Tuesday, April 23, 2013
Equations v. Inequalities
Answer the following about equations and inequalities.
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
2) How is graphing linear inequalities different? What does it help us understand?
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
This post is worth 8 points (2 per problem). You will be graded based upon the completeness and thoughtfulness of your answers.
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ReplyDeleteKatelin and Leona's answer
ReplyDelete1)Graphing linear equations help us see the relationships between the two values graphed on the coordinate plane. When it is written in equations, it is difficult to notice the relationship of the two values but on the line its more easier.
2)When it is an inequality we have to shade and sometimes include a boundary line to see all possible answers that can be plugged in the inequality. It helps us understand that there are more possible answers than just on the line unlike an equation.
3)Conjunction is the intersection and disjunction is the all possible solutions. Cupcakes can be used to be remember conjunction because you need a topping and a muffin. However when it is a doughnut all you need is a plain doughnut you don't need a topping when you eat it. You can have a topping, but you don't need to (you have a choice) You can remember conjunctions as cupcakes (C AND C) disjunction and doughnut (D AND D)
4)Katelin cooks meat and fish. Meat takes 2 hours to cook and fish takes 4 hours. She has 24 hours to spare. She wants atleast 2 meat and 2 fishes cooked. However when Leona comes over on Sunday she only has 13 hours to spare.
Normally:
m = 2
f = 2
2m+4f ≤ 24
When Leona comes over:
2m+4f ≤ 13
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ReplyDelete1.Graphing Linear Equations help us learn the relationships between two different equations, by letting us graphing it on a coordinate plane, and lets us also learn the specified equation’s intersections, slopes, intercepts, etc.
ReplyDelete2.Linear inequalities are different from linear equations because linear inequalities have multiple possible answers. Because there are multiple possible answers, when we graph linear inequalities we shade the answer. However, in linear equations, we don’t do that, because there is a fixed amount of solutions.
3.You can remember conjunctions and disjunctions like this. Conjunctions are cars, they transport the driver and the passenger. Disjunctions are dune buggies, they are meant to carry you or somebody else, but not both at the time. Cars carry the driver AND the passenger (conjunctions) while dune buggies carry you OR somebody else(disjunctions).
4.Brian set up a carnival stand, he has to make more than $300 for him to cover his expenses and turn a profit. The admission for children is $5 and the admission for adults is $10. If at more than twice as many adults came as children, at least how many adults came?
Children: x Adult: y
2x$300
Team is Jin Mo and Brian
1. In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteGraphing linear equations allow us to easily see what the values are and what the specific pattern of the equations are. For example, if the point (3,4) is on the line, we know for a fact that (3,4) is a solution. We also know that the next points on the lines are going to follow a specific pattern (the slope) However, if the point (-3,-4) is not on the line, we know that (-3,-4) is not a solution.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear inequalities are different because it is the most visually clear way that allows us to show (shading in) the whole solution set. It helps us understand which range of numbers are clearly in the solution set.
3. You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Think ‘and’ as a journey together. In the graph, when you graph conjunctions, the solutions set are the ones where both inequalities have. For example, if you are going on a journey together, you walk together. In the graph, the solution set of the inequalities are sets where both graphs meet.
Think ‘or’ as alone or together. It means that it can be both alone and together. Wherever the graph’s solutions are, they all count as a solution set.
4. Name one original real-world application for graphing a SYSTEM of inequalities.
Chloe and JinHo are going scuba diving. Before, they went underwater, the scuba-diving expert Mr. Jobe gave them some advice. “The prettiest fish in the ocean swim higher than -56 feet underwater, but swim lower than -14 feet underwater.” If Chloe and JinHo want to only see the prettiest fish in the ocean during their scuba-diving experience, where do they have to swim?
#3, the examples make sense mathematically, but I wouldn't say they're a great way to remember for someone who does not understand.
DeleteEquations vs. Inequalities
ReplyDeleteAnswer the following about equations and inequalities.
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
In our opinion, the point of graphing linear equations is to help us understand the equations with variables, such as x and y. Graphing this lines helps us narrow down the answers to the variable because there are too many numbers to begin with. Also we can learn the relationship between x and y.
2) How is graphing linear inequalities different? What does it help us understand?
When you’re graphing inequalities, you must make the line a solid line or dotted line. It helps us understand whether the variables are greater, less than, or equal to an equation. It also narrows down the answers by coloring in the area that the sign designates.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
The conjunction is the area which the two lines interact, so it can be remembered as playing football. When the oppositions has the ball, the team runs towards each other to get the ball. Disjunction can be after the game, the teams separate from each other to their locker rooms. This is because disjunctions because they are going opposite directions.
Name one original real-world application for graphing a SYSTEM of inequalities.
You could use the graphing system of inequalities as a real-world application vin situations such as when you are calculating amounts of money someone earns per some amount of time.
Eric has to save $600 to go to Guam in one month. He earns $6 per hour by working at the McDonalds and $8 per hour working at a internet cafe. By law, He cannot work more than 20 hours per week. Now graph 2 inequalities that Eric can use to determine the amount of hours he works at each job if he wants to make the trip.
This post is worth 8 points (2 per problem). You will be graded based upon the completeness and thoughtfulness of your answers.
Answer the following about equations and inequalities.
