Post by: spurcher on July 19, 2013, 06:30:01 pm
HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP HERE TO HELP
Currently in yr12 and just about finishing;Last year, in year 11 I studied this subject and finishes on 96. I am willing to help anyone with whatever question they may have and am willing to provide any extra material or links to external sites to get material from as well.......
Just saying ::) Here to help anyone who might want/need it....
xoxo
Post by: anotherworld2b on September 03, 2016, 10:25:21 am
Post by: jamonwindeyer on September 03, 2016, 10:29:47 am
Can i get help with c and d?
Hey! D isn't in your image! :P
For C though, it will be the inverse matrix of the one given for quadrilateral 1 to quadrilateral 2! That's the great thing about matrices representing transformations, to go backwards you just use the inverse matrix ;D So it will be your typical 2x2 matrix inverse formula:
Post by: anotherworld2b on September 03, 2016, 10:42:48 am
I also wanted to ask how do we prove matrices?
Hey! D isn't in your image! :P
For C though, it will be the inverse matrix of the one given for quadrilateral 1 to quadrilateral 2! That's the great thing about matrices representing transformations, to go backwards you just use the inverse matrix ;D So it will be your typical 2x2 matrix inverse formula:
Post by: jamonwindeyer on September 03, 2016, 10:55:30 am
Thank you very much ;D
I also wanted to ask how do we prove matrices?
For the question you provided, you would need to apply each transformation matrix (in order) to a general point, \(\binom{a}{b}\). So, take the general point, and apply each transformation by multiplying by the appropriate matrix. By the end, you should get back to the same point, \(\binom{a}{b}\).
Post by: anotherworld2b on September 03, 2016, 11:35:54 am
For matrices im confused in how to calculate the area. I followed the formula for the area of a triangle and i got 4 but the answer is 8?
Also i keep getting notifications that my images are too big and do not pass security checks?
For the question you provided, you would need to apply each transformation matrix (in order) to a general point, \(\binom{a}{b}\). So, take the general point, and apply each transformation by multiplying by the appropriate matrix. By the end, you should get back to the same point, \(\binom{a}{b}\).
Post by: jamonwindeyer on September 03, 2016, 12:26:55 pm
Thank you for your help :D
For matrices im confused in how to calculate the area. I followed the formula for the area of a triangle and i got 4 but the answer is 8?
Also i keep getting notifications that my images are too big and do not pass security checks?
I'm not quite sure what you mean by the "area" of a matrix, could you elaborate?
I'm not sure about your images, what type of image are they? You could compress the files if they are too big maybe? :)
Post by: anotherworld2b on September 03, 2016, 12:47:49 pm
I'm not quite sure what you mean by the "area" of a matrix, could you elaborate?
I'm not sure about your images, what type of image are they? You could compress the files if they are too big maybe? :)
Post by: jamonwindeyer on September 03, 2016, 12:58:30 pm
Im having a lot of trouble posting images. A notification keeps telling me to consult the forum administrator for security checks?
No idea what that could be, I'll pass it on, but whatever is letting you post the images you do post, just keep doing that! It could be a weird file extension or something :P
I've never seen the idea of using matrices to find area, but a quick Google search yielded a few things? Maybe one of them will help you ;D
Post by: anotherworld2b on September 03, 2016, 01:01:57 pm
Post by: jamonwindeyer on September 03, 2016, 01:14:23 pm
Heres the question ive been working on. I finally succeeded at posting it ;D
Awesome! I think you've misinterpreted a bit: ABCD is a square, not a triangle. Check the vertices and the question to confirm ;D
So your first sketch needs fixing, and then the area formula you need would change in response to that. Let me know how that goes.
Using the determinant to find the area: I've never seen that before, so I'll have to leave you with it :)
I think the misinterpretation of using a triangle instead of a square is causing your issues ;D
Post by: anotherworld2b on September 04, 2016, 03:01:20 pm
Post by: jamonwindeyer on September 04, 2016, 05:39:03 pm
Could I get help with these two questions?
Hey! Okay, so for Part A it's about finding the right way to consider the initial domains generally as a vector, then doing the transformation on the general point, thus proving the result for all points in the domain.
For example, we can express any point on the line \(y=5-3x\) as the following vector:
Apply the transformation to this vector, what you'll notice by doing the multiplication is that the x's cancel!
