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CSI Algebra Project

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by

Danyelle Adelman

on 24 November 2014

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Transcript of CSI Algebra Project

CSI Algebra Project
Crime Scene #2
Crime Scene #3
This crime scene took place in Trondheim, Norway at the Stiftsgarden Palace.
Crime Scene #6
Conclusion
Crime Scene #1
The answer is V= -2
The answer is s=1/3.
This crime took place in Sweden on the Streets of Malmo.
This crime took place in Stockholm, Sweden at a Haunted House.
Cryptic Puzzle Solver Text Message
m(2)+m(-2)+1/3 √(-d)+n
-----------------------------------
2

m(2)+m(-2)+1/3 √11+25
-----------------------------------
2
Cryptic Puzzle Solver Text Message
m(2)+m(-2)+1/3 √11+25
----------------------------------
2

(191.5)(2)+(191.5)(-2)+1/3 √11+25
-------------------------------------------------
2
Cryptic Puzzle Solver Text Message
mt+m(-2)+s √(-d)+n
------------------------------
t

m(2)+m(-2)+s √(-d)+n
--------------------------------
2

Cryptic Puzzle Solver Text Message
mt+mv+s √(-d)+n
--------------------------
t

mt+m(-2)+ √(-d)+n
-----------------------------
t
Cryptic Puzzle Solver Text Message
m(2)+m(-2)+s √(-d)+n
-------------------------------
2

m(2)+m(-2)+1/3 √(-d)+n
-----------------------------------
2
by: Danyelle Adelman 802
The answer is t=2.
Crime Scene #4
The answer is D=-11.
This crime scene took place in Nyboro, Sweden at the Kingdom of Crystal.
Crime Scene #5
The answer is n=25
This scene took place in Oslo, Norway at the Viking Ship Museum.
The answer is m=191.5
This scene took place in Sodankyla, Finland at the Global Warming Institute City.
(191.5)(2)+(191.5)(-2)+1/3 √11+25
------------------------------------------------- = 1
2
To find this answer, you first add 11 and 25 which is 36. Then you find the square root of that which is 6. 191.5 multiplied by 2 and 191.5 multiplied by -2 cancel each other out. Then you are left with 1/3(6)
all over 2. 1/3(6) equals 2 and 2/2=1. Therefore,
the answer is 1.

Murphy's favorite number is 1, therefore he is Algor Rhythmsson.
Who Is Algor Rhythmsson?
Explanation For Scene 1
To figure out which value is equal to v I solved the inequalities.
The first inequality is v+2>10. To solve this inequality you subtract 2 from both sides and you get v>8. When you graph this yo cross off every number greater than 8.
The next inequality is -12≥3v. To solve this inequality you divide both sides by 3 to get -4≥v. To help graph this inequality you flip it which makes the inequality v≤-4. When you graph this you cross off every number less than or equal to -4.
The third inequality is |v+5|≥6. To solve this inequality you get rid of the absolute value bars. To do this you create two inequalities: v+5≥6 and v+5≤-6. Then you subtract 5 from both sides to get v≥1or v≤-11. When you graph this you cross off every number greater than or equal to 1 and every number less than or equal to -11.
The fourth inequality is |2v|<2. To solve this inequality you have to get rid of the absolute value bars and to do that you create two inequalities which are: 2v<2 and 2v>-2. Next you divide by two on both sides to get v<1 and V>-1. When you graph this you cross off every number that is less than 1 but, greater than -1.
The fifth inequality is v>0. Therefore v>0. When you graph this you cross off every number greater than 0.
The next equation is |v|= 5. To solve this equation you have to get rid of the absolute value bars. To do this you have to create two equations: v=5 and v=-5. Therefore v={5,-5}. When you graph this you cross off 5 and -5.
The seventh inequality is 6<-3v. To solve this inequality you divide by -3 on both sides to get -2<v. To make graphing easier, you flip this inequality so you have the "v" on the other side which is v>-2. When you graph this you cross off every number greater than -2.
The last equation is |v|-5=-4. To solve this inequality you have to isolate the absolute value bars and to do that you have to add 5 to both sides which makes the equation |v|=1 (5-4=1). Then you have to get rid of the absolute value bars and to do that you create two equations which are v=1 and v=-1. To simplify this you write v={1,-1}. When you graph this you cross off 1 and -1.
There should be one number left which is -2. Therefore v=-2.
Explanation For Scene 2
To figure out which king's heart is bigger, I first had to do some research. The words in the problem in the packet are in Norwegian and when they are translated to English they are numbers. To figure out how big Haakon's heart is, I had to translate tre, sju, and tjueen. Tre means 3, sju means 7, and sjueen means 21. When you put those numbers back into the equation, you get 3a(the variable for the heart)+7=21. To solve this, you have to subtract 7 from both sides. Then you have 3a=14. Next, you divide both sides by 3 and you get a=4.66 repeating. Therefore Haakon's heart is equal to 4.66 repeating.
Then you have to find Magnus's heart. The Norwegian words in this equation are nitten, fire, and femti. Nitten means 19, fire means 4, and femti means 50. When you put those numbers back into the equation you get 19a-4=50. To solve this you first have to add 4 to both sides. Then you have 19a=54. Next, you divide both sides by 19 and you get a=2.84.
4.66 repeating(Haakon's heart) is greater than 2.84(Magnus's heart). Therefore, since Haakon's heart is greater than Magnus's heart the variable "t" is equal to 2.
Explanation For Scene 3
To write the inequality that represents the situation, I realized that x should represent how much he must sell and since he must sell at least $400. The inequality would be x≥$400.

