Explain in your own words what the meaning of domain is. Also, explain why a den

Explain in your own words what the meaning of domain is. Also, explain why a denominator cannot be zero.
Find the domain for each of your two rational expressions.
Write the domain of each rational expression in set notation (as demonstrated in the example).
Do both of your rational expressions have excluded values in their domains? If yes, explain why they are to be excluded from the domains. If no, explain why no exclusions are necessary.
Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing. Do not write definitions for the words; use them appropriately in sentences describing your math work.
Domain
Excluded value
Set
Factor
Real numbers
Your initial post should be at least 250
Solving:4x^2-1/6x-18
Solving :r^2+2r-24/r-12

Please complete assignment as Microsoft Word Doc with all calculations and expla

Please complete assignment as Microsoft Word Doc with all calculations and explanations
Written Assignment
Why Can’t I Sleep?
The half-life of caffeine is about 5.7 hours. This means that half of the caffeine intake will still be in your system after 5.7 hours. The general formula (using rational exponents) is:
where:
t = the hours since drinking the caffeine
k = the half-life of caffeine (about 5.7 hours*)
C = the milligrams of caffeine ingested
A = the milligrams of caffeine left in your body after t hours
* Statland BE, Demas TJ. Serum caffeine half-lives. Healthy subjects vs. patients having alcoholic hepatic disease. Am J Clin Pathol. 1980 Mar;73(3):390-3. doi: 10.1093/ajcp/73.3.390. PMID: 7361718.
Find the amount of caffeine in your favorite caffeinated beverage by checking the nutrition label or doing research on the internet. Be sure to find the amount of caffeine in the entire container, not just in one serving. This will be C in the equation. Assume you drink the entire beverage in one sitting. Include the name of your favorite caffeinated beverage and the amount of caffeine in that beverage.
1) Calculate the amount of caffeine (mg) remaining in your body after t = 2 hours after you drank the beverage. Show all steps in your calculations and round your answer to the thousandths place (three decimal places.)
Now, consider different times of the day that you might drink caffeine and:
2) Pick a time between 11am and 6pm. Determine how many hours until 9pm (an approximate bedtime). This is your value for t. How much caffeine (mg) remains in your body at 9pm? Show all steps in your calculations and round your answer to the thousandths place (three decimal places.)
3) Reflect on your calculations. What effect might caffeine have on your work, exercise or other daily activities? When do you think you should drink your caffeinated beverage in order to get a quality night’s sleep?

Breakeven analysis uses two functions to describe the revenue and cost of a part

Breakeven
analysis uses two functions to describe the revenue and cost of a particular
product. The breakeven point is the number of products that a business
must produce and sell so that the money coming in is equal to the money going
out. In this assignment, you will be asked to create a system of equations
based on the cost and revenue of a particular business. You will have to solve the
system to determine the business’ breakeven point.

It is difficult to learn how to do story problems because there are so many diff

It is difficult to learn how to do story problems because there are so many
different types. If you want to do well on this week’s test, FOLLOW THESE
INSTRUCTIONS!
Step 1: Read the file entitled “Read This First”
Step 2: Open the file “Systems of Equations with Answers”.
Step 3: Go through ALL the story problems provided and try to solve them. Pretend it’s a Practice Test. Check your answers with the key provided.
Step 4: Pick ONE of the problems that you got right (that has not already been solved by a classmate) and demonstrate its solution for the rest of us.
Step 5: Study how your classmates solved the problems that you missed. Remember that these may be on the test!
Note: Problems are selected on a first-come basis. If a classmate has already chosen a problem you had wanted to answer, please select a different problem. Our goal is to answer and discuss as many different problems as possible.
To demonstrate your problem, select Start a New Conversation and make the subject of your post BOTH the problem number and topic (#10 Jarod and the Bunnies).
Begin your post with a statement of the problem so that we can understand what you are doing.
The answers are at the end of the file, so don’t just give an answer—we can already see what the answers are. Don’t post an explanation unless your answer matches the correct one!

Digital music distribution provides an opportunity for everyone to get their mus

Digital music distribution provides an opportunity for everyone to get their music heard. In order to get on a service like iTunes, one needs to pay for distribution through a service like Tunecore or CD Baby. These services make sure that your music is heard on different platforms. One of the most important streaming services is SPOTIFY.
Suppose the distributor charges the artist a $50.00 cost for distribution, and the streaming services pay $5.00 per unit. (Note: One unit = one thousand streams)
Model the profit for the total number of streams by answering the questions below:
1. Use the cost for distribution to build the y-intercept. What is the y-intercept?
(Hint: the y-intercept is a point on the y axis, so the answer should be an ordered pair (x,y). Keep in mind that money is being spent, and therefore must be deducted from the profit. If the y-intercept is incorrect, all related numbers will be incorrect.)
2. Use the payment per unit to build the slope. What is the slope?
3. Use the slope-intercept format (y=mx+b) to give the equation of the line. What is the equation of this line?
4. Graph the line by adjusting the sliders below. Show the line by attaching an image of the graph below. (Hint: take a screenshot and upload it as an image.)
Use the equation from question 3 to answer questions 5−7. (Hint: Remember one unit = one thousand streams.)
5. After how many streams will the distributor charges be paid? (Hint: this is where the line crosses the x-axis. This is the break-even point.)
6. How many streams would it take to profit $950,000?
7. According to new research in 2021, Puerto Rican Reggaeton star Bad Bunny again took the title of most-streamed artist in the world on Spotify. He received over 9.1 billion streams (9,100,000,000)without releasing a new album last year.
Use this number of streams with your equation to calculate how much money Bad Bunny may have made via Spotify. (Worlds Most Streamed Songs (Spotify), 2021)
Fun Facts:
Bad Bunny is followed by singer-songwriter Taylor Swift, whose “Red” (Taylor’s Version) gave old and new fans alike a reason to relive the artist’s early groundbreaking work. Rounding up 2021’s top three is BTS. The globally beloved K-pop group had a standout year thanks to their single “Butter.”
Canadian hip-hop artists Drake—who released Certified Lover Boy in September—and Justin Bieber—whose 2021 album Justice featured collaborations with artists from across the globe—take spots four and five, respectively.
How much does Spotify pay per stream? (2021, February 24). Businessinsider.Com. Retrieved January 30, 2022, from https://www.businessinsider.com
Worlds Most Streamed Songs (Spotify). (2021, January 12). Spotify.Com. Retrieved January 30, 2022, from https://newsroom.spotify.com/2021-12-01/what-the-world-streamed-most-in-2021/