So the point in question is (10,5)! You'll do a similar thing for Part B, just consider a general point \(\binom{x}{y}\), and you'll find it maps to something that only has x's in it: This is a line!
Your second question, again the same principle. If we want to consider the transformation of the line, we can just consider the transformation of a general vector representing any point on the line!
Apply the matrix transformation to the vector, and you should get ANOTHER line with a new gradient, make the comparison as required ;D if you have trouble snap a pic of your working and give me a look and I'd be happy to give more of a hand!
Post by: anotherworld2b on September 05, 2016, 11:42:42 pm
Hey! Okay, so for Part A it's about finding the right way to consider the initial domains generally as a vector, then doing the transformation on the general point, thus proving the result for all points in the domain.
For example, we can express any point on the line \(y=5-3x\) as the following vector:
Apply the transformation to this vector, what you'll notice by doing the multiplication is that the x's cancel!
So the point in question is (10,5)! You'll do a similar thing for Part B, just consider a general point \(\binom{x}{y}\), and you'll find it maps to something that only has x's in it: This is a line!
Your second question, again the same principle. If we want to consider the transformation of the line, we can just consider the transformation of a general vector representing any point on the line!
Apply the matrix transformation to the vector, and you should get ANOTHER line with a new gradient, make the comparison as required ;D if you have trouble snap a pic of your working and give me a look and I'd be happy to give more of a hand!
Post by: jamonwindeyer on September 06, 2016, 01:25:25 am
I'm still confused about how to do q21. I also tried to other questions 15 qne 16 but im not getting the right answer. I also wanted to ask for q17 what exactly is it asking?
Where are you up to with Q21? Have you started by multiplying the vector I suggested above with the matrix given? That will apply the linear transformation, did you get that or is that operation troubling you? :)
Question 15 isn't really attackable with the method you used, you are better off using simultaneous!
Using the statement given, we conclude the following:
Do a similar thing for the multiplication of BA (the other way around), then you'll have four sets of simultaneous equations. Solve each to obtain an answer ;D
For Q16 ,you have the right idea, but remember that matrix multiplication is not commutative! That is:
When you factored, you put the P out the front, it should have been out the back to preserve the initial order of the matrices, try again with:
Question 21 is asking you to consider general vectors and do a general proof of the statements given, kind of like a standard algebraic proof! :) so, consider A and B as non-singular (invertible) square matrices where \(AB=BA\), and prove generally that:
Let me know how you go! ;D
Post by: anotherworld2b on September 06, 2016, 11:27:06 pm
I was wondering for q15 am I doing something wrong? Because im getting the wrong answers for x and y so far. Also for q17 how do I prove generally?
Where are you up to with Q21? Have you started by multiplying the vector I suggested above with the matrix given? That will apply the linear transformation, did you get that or is that operation troubling you? :)
Question 15 isn't really attackable with the method you used, you are better off using simultaneous!
Using the statement given, we conclude the following:
Do a similar thing for the multiplication of BA (the other way around), then you'll have four sets of simultaneous equations. Solve each to obtain an answer ;D
For Q16 ,you have the right idea, but remember that matrix multiplication is not commutative! That is:
When you factored, you put the P out the front, it should have been out the back to preserve the initial order of the matrices, try again with:
Question 21 is asking you to consider general vectors and do a general proof of the statements given, kind of like a standard algebraic proof! :) so, consider A and B as non-singular (invertible) square matrices where \(AB=BA\), and prove generally that:
Let me know how you go! ;D
Post by: jamonwindeyer on September 07, 2016, 12:07:03 am
I'll ask about q21 if i have any more queries about it. :)
I was wondering for q15 am I doing something wrong? Because im getting the wrong answers for x and y so far. Also for q17 how do I prove generally?
Hmm, I don't see any errors in your working immediately, what are the answers supposed to be? :)
An example for 17a) to show you a general proof:
At no stage do I specify what A or B should be, I've proved it generally!
Post by: anotherworld2b on September 07, 2016, 12:21:31 am
X= -1 , y= -2 , p= -5 , q= 7 , r= -7 , s=2 but now sure why.
Oh okay I get how to do q17 now thank you ;D
I also want to ask for q13 what would be the best way to do it?