To figure out if the street vendor will cover his costs, I had to do some multiplying. First I multiplied 68 by 3 because he sold 68 Atlantic herring which is sold at $3 a piece. That equals $204. Then I multiplies 38 by 5 because he sold 38 meatballs and $5 a piece. That equals to $190. You have to add them together to find out how much money he has total. Which is $394. $394 is less than $400.

Therefore, no he will not cover his costs. Which means the variable "s" equals 1/3.
Explanation For Scene 5
To figure out whether or not 25 is in the solution to every answer or not, I have to make inequalities.
For the first example, I added 25 and 30 to see how many Viking coins he had already spent which is 55. Then I subtracted that amount from his total amount (85) and got 30. The inequality I created was x≤30 Viking coins.

For the second example, I added 13 and 5 to see how many houses he had already robbed which was 18. Then I subtracted that from the total he had to at the very least rob (45) and got 27. The inequality I created was x≥27 robberies.

For the third example, I subtracted 20 from 30 because that would give me how much Viking coins he has left which would be 10. Then I divided that number by .25 (amount of Viking coins per text message) and got 40. Therefore, the inequality I created was x≥40 text messages.

For the fourth example, I added up his three test scores (91, 88,95) which was 274. Then I did some guessing and checking. I added 95 and 274 and got 369 and when I divided it by 4 I got 92.25. While 95 would work, he wanted to know what score he needed to at the very least get to get his 92 average. I tried 94. I added 94 and 274 and got 368 and when I divided it by 4, I got 92. Therefore, the inequality I created was x≥94 test score.

Since 25 was NOT in the solution set of every answer, n=25.
Explanation For Scene 4
To figure out which variable is equal to -11, I have to solve and graph the inequalities.
The first set of inequalities is 6r≥12 and -2r≥-8. To solve the first inequality you divide both sides by 6 and get r≥2. To solve the second inequality you divide both sides by -2 to get r≤4 because when you divide by a negative number you switch the sign. When you graph this you put a closed circle on 2 and 4 and shade the area in between them. Which is equivalent to letter A.
The second set of inequalities is 7<-1+2r or 7r-3>4. To solve the first inequality you add 1 to both sides to get 8<2r. Then you divide both sides by 2 to get 4<r. To make it easier to graph you have to flip the inequality which would make it r>4. To solve the second inequality you add 3 to both sides to make it 7r>7. Then you divide both sides by 7 to get r>1. When you graph this, the graphs overlap which makes the graph look like just one where the 1 has an open circle and it is shaded to the right. Which is exactly what letter V is.
The third set of inequalities is |r-1|<2. To solve this inequality you have to get rid of the absolute value bars and to do that you have to create two inequalities which are: r-1<2 and r-1>-2. To solve both of those inequalities you add 1 to both sides in each equation to get r<3 and r>-3. When you graph this you put an open circle on 3 and -3 and shade the area in between.
The fourth set of inequalities -2|r-2|≤ -6. To solve this inequality you have to first divide both sides by -2 to get |r-2|≥ 3. Then, to get rid of the absolute value bars, you create two equations and they would be r-2≥ 3 or r-2≤ -3. Then you add 2 to both sides of both inequalities which makes them r≥5 or r≤-1. When you graph this you put closed circles on 5 and -1 and shade to the right of 5 and to the left of -1. Which is equivalent to letter T.

The letter left out is D and therefore D=-11.
Explanation For Scene 6
To calculate the number of miles you can travel in each mode of transportation while remaining under 24.80 pounds of CO2 I did a lot of dividing.

For the average car, I divided 24.80 by 1.10 which is approximately 22.5 miles. The inequality to describe this is m≤ 22.5.

For the average SUV, I divided 24.80 by 1.67 which is approximately 14.9 miles. The inequality to describe this is m≤ 14.9.

For the jet, I divided 24.80 by 0.97 which is approximately 25.6 miles. The inequality to describe this is m≤ 25.6.

For the mass transit (1/4 full), I divided 24.80 by 0.75 which is approximately 33.1 miles. The inequality to describe this is m≤ 33.1.

For the mass transit (3/4 full), I divided 24.80 by 0.26 which is approximately 95.4 miles. The inequality to describe this is m≤ 95.4.

When you add all the miles up 22.5+14.9+25.6+33.1+95.4= 191.5 Therefore, m=191.5.

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