Kappa Sigma - ΚΣ Fraternity Ratings at UCM
- Total Ratings: 56
- Overall Average:
By: ASIPPosted:
For the ï¿½ x terms: ï¿½ 2 âˆ’ 2 ï¿½ x 2 âˆ’2x We add and subtract ( 2 2 ) 2 = 1 ( 2 2 â€‹ ) 2 =1 to complete the square. This gives us ï¿½ 2 âˆ’ 2 ï¿½ + 1 âˆ ’ 1 = ( ï¿½ âˆ’ 1 ) 2 â ˆ’ 1 x 2 âˆ’2x+1âˆ’1=(xâˆ’1) 2 âˆ’1. For the ï¿½ y terms: ï¿½ 2 âˆ’ 6 ï¿½ y 2 âˆ’6y We add and subtract ( 6 2 ) 2 = 9 ( 2 6 â€‹ ) 2 =9 to complete the square. This gives us ï¿½ 2 âˆ’ 6 ï¿½ + 9 âˆ ’ 9 = ( ï¿½ âˆ’ 3 ) 2 â ˆ’ 9 y 2 âˆ’6y+9âˆ’9=(yâˆ’3) 2 âˆ’9. Rewriting the Function Substituting these into the original function, we get: ï¿½ ( ï¿½ , ï¿½ ) = ( ï¿½ âˆ’ 1 ) 2 âˆ’ 1 + ( ï¿½ âˆ’ 3 ) 2 âˆ’ 9 f(x,y)=(xâˆ’1) 2 âˆ’1+(yâˆ’3) 2 âˆ’9 This can be further simplified to: ï¿½ ( ï¿½ , ï¿½ ) = ( ï¿½ âˆ’ 1 ) 2 + ( ï ¿½ âˆ’ 3 ) 2 âˆ’ 10 f(x ,y)=(xâˆ’1) 2 +(yâˆ’3) 2 âˆ’10 Analyzing the Function The squared terms ( ï¿½ âˆ’ 1 ) 2 (xâˆ’1 ) 2 and ( ï¿½ âˆ’ 3 ) 2 (yâˆ’3 ) 2 are always non-negative since any real number squared is non-negative. The smallest value these squares can take is 0, which occurs when ï¿½ = 1 x=1 and ï¿½ = 3 y=3. Thus, the smallest value of ï¿½ ( ï¿½ , ï¿½ ) f(x, y) is âˆ’ 10 âˆ’10, achieved at the point ( 1 , 3 ) (1,3). There is no upper bound for ï¿½ ( ï¿½ , ï¿½ ) f(x, y) since the squared terms can grow indefinitely as ï¿½ x and ï¿½ y move away from 1 and 3, respectively. Conclusio n The smallest value of ï¿½ ( ï¿½ , ï¿½ ) f(x, y) is âˆ’ 10 âˆ’10, occurring at ( 1 , 3 ) (1,3). The function ï¿½ ( ï¿½ , ï¿½ ) f(x, y) has no largest value; it grows indefinitely as ï¿½ x and ï¿½ y move away from 1 and 3, respectively. User can you just show the math no need for an explnation such as if it was for hw ChatGPT Certainly! Here's the concise mathematical work for the problem: Problem: Find the largest and smallest values of ï¿½ ( ï¿½ , ï¿½ ) = ï¿ ½ 2 âˆ’ 2 ï¿½ + ï¿½ 2 â ˆ’ 6 ï¿½ f(x,y)=x 2 âˆ’2x+y 2 âˆ’6y. Solution: Comp lete the square for ï¿½ x: ï¿½ 2 âˆ’ 2 ï¿ ½ = ( ï¿½ âˆ’ 1 ) 2 âˆ’ 1 x 2 âˆ’2x=(xâˆ’1) 2 âˆ’1 Complete the square for ï¿½ y: ï¿½ 2 âˆ’ 6 ï¿ ½ = ( ï¿½ âˆ’ 3 ) 2 âˆ’ 9 y 2 âˆ’6y=(yâˆ’3) 2 âˆ’9 Rewrite ï¿½ ( ï¿½ , ï¿½ ) f(x, y): ï¿½ ( ï¿½ , ï¿½ ) = ( ï¿½ âˆ’ 1 ) 2 âˆ’ 1 + ( ï¿½ âˆ’ 3 ) 2 âˆ’ 9 f(x,y)=(xâˆ’1) 2 âˆ’1+(yâˆ’3) 2 âˆ’9 Simplify: ï¿½ ( ï¿½ , ï¿½ ) = ( ï¿½ âˆ’ 1 ) 2 + ( ï¿½ â ˆ’ 3 ) 2 âˆ’ 10 f(x,y)= (xâˆ’1) 2 +(yâˆ’3) 2 âˆ’10 Analyze the function: Minimum: ï¿½ ( ï¿½ , ï¿½ ) f(x, y) is minimized when ( ï¿½ âˆ’ 1 ) 2 = 0 (x âˆ’1) 2 =0 and ( ï¿½ âˆ’ 3 ) 2 = 0 (y âˆ’3) 2 =0, i.e., at ( ï¿½ , ï¿½ ) = ( 1 , 3 ) (x,y)=(1,3). Minimu m value: ï¿½ ( 1 , 3 ) = 0 + 0 âˆ’ 10 = âˆ’ 10 f(1,3)= 0+0âˆ’10=âˆ’10. No maximum value since ( ï¿½ âˆ’ 1 ) 2 (xâˆ’1 ) 2 and ( ï¿½ âˆ’ 3 ) 2 (yâˆ’3 ) 2 can grow indefinitely. Results: Smallest value of ï¿½ ( ï¿½ , ï¿½ ) f(x, y) is âˆ’ 10 âˆ’10, at ( 1 , 3 ) (1,3). No largest value for ï¿½ ( ï¿½ , ï¿½ ) f(x, y).\n\n\n\n\n
