Thread: algebra identity

Hey I'm in Contemp Math, so I'm just studyign but can someone give me examples

To find a counter example to show that each conjecture is false

_______
1./ x^2=x


2. any number divided by itself equal to 1

3. for all x |x-14|<x

thank you!!

Originally Posted by Dillon658

Hey I'm in Contemp Math, so I'm just studyign but can someone give me examples

To find a counter example to show that each conjecture is false

_______
1./ x^2=x

come on, pick a random number. there are only two real numbers for which this works, your chances of being right through randomly guessing are actually pretty good

2. any number divided by itself equal to 1

hint: is there a number that we can't divide by?

3. for all x |x-14|<x

thank you!!

hint: whatever is in absolute values becomes non-negative. meaning we must have $\displaystyle |x - 14} \ge 0$ for all x

I think the OP meant to have a square root sign over x^2: $\displaystyle \sqrt{x^2} = x$.

Note that: $\displaystyle \sqrt{x^2} = |x|$ Can you think of a number that will be a counterexample to $\displaystyle \sqrt{x^2} = x$

Originally Posted by Jhevon

come on, pick a random number. there are only two real numbers for which this works, your chances of being right through randomly guessing are actually pretty good

hint: is there a number that we can't divide by?

hint: whatever is in absolute values becomes non-negative. meaning we must have $\displaystyle |x - 14} \ge 0$ for all x

Hey Jhevon

Ok let me see

the first one I got 1^2=1??? orrrrr 2^2=4

?? is that right? 1 or 2??

and for number 2 I got 0?

working on third THANK YOU!!

$\displaystyle 0^2 = 0$

$\displaystyle 1^2 = 1$

" In a soccer league with 10 teams, each team plays each of the other teams 3 times. How many league games will be played?"



Determine the nth-term formula for a sequence that has the first 3 terms of
9, 12, 15.....



if you can help me with those too? and that last one it messed up

for all x, |x-14|< 14

Originally Posted by Dillon658

Hey Jhevon

Ok let me see

the first one I got 1^2=1??? orrrrr 2^2=4

?? is that right? 1 or 2??

you realize counter-example means here to find a number for which it does NOT work, right? clearly it works for 1...

if you let x = 1, is x^2 = x?

if you let x = 2, is x^2 = x?

by the way, o_O suggested your question might be something else, was he right?

and for number 2 I got 0?

yes. 0/0 is not 1, because we can't divide by 0

yes 0_0 was correct its all under the square root thingy

and thank you for helping me


quick question
"All ancient greek mathaticians were also philosphers. Euclid was an ancient Greek mathematician, so Euclid was also a philosopher."

Is that inductive reasoning or deductive?

Originally Posted by Dillon658

" In a soccer league with 10 teams, each team plays each of the other teams 3 times. How many league games will be played?"

ok, call the teams team1, team2, etc

and lets think through this.

team1 plays the other 9 teams 3 times each, so team 1 plays 3x9 = 27 games

team2 has to play the other 9 teams 3 times as well. but it already played team1 3 times, so it remains to play the other 8 teams 3 times. thus we have an additional 3x8 = 24 games

team3 has to play the other 9 teams 3 times as well. but it already played team1 3 times AND team2 3 times, so it remains to play the other 7 teams 3 times. thus we have an additional 3x7 = 21 games

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.
.
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continue the same reasoning. how much do you end up with?

Determine the nth-term formula for a sequence that has the first 3 terms of
9, 12, 15.....

try thinking of a common difference between the numbers.

if you can help me with those too? and that last one it messed up

for all x, |x-14|< 14

we want |x - 14| < x NOT to work. so what do we have to pick x to be? i told you, the absolute value of something CANNOT be negative. so what kind of x are we looking for?

Originally Posted by Dillon658

yes 0_0 was correct its all under the square root thingy

ok, then my advice with that question is the same as with the |x - 14| < x question.

did you find an answer yet?

quick question
"All ancient greek mathaticians were also philosphers. Euclid was an ancient Greek mathematician, so Euclid was also a philosopher."

Is that inductive reasoning or deductive?

do you know what "inductive" and "deductive" reasoning means?

also, you should really ask new questions in new threads. if all your questions are related, then post all at once. we would appreciate it if you are honest and tell us if it is for homework or a take home test or something to be graded.

ok for one I got 72 games??

number 2 I got 18 just add +3? the determine the formula what gets me


number 3 I got 15? if 15-14 is 1? it cant be greater than 14

For number 2, think of it as an arithmetic sequence with a common difference d. Then, use this equation:

$\displaystyle t_n = t_1 + (n-1)(d)$

...to find the nth formula. $\displaystyle t_n$ is the nth term and $\displaystyle t_1$ is the first term.

$\displaystyle \underbrace{9}_{\text{first term}}, \underbrace{12}_{\text{second term}}, \underbrace{15}_{\text{third term}}, \ldots$

As for number 3:

$\displaystyle |x-14|<x\ \text{for all}\ x$ is a statement that could be either true or false. You need to find a counterexample, which is an example that makes the statement false.

Understand what you are given here. Anything that comes out of an absolute value will be positive. So when is it ridiculous that a positive number is less than a given number?