it comes to representing practical situations marked by non-linear and rapid changes. Recognizing logarithms as the inverse of exponential functions will enable you to solve equations involving exponential functions using logarithmic properties.
Within this assignment, you will delve into the properties of logarithms and acquire the skill to express scenarios using either exponential or logarithmic functions.
You are required to complete all the 3 tasks in this assignment, answer the following questions, and show stepwise calculations. When you are instructed to make a graph in this assignment, please use GeoGebra graphing tool for drawing the graphs.
Task 1.
Please answer the following questions related to exponential and logarithmic functions:
(i)What are exponential and logarithmic functions? How are they related? What are their key factors (Explain the variables used in the definitions of these functions)? Discuss their domain and range.
(ii) What is the difference between exponential, logarithmic, and power functions? Provide one mathematical example for each and illustrate the differences of growth patterns and any special points (such as asymptotes, intercepts, and zeros), if applicable. Graph the examples.
(iii)How to explain if a function has exponential growth?
(iv)Between exponential and logarithmic functions, which one grows faster? Provide an explanation for your answer.
(v) Write the observations of growth patterns and special points (if any) by drawing the graphs for the examples given
Task 2. Before working on task 2, please read the following reading: 
Reading section 4.1- Exponential Growth and Decay of the following textbook will help you in understanding the concepts better.
Yoshiwara, K. (2020). Modeling, functions, and graphs. American Institute of Mathematics. https://yoshiwarabooks.org/mfg/frontmatter.html
Write the logarithmic properties at each step to solve the following questions:
(i) Simplify using logarithmic properties,
(ii) Condense the complex logarithm into single term
(iii) Solve:
Task 3. A research laboratory has been conducting experiments on the rapid increase of cancer cells in an animal. They have observed that cancer cell growth increases by 2% every year with certain medication. Initially, in the year 2018, there were 232.26 units of these cells in the animal.
Using the above data, answer the following questions:
(i) Create a table to illustrate the yearly increase in cancer cells up to the year 2023.
(ii) Examine the table of values and identify the mathematical function that represents this growth pattern, specifying the key factors of the mathematical function.
(iii) Utilize this mathematical function to project the level of cancer cells in 10 years, assuming the growth rate continues at the same pace.
(iv) Illustrate the growth pattern by plotting a graph (Take scale 100units on X and Y-axes).

To solve the equation
3?3−2?2+7?−5=03×3−2×2+7x−5=0, you can try factoring, but in this case, it doesn’t seem to factor easily. So, you can use numerical methods like the Newton-Raphson method or the bisection method to approximate the roots.