Associates with:
Sigma Chi Fraternity
Delta Gamma Sorority
- Reputation: Wealthy
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By: BobcatPosted:
The only frat that actually has a chapter house. Parties are coo and their brothers are inclusive. Overall decent ppl
Associates with:
Kappa Kappa Gamma Sorority
- Reputation: Social
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By: Greek_RankPosted:
Bottom tier fraternity. Give bids to anyone/everyone. All other fraternities do not associate with them because they are mostly all rats and untrustworthy. You should really consider choosing the other fraternities rather than this one. They used to be top house and had some cool dudes, but that has now all changed. The only thing they have now are their looks.
Associates with:
Kappa Kappa Gamma Sorority
- Reputation: Looks
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By: KKGPosted:
This chapter of Kappa Sigma is beyond amazing. Every member takes their time to be sincere, helpful, and kind. Each one holds their values to heart and this is commendable.
Associates with:
Kappa Kappa Gamma Sorority
- Reputation: Looks
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By: Bren Posted:
Honestly trash. Very secluded from many. The culture here is fake, brothers cause really bad issues for their chapter. Not really the best frat on campus, but not the worst! They could do a lot better!
Associates with:
Kappa Kappa Gamma Sorority
- Reputation: Social
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By: Kakasig Posted:
They aight but Iâ€™ve heard many stories about them and a lot about what goes on at parties. I have encountered some genuine men but when it comes to being drunk these guys are animals ,
Associates with:
Sigma Chi Fraternity
Kappa Kappa Gamma Sorority
- Reputation: Social
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By: Snow bunnyPosted:
Interesting group of men who are fun and caring. They are also the top dogs on campus who are involved in different aspects of the campus.
Associates with:
Sigma Chi Fraternity
Kappa Kappa Gamma Sorority
- Reputation: Social
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By: LolPosted:
Everyone in campus knows theyâ€™re too. Theyâ€™re party animals but still care about their brotherhood
- Reputation: Social
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By: Pol Posted:
Some of their brothers were very pushy I did t really like how they can pressure people to do things. Cool parties but kinda creepy
- Reputation: Social
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By: CatPosted:
Very messy and definitely do not feel very safe around them. Only known for being party animals, brotherhood is weak.