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!!
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!!
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?2. any number divided by itself equal to 1
hint: whatever is in absolute values becomes non-negative. meaning we must have $\displaystyle |x - 14} \ge 0$ for all x3. for all x |x-14|<x
thank you!!
" 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
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?
yes. 0/0 is not 1, because we can't divide by 0and for number 2 I got 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?
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
.
.
.
.
continue the same reasoning. how much do you end up with?
try thinking of a common difference between the numbers.Determine the nth-term formula for a sequence that has the first 3 terms of
9, 12, 15.....
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?if you can help me with those too? and that last one it messed up
for all x, |x-14|< 14
ok, then my advice with that question is the same as with the |x - 14| < x question.
did you find an answer yet?
do you know what "inductive" and "deductive" reasoning means?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?
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.
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?