I also tried q14 but i also got the answer wrong for some reason
Hmm, I don't see any errors in your working immediately, what are the answers supposed to be? :)
An example for 17a) to show you a general proof:
At no stage do I specify what A or B should be, I've proved it generally!
Post by: anotherworld2b on September 07, 2016, 10:15:25 pm
Post by: jamonwindeyer on September 07, 2016, 10:39:59 pm
The answers for q15 are:
X= -1 , y= -2 , p= -5 , q= 7 , r= -7 , s=2 but now sure why.
Oh okay I get how to do q17 now thank you ;D
I also want to ask for q13 what would be the best way to do it?
I also tried q14 but i also got the answer wrong for some reason
Oh! The matrix I gave you in my original explanation had a sign error for Q15, dictation error, sorry! Go back and look at your first line of working, do the matrix multiplication again, fix the sign errors and repeat, your method is 100% correct ;D
Question 13, best way to do it would (I think) just be considering a general matrix \(\begin{bmatrix}a & b\\c &d\end{bmatrix}\) and setting up simultaneous equations just like above!
Question 14, your attempt isn't quite correct. To make it clearer, try drawing a little diagram!
Triangle 1 ------ (Matrix A) -------> Triangle 2
Triangle 1 ------ (Matrix B) -------> Triangle 3
The idea here is to go from Triangle 2 to Triangle 3. We can do this by going back to Triangle 1, then to triangle 3, the matrix therefore being:
where A is the first matrix given, B is the second matrix given :)
Have you seen this method before? If not happy to explain! :)
I was also wondering if i can get help with these two questions. Particularly q13
Question 12 should be fairly straightforward, calculate the inverse:
Then multiply it by itself, form 4 equations and then solve for the missing variables! Show me your working if that doesn't quite work! :P
Then Q13 I addressed above ;D
Hope this helps!! ;D
Post by: anotherworld2b on September 08, 2016, 01:07:23 am
Thank you for your help I rewlly appreciate it.
Oh! The matrix I gave you in my original explanation had a sign error for Q15, dictation error, sorry! Go back and look at your first line of working, do the matrix multiplication again, fix the sign errors and repeat, your method is 100% correct ;D
Question 13, best way to do it would (I think) just be considering a general matrix \(\begin{bmatrix}a & b\\c &d\end{bmatrix}\) and setting up simultaneous equations just like above!
Question 14, your attempt isn't quite correct. To make it clearer, try drawing a little diagram!
Triangle 1 ------ (Matrix A) -------> Triangle 2
Triangle 1 ------ (Matrix B) -------> Triangle 3
The idea here is to go from Triangle 2 to Triangle 3. We can do this by going back to Triangle 1, then to triangle 3, the matrix therefore being:
where A is the first matrix given, B is the second matrix given :)
Have you seen this method before? If not happy to explain! :)
Question 12 should be fairly straightforward, calculate the inverse:
Then multiply it by itself, form 4 equations and then solve for the missing variables! Show me your working if that doesn't quite work! :P
Then Q13 I addressed above ;D
Hope this helps!! ;D
Post by: jamonwindeyer on September 08, 2016, 09:36:39 am
I was able to get q11 right but i could get q13 right. For q14 i followed an example from our textbook but i atill didnt get the answer.
Thank you for your help I rewlly appreciate it.
Q13A should be:
That's if you wanted to do it with two separate equations instead of one big one. Note that the second vector must be a column vector, otherwise the transformation doesn't make sense. Of course what we notice is that the answer is actually just formed with the columns of the vectors in the question, that's a consequence of transforming the standard basis vectors in \(\mathbb{R}^2\), but it's cool if you don't spot that ;D
Have another go ;D
As I said for 14, incorrect working, your worked example in the textbook is slightly different to your question. It's not the triangle \(P'Q'R'\) being transformed to \(P''Q''R''\), it is \(PQR\).
You need the method I showed you above (or something similar) :)
Post by: anotherworld2b on September 08, 2016, 10:01:12 am
I'm not sure how to do q14?
Q13A should be:
That's if you wanted to do it with two separate equations instead of one big one. Note that the second vector must be a column vector, otherwise the transformation doesn't make sense. Of course what we notice is that the answer is actually just formed with the columns of the vectors in the question, that's a consequence of transforming the standard basis vectors in \(\mathbb{R}^2\), but it's cool if you don't spot that ;D
Have another go ;D
As I said for 14, incorrect working, your worked example in the textbook is slightly different to your question. It's not the triangle \(P'Q'R'\) being transformed to \(P''Q''R''\), it is \(PQR\).
