5

11. Prove: For all integers n, n^2 +n +11 is odd....

Question

11. Prove: For all integers n, n^2 +n +11 is odd.

11. Prove: For all integers n, n^2 +n +11 is odd.



Answers

Prove that $n$ is odd if and only if $n^{2}$ is odd. (See Problem 73.)

Okay, So for this question, wanna prove that any are if it on five and six days off. So the first thing we'll do is improve the four occupation. So it's in his hole. They're working. And as being true to the cave close by one. Okay, Some indigent. Yes. A genie back into fighting six is equal to find time to UK plus one possible six. This is 10 10 k plus bye bye Seeks. This is 10 k last night, 11 so we could write this to fire Cape five. Well, now this is just some interject looking what is, as true, a plus one. Where and use it to five k. Possible. Why? Which is just a job. It's a death for five plus six is off. Some improved forward terribly. That's approved a backwards direction. Well, do you provide? So we wouldn't appreciate that Impossible sixties. This implies that it is all because of truth in what contradiction we have, Steven. So if it's even in as being to tell it to be for something, something to get me, substitute that into here. Phantom to be six. This is 10 b six. This giri irritable by the plus six. So once again, this is just on inter gender. And so therefore this must be leaving. Well, it predicts the presupposition that is all, therefore, and not even muster to proven the backwards indication. So therefore and it's odd, isn't it? Impresses is on.

Okay, So in this question, we want to prove that the floor and divided by two is equal to end over two for n even an end once one divided by two went in on. So how do we do this? It was first it up. So that and be even. Well, if it is, even then we know that exists and interject and m such that and it's equal to chew em on. That is m is equal to and why. So we substitute this into our floor function. So to em, divided by two the truth is capital out. So this is for him since M isn't it? Georgia? The floor damages. We also know that M is equal to end it. What about you? So the first part sounds fine dispute. Now we let and be on. So in this case, that exists an easy job. Em such dense. And is it to shoot and plus one? Well, this is me. It means that I am so we subtract the one over. And you did too. The end If it was end once. One black budget. Now you put this into our floor function. But this is going to be floor all to M plus one divided by two. So this is in just a, huh? Now, how do we solve this? So am I, Is an insurgent and m plus one. And hop is right here. So because we're taking floor, we're going to take the incident that is right next to us. So this is just beat him. But when I missed the end, while it's one divided by two and minus one people about to so therefore the second part satisfied with trivial they're combining these two things together. We have our question.

Immigration is one by one into four, plus one by foreign to seven. So one it was won by three in minus two in do three and plus one week will toe end by three and plus one. Let's tow N is equal to one, so that will be won by one in four. And here it is, one by for us aboard the similar. So let's do in is equal to Keano. That would become one body when my one into four. One by one into four, plus one by four into seven, plus a war less one, my three K minus two into three K plus one and the audits is his key by three key plus once, let's add one by three K plus one you do three key plus four on would say, If you do that, we will get Let's see only the artist. It will mean key by pre K plus one plus one by three K plus one into three key plus four so we can take one by three K plus one common and we keep plus one by three key less For so taking LCN, it's become the case quit plus four key plus one by three k plus one Indu to be key less for so next. Soldering that we will get three K in Duke A plus one close K plus one by K plus one in do three key plus four that is equal Do K plus one into a three year plus one by K plus one into three K plus four. So this will give us K plus one name. Toe the nominal interest. We K plus one indoor three K plus four So the still give escape plus 1 May three Key less so substituting Keep lis one. This in SK Plus one. Witches and music will do K plus one so we will get one. My one got four plus one by $4 7 plus. The one was won by three K plus one into three Key Plus four, which is equal toe K plus one by three K plus foot soldiers in the Spar similar hands. The equation is fully satisfied

Okay. In this question, we want to prove that end square is equal to is equivalent to one more eight. When n is an odd positive integer So we basically want to Seoul and square and squid mud. Thanks. So this is equivalent off solving and mud aids squared and he wants it more than eight. So now it's useful to think about what values this first more can take. So if n isn't odd, didja zero copy this value But it could be you could take on one because you can't take onto it can take out three can't taken four We'll take a five on dhe seven. So then, from one you have one squared more. Eight. So this is just one. You have three squid which gives you night mud eight. So this is 15 squared gives you 25 which is 20 by minus What equivalent to minus y three times by eight 18 So this number right here it has freed give you 24 So 25 minus 24 which is just one finally seven gives you seven squared gives you 49 so this is equivalent to 49 months by 56 times by eight 18 So it's six times 8 48 now 49 minus 48 which is simply one. So therefore, n squared is equal to one month. Eight if m is a positive integer.