ReplyDelete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
The point of graphing linear equations is to prove that the answer is right. It helps us understand visually. For example, if there is a real life situation where you need to know how much money we have to spend for two different things, we know the boundaries and limits of how much we need to spend.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear inequalities are different because it gives the specific shading area or the solution. Also, it gives the specific direction where the answer can be by claiming less than, greater than, less than or equal to, and greater than or equal to. It helps us understand because it gives us specific area that can be the solution. Also, it visualizes the answer
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Conjunctions can represent the classroom and disjunction can represent the detentions. For example, for conjunction, students go inside the classroom and stay in one room. For the disjunction, if student's detentions like after school detention, lunch detention, and suspension, students might end up getting expelled from the school and be in the different places. In addition, classroom starts with "c" and detentions start with "d".
4) Name one original real-world application for graphing a SYSTEM of inequalities.
TOEFL test is the real world application for graphing a system of inequalities. To go to a high- ranked boarding school, we need to get the score between 100- 120, which is very difficult to get.
x≥100, x≤120
This post is worth 8 points (2 per problem). You will be graded based upon the completeness and thoughtfulness of your answers.
1) The point of graphing linear equations is to see the slope of the line the and y-intercept. Since you cannot keep only solving the answers, graphing a line helps us understand and find out all possible solutions. Every point on the line are solutions for the linear equation. Graphing also helps us figure out if the line is a positive or negative slope.
ReplyDeleteIn word problems, graphing linear equations helps us understand the increase/decrease of something. A steeper line helps us know that the increase/decrease occurs faster. (Graphing systems of linear equations helps us understand the intersection of the lines.)
2) Graphing linear inequalities is different because the lines are either solid OR dotted. There is a boundary line if the line is solid and no boundary line if it is dotted. Also, you need to color in one of the two parts. Graphing linear inequalities help us understand all available solutions for an inequality problem. It shows that there may be more solutions than linear equations.
3) A conjunction is the intersection of two inequalities, and a disjunction is all possible solutions. A conjunction is usually represented with the word “and,” and a disjunction is usually represented with the word “or.” In a conjunction, if the arrows are pointing to each other, it is showing the inequalities. If the arrows are pointing opposite to each other, then there is no solution because there is no intersection. In a disjunction, if the arrows are pointing opposite to each other, then that is just the solution. However, if the arrows are pointing towards each other, then the solution is all real numbers because the intersection shows all possible solutions.
Conjunctions and disjunctions could be understood by a band. A conjunction, the conductor, wants the whole band to play together, listen together and “intersect” together to make one whole sound. However, a disjunction, an individual player, can play alone or he can play with the whole band. He has two possibilities to play his instrument! We can memorize conjunction because conjunction and conductor both start with the letter c. The disjunction would be the other one.
4) Hyunjeong has to earn at least $100 to donate to charity. She starts out with $0, and decides to work in a Chinese restaurant in the morning, and in a clothes shop in the evening. She earns $4 per hour in the Chinese restaurant and $3 per hour in a clothes shop. Because she has a curfew, she can only work 12 hours a day. How many hours can she work in each job?
x = hours worked in the chinese restaurant
y = hours worked in the clothes shop
4x + 3y ≥ 100
x + y ≤ 12
1. We think that graphing linear equations help us look at math not only as a written equation, but a picture, something that we are able to see. So graphing linear equations help us view math not only as something difficult and abstract, but something we can see, which helps us get familiar to math and have more friendly feelings toward it. Also, linear equations always have two variables - the x and the y - and the two variables always have a certain pattern. So basically, when something happens to x, then something happens to y with a certain pattern, a certain trend, and it can be easily seen when graphed, and that’s why we are graphing linear equations.
ReplyDelete2.When you are graphing linear equations, there is a certain answer, no answers, or all real numbers, while when you are graphing linear inequalities, you find their answers are too many to list, and hence a graph is required, which when shaded, represents the direction of solutions are and therefore displays the number of answers possible. Without these essential graphs, it will be impossible to show the solutions that are possible (well it may be possible, but it will take you years). Thus, the graphs are required and should they have not existed, it would be near impossible to list the solutions of a particular inequality.
3. Conjunctions usually have the word ‘and’ in it, but disjunctions usually have the word ‘or’ in the question. If the inequality does not have any specified or assigned words such as the “and” or “or”, it is usually a conjunction. If there are two inequality signs, then also it is a conjunction. When graphing conjunctions, the solution is the where the two lines intersect. If they don’t, then there is no solutions. When graphing disjunctions, simply graph all possible answers. It does not matter where the lines intersect or anything but simply graph the spectrum of solutions. Analogy - Conjunctions are like living in a community. When you are living in a community, you intersect with each other and what you do alone does not matter as a whole. Disjunctions are like living in a cave. When you are in a cave, everything you do matters because it affects you.
4. Zlatan is hungry because it is lunchtime, and he trained for his next match very hard. He went down to the cafeteria and realized that he had to choose from his two favorite dishes: Swedish pancakes or fish and chips. But Zlatan is so hungry that he decides to get at least three dishes of food. If the Swedish pancake costs 75 dollars and the fish and chips cost 50 dollars, and Zlatan had 200 dollars to spend, how many dishes of Swedish pancakes and how many dishes of fish and chips did Zlatan get for lunch?
x+y≥3
75x+50y≤200
These two sets of equations can be simplified to be
y≥-x+3
y≤-3x/2+4