You need the method I showed you above (or something similar) :)
Post by: jamonwindeyer on September 08, 2016, 10:12:50 am
Question 14, your attempt isn't quite correct. To make it clearer, try drawing a little diagram!
Triangle 1 ------ (Matrix A) -------> Triangle 2
Triangle 1 ------ (Matrix B) -------> Triangle 3
The idea here is to go from Triangle 2 to Triangle 3. We can do this by going back to Triangle 1, then to triangle 3, the matrix therefore being:
where A is the first matrix given, B is the second matrix given :)
This was the explanation I provided earlier. Again, the idea is that to go from Triangle 2 (P'Q'R') to Triangle 3 (P''Q''R''), we need to go back to Triangle 1 by multiplying by the inverse of the matrix given, THEN multiply (on the left) to get to Triangle 3. The product of those matrices must, by definition, be the same as the matrix we need, which is where that expression above comes from ;D
Post by: anotherworld2b on September 08, 2016, 10:21:18 am
This was the explanation I provided earlier. Again, the idea is that to go from Triangle 2 (P'Q'R') to Triangle 3 (P''Q''R''), we need to go back to Triangle 1 by multiplying by the inverse of the matrix given, THEN multiply (on the left) to get to Triangle 3. The product of those matrices must, by definition, be the same as the matrix we need, which is where that expression above comes from ;D
Post by: jamonwindeyer on September 08, 2016, 10:23:30 am
Then would you do the same thing for Q13b?
Nope, 13B is the same as 13A :)
Post by: anotherworld2b on September 08, 2016, 07:22:58 pm
I tried q8 and got k=3 or k=-4
But the answer only has k=3?
I also tried q10 but i am not sure where to go
I have a test on matrices tomorrow and i was wondering what would you recommend I should memorise and what should be put on notes? Did you get matrix proofs?
Nope, 13B is the same as 13A :)
Post by: anotherworld2b on September 08, 2016, 07:24:44 pm
Post by: RuiAce on September 08, 2016, 07:37:36 pm
Questions for ^
Post by: jamonwindeyer on September 09, 2016, 12:10:00 am
Thank you very much for your help i finally understand q13. i was wondering for q14 if there was 4 triangles would you have the first matrix that is given being post multipled by the inverse of the 3rd matrix?
I tried q8 and got k=3 or k=-4
But the answer only has k=3?
I also tried q10 but i am not sure where to go
I have a test on matrices tomorrow and i was wondering what would you recommend I should memorise and what should be put on notes? Did you get matrix proofs?
Hmm, not quite sure what you mean there, I'd have to see the question! :)
Question 8 dictates \(p>0\), which will exclude \(k=-4\) from your possibilities ;D
Good luck with your test tomorrow! I never did matrices at high school level, but my first year algebra course did have a bunch of matrix proofs in the final :) just relax and do the best you can, sure you'll smash it! ;D
Post by: anotherworld2b on September 11, 2016, 06:16:09 pm
I've tried to do them multiple times with no success
Post by: jamonwindeyer on September 11, 2016, 06:38:53 pm
Hi i was wondering if i could get help with these questions please.
I've tried to do them multiple times with no success
For Question 15, consider the formulae for arithmetic series (\(T_n=a+(n-1)d\)), and geometric series (\(T_n=ar^{n-1}\)). You have two terms for certain, and so can solve for a and d (or a and r). That will let you find x.
Question 13, graph on the right is easier, by how much does each term increase by the one before it? First term is 5, second term is 8, third term is 11, what's the difference there? That will let you find a. The graph on the left is similar, but perhaps trickier, what number are you multiplying by each time?
Question 10, you have:
Then, use the given term to solve for k, and then use that value to solve for the 21st term ;D
Your final question:
You have there a set of simultaneous, that will let you find your missing values! ;D
Most of these questions are fairly standard applications of the same principle: Using the equations and solving simultaneously. Are those equations something you are familiar with and/or do you need help understanding them at all?
Post by: RuiAce on September 11, 2016, 06:40:07 pm
Hi i was wondering if i could get help with these questions please.