Similar Solved Questions

5 answers
An inductor 20 10 3 H, a capacitor 1OOpF and resistor 5092 are connected in series across source emf V = 10 sin 314 t The energy dissipated in the circuit in 20 min is nearly A) 960 J B) 900 C) 720 _ D) 1080 J
An inductor 20 10 3 H, a capacitor 1OOpF and resistor 5092 are connected in series across source emf V = 10 sin 314 t The energy dissipated in the circuit in 20 min is nearly A) 960 J B) 900 C) 720 _ D) 1080 J...
5 answers
2 2 2 3 2 2 [ 7 P1A ~14 #H 044 8 8 ! 5 1 [ 6 12 5 2 2 2 2 2 3 7 I7 m 8 2 f 15 2 2 2 2 2 7 7 6 2 5 8 5 1 1 2 2 ; 1 0 0 E 1F 47 2 7 X15" L
2 2 2 3 2 2 [ 7 P1A ~14 #H 044 8 8 ! 5 1 [ 6 1 2 5 2 2 2 2 2 3 7 I7 m 8 2 f 1 5 2 2 2 2 2 7 7 6 2 5 8 5 1 1 2 2 ; 1 0 0 E 1 F 4 7 2 7 X 1 5" L...
5 answers
Scho br utel %RL3DB1AL/o
scho br utel % RL3D B1A L/o...
5 answers
Three resistors having resistances of 40 Q are connected in parallel to battery that has negligible interna resi stance: Find (a) the equivalent resistance of the combination; (b) the current in each resistor; (c) the total current through the battery; 5 (d) the voltage across each resistor; (e_ the power dissipated in each esistor. (f) Which resistor dissipates the most power: the one with the greatest resistance or the east resistance? Explain why this should be.
Three resistors having resistances of 40 Q are connected in parallel to battery that has negligible interna resi stance: Find (a) the equivalent resistance of the combination; (b) the current in each resistor; (c) the total current through the battery; 5 (d) the voltage across each resistor; (e_ the...
5 answers
Solvedr,9 (1/2) = 2
Solve dr ,9 (1/2) = 2...
5 answers
Submi: nnewer Suve ProgressFnctice antounes VersionJnointe SCacb = KruaEUANME the function for values 0f X that uppmodeh(rom thc left and Irom the right:F(*)Need Help?Wnt
Submi: nnewer Suve Progress Fnctice antounes Version Jnointe SCacb = Krua EUANME the function for values 0f X that uppmodeh (rom thc left and Irom the right: F(*) Need Help? Wnt...
5 answers
[W1 Foints]DETAILSPREVIOUS ANSWERSLARCALCT1 8.4.023.Find the indefinite Integrat {RemcmoctUSC dosclute valuict Whcro appropriate_for the constant of Integration; )nresinNood Holp?
[W1 Foints] DETAILS PREVIOUS ANSWERS LARCALCT1 8.4.023. Find the indefinite Integrat {Remcmoct USC dosclute valuict Whcro appropriate_ for the constant of Integration; ) nresin Nood Holp?...
5 answers
Based on these results, Pseudomonas aeruginosa demonstrates resistance {0 which of the lollowing entibiotics? Peniciilin (P10) Cefoxitin (FOX3O) Nalidixic Acid (NA3O) Azithromycin (AZM1S) Tetracycline (TE3O) Vancomycin (VA3O) - Gentamycin (CNIO) Trimethoprin Sulfamethoxazole (SXT25SubmlPreylulALixers EoquuMIUIncorrece; Try Aqjin; atemprs renijining
Based on these results, Pseudomonas aeruginosa demonstrates resistance {0 which of the lollowing entibiotics? Peniciilin (P10) Cefoxitin (FOX3O) Nalidixic Acid (NA3O) Azithromycin (AZM1S) Tetracycline (TE3O) Vancomycin (VA3O) - Gentamycin (CNIO) Trimethoprin Sulfamethoxazole (SXT25 Subml PreylulALix...
5 answers
(25 pts_ each) Find general solutions of the following systems(1) 4-(- 4)x (2) 4-( 9)x
