peterbat
Regular
I think he meant if you add the results of all 10 dice each time you throw them on the table, what sum do you get the most often.
Hint: 10 and 60 occur least often.
Math Question
- Thread starter darkzelkova
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I think he meant if you add the results of all 10 dice each time you throw them on the table, what sum do you get the most often.
Hint: 10 and 60 occur least often.
shelley
chang
How do you know what level math he's familiar with? If he were in 1st grade, these problems would be very challenging indeed.
And yeah, question 1? I make a little more than that but I have to work for it. And I have to pay rent. What kind of allowance is this?
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fanwuq
Legend
Gparker
Veteran
Yes i am in 7th grade, but weve messed around with geometry and stuff, i guess yall think its easy because yall are higher up in math O.o
Lord Voldemort
He-Who-Must-Not-Be-Named
Well, 1 can be done with only knowledge of arithmetic and reasoning.
2 is the hardest for me, 3 you can do guess and check but it's easier if you can set up an equation, 4 might be hard to derive yourself, but doable, 5 is just badly worded.
2 is the hardest for me, 3 you can do guess and check but it's easier if you can set up an equation, 4 might be hard to derive yourself, but doable, 5 is just badly worded.
shelley
chang
Hint for problem 2: it's quite repetitive. Try making some substitutions. (That's one way to go about it anyway)
You do have the right answer. Now just figure out how to get there.
Gparker
Veteran
I feel so stupid 
An 8th grader had to do this.
Let f be the function given by f(x)= e^(-2x^2) (read as e raised to the negative 2 x squared)
(a) Find the first four nonzero terms and the general term of the power seriews for f(x) about x=0.
(b) Find the interval of convergence of the power seriews for f(x) about x = 0. Show the analysis that leads to your conclusion.
(c) Let g be the function given by the sum of the first four nonzero terms of the power seriews for f(x) about x=0. Show that l f(x) - g(x) l < 0.02 for -0.6 less than or equal to x less than or equal to 0.6.
And thank you to everyone that helped me. I think I figured #2 on my own before i saw voldemorts ansewer. But like he said im not that sure, ill make substitutions as shelly said.
An 8th grader had to do this.
Let f be the function given by f(x)= e^(-2x^2) (read as e raised to the negative 2 x squared)
(a) Find the first four nonzero terms and the general term of the power seriews for f(x) about x=0.
(b) Find the interval of convergence of the power seriews for f(x) about x = 0. Show the analysis that leads to your conclusion.
(c) Let g be the function given by the sum of the first four nonzero terms of the power seriews for f(x) about x=0. Show that l f(x) - g(x) l < 0.02 for -0.6 less than or equal to x less than or equal to 0.6.
And thank you to everyone that helped me. I think I figured #2 on my own before i saw voldemorts ansewer. But like he said im not that sure, ill make substitutions as shelly said.
Lord Voldemort
He-Who-Must-Not-Be-Named
Oh duh. It's just an infinite geometric series with starting term 1/2 and common ration 1/2. Just carry it to a few repetitions, ignore the last 1/2 and it's clear.
EDIT: Are you sure that's not your homework?
Seems a bit suspicious to me.
Isn't power series usually with Taylor's series? I don't know what a power series is, and I don't really care to find out. How do you go from basic algebra to something like this in one year?
EDIT: Are you sure that's not your homework?
Seems a bit suspicious to me.
Isn't power series usually with Taylor's series? I don't know what a power series is, and I don't really care to find out. How do you go from basic algebra to something like this in one year?
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Gparker
Veteran
Wait what? The problems i gave were extra credit, we havnt learned much about that kind of stuff yet and she just wanted for us to try it, and plus you dont have to even try it. And the one that the 8th grader sent me was also for his extra credit.
Lord Voldemort
He-Who-Must-Not-Be-Named
Well, posting two sets of problems, it does seem like we might be doing your home work for you. This is more complex than the first set though, so I doubt this is from the same extra credit set. Taylor's Series are usually introduced in first year calculus as far as I know.
Gparker
Veteran
Wow, i can do my own math homework thank you. The first set was my set, i didnt ask for ansewers, i asked for help. But if you like just gave me the ansewer ii would have to figure out how you got it. The second one was from a friend of mine. And plus, the last 2 weeks of school with finals over and i cant do my own math homework? Its just extra credit, thats all. She would never give it to us for a grade since it wouldent be fair. Honestly, do you think any of that is pre-algabra stuff?
Bryan
Premium Member
Isn't extra credit something that boosts your grades? It doesn't matter if it's base homework or extra homework. The fact is if you're not figuring it out on your own and submitting our answers, you're unethically inflating your grades.
fanwuq
Legend
Is the 8th grader doing typical 8th grade math? I've not encountered any of the stuff in the 2nd set and I just finished AP Calculus AB. Series does sound like a topic from BC.
The first set is pre-algebra other than 2nd and 4th problem. 4th problem would have been better if it asks you to prove it. I would say there is about a 6 year difference between the level of the 1st and 2nd set of problems.
Bryan: Agreed.
The first set is pre-algebra other than 2nd and 4th problem. 4th problem would have been better if it asks you to prove it. I would say there is about a 6 year difference between the level of the 1st and 2nd set of problems.
Bryan: Agreed.
Gparker
Veteran
I'm really sorry then, I know no one will believe me but I promise i wont send them in. I dont even need the extra credit anyway. I put it on here for help and to see if it was a challenge to anybody else. I'm very sorry and i aplogize deeply.