I've tried to do them multiple times with no success
Post by: anotherworld2b on September 11, 2016, 06:55:38 pm
I really appreciate it :)
For Question 15, consider the formulae for arithmetic series (\(T_n=a+(n-1)d\)), and geometric series (\(T_n=ar^{n-1}\)). You have two terms for certain, and so can solve for a and d (or a and r). That will let you find x.
Question 13, graph on the right is easier, by how much does each term increase by the one before it? First term is 5, second term is 8, third term is 11, what's the difference there? That will let you find a. The graph on the left is similar, but perhaps trickier, what number are you multiplying by each time?
Question 10, you have:
Then, use the given term to solve for k, and then use that value to solve for the 21st term ;D
Your final question:
You have there a set of simultaneous, that will let you find your missing values! ;D
Most of these questions are fairly standard applications of the same principle: Using the equations and solving simultaneously. Are those equations something you are familiar with and/or do you need help understanding them at all?
Post by: anotherworld2b on September 11, 2016, 09:20:39 pm
I am a bit confused about the simultaneous equations.
Also how do you do q4b?
For Question 15, consider the formulae for arithmetic series (\(T_n=a+(n-1)d\)), and geometric series (\(T_n=ar^{n-1}\)). You have two terms for certain, and so can solve for a and d (or a and r). That will let you find x.
Question 13, graph on the right is easier, by how much does each term increase by the one before it? First term is 5, second term is 8, third term is 11, what's the difference there? That will let you find a. The graph on the left is similar, but perhaps trickier, what number are you multiplying by each time?
Question 10, you have:
Then, use the given term to solve for k, and then use that value to solve for the 21st term ;D
Your final question:
You have there a set of simultaneous, that will let you find your missing values! ;D
Most of these questions are fairly standard applications of the same principle: Using the equations and solving simultaneously. Are those equations something you are familiar with and/or do you need help understanding them at all?
Post by: jamonwindeyer on September 11, 2016, 10:10:05 pm
I was wondering i am not getting the correct answer for q13b. I did 2×19?
I am a bit confused about the simultaneous equations.
Also how do you do q4b?
13B is an arithmetic progression, you aren't multiplying, you are adding! Try and see how much is added each time! ;D
4B is a little weird, but it is just a slight re-work of the same method you used in Part A. Just take a new form of the equations you solved in Part A, this time considering \(r^n\) in the equation, instead of \(r^{n-1}\).
Solve those and you'll have the new form of your answer! ;D
Post by: anotherworld2b on September 12, 2016, 12:01:48 am
I also tried q4b and was wondering is there a quicker way to do it than what ive done?
I also got the answer wrong for some reason?
I also wanted to ask for q17 im confused from where do I start counting the terms? I always seem to have trouble knowing when to start and end where i am required to count for questions like this :'(
I'm sorry for asking for so many questions.
Post by: anotherworld2b on September 14, 2016, 11:15:53 pm
Post by: anotherworld2b on September 14, 2016, 11:17:37 pm
Post by: jamonwindeyer on September 14, 2016, 11:42:05 pm
I am confused on how to use the given term to solve for k, and then using that value to solve for the 21st term for q10?
Sorry I missed this earlier:
Pop that into a similar expression for the 21st term ;D
Quote
I also tried q4b and was wondering is there a quicker way to do it than what ive done?
I also got the answer wrong for some reason?
Check your working, you use the correct \(ar^n\) at the start then swap back to \(ar^{n-1}\), carry the first one all the way through. Method is correct though :)
Quote
I also wanted to ask for q17 im confused from where do I start counting the terms? I always seem to have trouble knowing when to start and end where i am required to count for questions like this :'(
This one is a little confusingly worded! The trick is to write out explanations until you see the pattern.
First term is 20 days before
Second term is 19 days before
Third term is 18 days before
...
Twentieth term is 1 day before
So the sequence has 20 terms, you are summing 20 terms and finding the value of the 20th term :)
I was wondering am I doing q2 right? I didnt get the right answer and Im not sure how to do q3.