(25 pts_ each) Find general solutions of the following systems (1) 4-(- 4)x (2) 4-( 9)x...
1 answers
Solve each equation for exact solutions over the interval $[0,2 \pi)$. $$ 2 \sec x+1=\sec x+3 $$
Solve each equation for exact solutions over the interval $[0,2 \pi)$. $$ 2 \sec x+1=\sec x+3 $$...
5 answers
67xCi0 0Remaining Time: hour; 29 minutes.37 secondsQuestion Completion Status:AABBCC DD EEHHGGWhat binds at the area indicated by EE? T T I Aral J (2p1
67xCi0 0 Remaining Time: hour; 29 minutes.37 seconds Question Completion Status: AA BB CC DD EE HH GG What binds at the area indicated by EE? T T I Aral J (2p1...
5 answers
Fundamental conditions which are differentiated the Oppenaur and meerwein Pondrof reactions?
Fundamental conditions which are differentiated the Oppenaur and meerwein Pondrof reactions?...
5 answers
2.30 g of an unknown metal bromide (MBr2, where M is the unknownmetal) was treated with excess AgNO3(aq). The isolated precipitateweighed 3.492 g. What is the identity of the metal bromide? (Choosethe closest answer). Use the course data sheet for any requireddata. CaBr2 (mw = 199.88 g mol−1) MgBr2 (mw = 184.11 g mol−1) SrBr2(mw = 247.42 g mol−1) ZnBr2 (mw = 225.18 g mol−1) CuBr2 (mw =223.35 g mol−1)
2.30 g of an unknown metal bromide (MBr2, where M is the unknown metal) was treated with excess AgNO3(aq). The isolated precipitate weighed 3.492 g. What is the identity of the metal bromide? (Choose the closest answer). Use the course data sheet for any required data. CaBr2 (mw = 199.88 g molâˆ...
4 answers
(3 points) Find the eigenvalues Ap Az and associated orthonormal eigenvectors of the symmetric matrix_1 ~3 ~1 A =~1~3has associated orthonormal eigenvectorshas associated orthonormal eigenvectorsNote: The eigenvectors above form an rthonormal eigenbasis for A
(3 points) Find the eigenvalues Ap Az and associated orthonormal eigenvectors of the symmetric matrix _1 ~3 ~1 A = ~1 ~3 has associated orthonormal eigenvectors has associated orthonormal eigenvectors Note: The eigenvectors above form an rthonormal eigenbasis for A...
5 answers
6 fee" dt8 . J 3*e* dx.'qi fevt+a dz _ 12 J xeer dx T-
6 fee" dt 8 . J 3*e* dx. 'qi fevt+a dz _ 12 J xeer dx T-...
4 answers
Are the vectors'-[HJ; :-[J; ;-[HJ linearly independent? Either show that they are independent_ Or give all explicit linear combination that shows dependence. (6) Is there homogeneous linear system of o.d.e s with constant coefficients for which all three of the functions hi(t) = e'vi , h2(t) = e2v2 , hs(t) = e3tu3 where vectors v; are those in the previous part of this problem) are solutions? Explain why Or why not_
Are the vectors '-[HJ; :-[J; ;-[HJ linearly independent? Either show that they are independent_ Or give all explicit linear combination that shows dependence. (6) Is there homogeneous linear system of o.d.e s with constant coefficients for which all three of the functions hi(t) = e'vi , h2...
4 answers
EJWNEI Find the moments of inertia I , Iy, and Io of & bomogeneous disk D with density p(x,y) P, cehter the origin, and radius a.
EJWNEI Find the moments of inertia I , Iy, and Io of & bomogeneous disk D with density p(x,y) P, cehter the origin, and radius a....

-- 0.017698--