Lord Voldemort
He-Who-Must-Not-Be-Named
I never outright accused you, I just suggested it may have been a possibility. As for the answers/help thing, they can be rather ambiguous without anything else to go by. School isn't over for everyone, only in America. And no, as I said, it seems like calculus with isn't Pre-Algebra.
I had a similar response to fanwuq, and it was somewhat suspicious. If someone else asked questions and then more questions, then what would you think?
I had a similar response to fanwuq, and it was somewhat suspicious. If someone else asked questions and then more questions, then what would you think?
Gparker
Veteran
Well, the second set was just for people to try. Have some fun you know?
Let f be the function given by f(x)= e^(-2x^2) (read as e raised to the negative 2 x squared)
(a) Find the first four nonzero terms and the general term of the power series for f(x) about x=0.
e^x = 1+x+x^2/2+x^3/3!+x^4/4!+...
e^-x = 1-x+x^2/2-x^3/3!-x^4/4!+x^5/5!...
e^(-2x^2)=1-2x^2+2x^4/2-2x^6/3!-2x^8/4!+2x^10/5!-...
general term:
2x^(2n)/n!*(-1)^n
(b) Find the interval of convergence of the power series for f(x) about x = 0. Show the analysis that leads to your conclusion.
Hint: -1< e^(-2(x+1)^2) /e^(-2x^2) < 1
Solve and then look at the series when it's at 1 and -1 and if it does not diverge, then that is also included in the answer.
(c) Let g be the function given by the sum of the first four nonzero terms of the power seriews for f(x) about x=0. Show that l f(x) - g(x) l < 0.02 for -0.6 less than or equal to x less than or equal to 0.6.
Lagrange Error Form is annoying, but that's a hint.
The following problems seem very unrelated and much much easier.
2. If 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y,
then x = ?
It's just 1/2x+1/4x+1/8x+...+1/(x*2^n) so x = y
(easily shown with geometric series and it's well known as well)
5. What number shows up most often when you roll 10 dice?
35
Also:
LOL @ SPDCBR
(a) Find the first four nonzero terms and the general term of the power series for f(x) about x=0.
e^x = 1+x+x^2/2+x^3/3!+x^4/4!+...
e^-x = 1-x+x^2/2-x^3/3!-x^4/4!+x^5/5!...
e^(-2x^2)=1-2x^2+2x^4/2-2x^6/3!-2x^8/4!+2x^10/5!-...
general term:
2x^(2n)/n!*(-1)^n
(b) Find the interval of convergence of the power series for f(x) about x = 0. Show the analysis that leads to your conclusion.
Hint: -1< e^(-2(x+1)^2) /e^(-2x^2) < 1
Solve and then look at the series when it's at 1 and -1 and if it does not diverge, then that is also included in the answer.
(c) Let g be the function given by the sum of the first four nonzero terms of the power seriews for f(x) about x=0. Show that l f(x) - g(x) l < 0.02 for -0.6 less than or equal to x less than or equal to 0.6.
Lagrange Error Form is annoying, but that's a hint.
The following problems seem very unrelated and much much easier.
2. If 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y,
then x = ?
It's just 1/2x+1/4x+1/8x+...+1/(x*2^n) so x = y
(easily shown with geometric series and it's well known as well)
5. What number shows up most often when you roll 10 dice?
35
Also:
LOL @ SPDCBR
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Gparker
Veteran
I have no idea if thats right. But it looks good, i wonder if anyone else could do it. Was it hard?
Also, for #5, could you say how you got 35?
qqwref
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Here's an interesting math problem to think about. It is not as easy as you think!
Suppose you have N boxes and K objects. The boxes are numbered from 1 to N; for each object, we randomly choose a box number, and write that down. Now we place the objects in the boxes, according to what number each object was given.
Okay, so here's the question: we're going to choose a random object and look in the box corresponding to that object. What is the expected value of the number of objects that will be in that box (i.e. on average, how many objects will be there)?
EDIT: If you can solve that, try this harder version: at the last part, instead of choosing a random object, we're going to choose (at random) one of the boxes that is not empty. What's the expected value of the number of objects in that box now?
Suppose you have N boxes and K objects. The boxes are numbered from 1 to N; for each object, we randomly choose a box number, and write that down. Now we place the objects in the boxes, according to what number each object was given.
Okay, so here's the question: we're going to choose a random object and look in the box corresponding to that object. What is the expected value of the number of objects that will be in that box (i.e. on average, how many objects will be there)?
EDIT: If you can solve that, try this harder version: at the last part, instead of choosing a random object, we're going to choose (at random) one of the boxes that is not empty. What's the expected value of the number of objects in that box now?
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jacob15728
Regular
I feel so stupid
An 8th grader had to do this.
Let f be the function given by f(x)= e^(-2x^2) (read as e raised to the negative 2 x squared)
(a) Find the first four nonzero terms and the general term of the power seriews for f(x) about x=0.
(b) Find the interval of convergence of the power seriews for f(x) about x = 0. Show the analysis that leads to your conclusion.
(c) Let g be the function given by the sum of the first four nonzero terms of the power seriews for f(x) about x=0. Show that l f(x) - g(x) l < 0.02 for -0.6 less than or equal to x less than or equal to 0.6.
And thank you to everyone that helped me. I think I figured #2 on my own before i saw voldemorts ansewer. But like he said im not that sure, ill make substitutions as shelly said.
That was completely unnecessary.