You uploaded the working twice, just show me the question when you can :)
Post by: anotherworld2b on September 15, 2016, 01:29:09 am
I was also wondering when would my responses for english be marked? Im stressing out because i have only one day before my test on Friday
Post by: RuiAce on September 15, 2016, 07:27:39 am
Here are the questions :)
I was also wondering when would my responses for english be marked? Im stressing out because i have only one day before my test on Friday
Post by: jamonwindeyer on September 15, 2016, 08:51:08 am
Here are the questions :)
I was also wondering when would my responses for english be marked? Im stressing out because i have only one day before my test on Friday
I'm about to do a marking session, so imminently ;) understand that we are uni students though, we never delay marking more than we need to, but we have assignments and lectures and other stuff that we have to do as well. Point being, if you are stressed, you need to give us more time than 24 hours for turnaround, we won't always be able to get it done immediately :) plus that means you have more than one night to improve it, which is good for you too :)
Post by: anotherworld2b on September 15, 2016, 09:26:50 am
I'm about to do a marking session, so imminently ;) understand that we are uni students though, we never delay marking more than we need to, but we have assignments and lectures and other stuff that we have to do as well. Point being, if you are stressed, you need to give us more time than 24 hours for turnaround, we won't always be able to get it done immediately :) plus that means you have more than one night to improve it, which is good for you too :)
Post by: jamonwindeyer on September 15, 2016, 09:29:11 am
I'm sorry for being inconsiderate :(
No no don't apologise, totally not necessary! Just know that we'll always get it done ASAP for you, but that won't always be within 24 hours, just keep it in mind for when you get feedback in the future because I'd hate to not be able to help you out ;D
Post by: conic curve on September 15, 2016, 09:33:52 am
No no don't apologise, totally not necessary! Just know that we'll always get it done ASAP for you, but that won't always be within 24 hours, just keep it in mind for when you get feedback in the future because I'd hate to not be able to help you out ;D
Jamon sorry to get off track but where are your prelim legal studies notes?
Post by: jamonwindeyer on September 15, 2016, 09:39:34 am
Jamon sorry to get off track but where are your prelim legal studies notes?
Right Here :)
Post by: conic curve on September 15, 2016, 09:41:03 am
Right Here :)
Oh right thanks
Does it cover every single dotpoint in the prelim syllabus?
Post by: jamonwindeyer on September 15, 2016, 09:57:09 am
Oh right thanks
Does it cover every single dotpoint in the prelim syllabus?
From memory it covers most of them, but I might have missed stuff in the case studies towards the end? Best to compare with the syllabus to confirm ;D
Post by: RuiAce on September 15, 2016, 12:40:28 pm
The file was too large.question pic
Post by: anotherworld2b on September 17, 2016, 01:34:22 am
Thank you very much for your help ruiace and jamonwindeyer I really appreciate your help with answering my questions :)
I will ensure that if I have essay i
Would liked marked i will post it days before its due.
Post by: RuiAce on September 17, 2016, 07:31:30 am
Hi im back with some more questions. I am having trouble understanding how to approach q7. I was a bit confused how to do the other question as well.
Thank you very much for your help ruiace and jamonwindeyer I really appreciate your help with answering my questions :)
I will ensure that if I have essay i
Would liked marked i will post it days before its due.
Leaving this post unfinished for you to do some work yourself. Come back later if you tried and still couldn't finish
Post by: RuiAce on September 17, 2016, 07:49:56 am
Hi im back with some more questions. I am having trouble understanding how to approach q7. I was a bit confused how to do the other question as well.
Thank you very much for your help ruiace and jamonwindeyer I really appreciate your help with answering my questions :)
I will ensure that if I have essay i
Would liked marked i will post it days before its due.
Post by: anotherworld2b on September 17, 2016, 01:11:55 pm
I am a bit confused on how to do these questions as well
Post by: RuiAce on September 17, 2016, 01:20:10 pm
Thank you for your help ruiaceFirst question just asks you to subtract one y-value from the other.
I am a bit confused on how to do these questions as well
For average rate of change, use the gradient formula rise/run.
Instantaneous just means compute the derivative and substitute in your value. Because that's what the derivative essentially is in physics.
Post by: jamonwindeyer on September 17, 2016, 01:23:37 pm
Thank you for your help ruiace
I am a bit confused on how to do these questions as well
Hey!
a) Substitute x=2 and x=5 into the equation, tell me by how much y changes between the two!
b) Remember we define the average rate of change between two points as:
c) and d) Are your derivatives, \(\frac{dy}{dx}\) at each respective point. Remember that instantaneous change is what the derivative measures! ;D
And your final question is simultaneous equations, and then once you have two solutions, finding the value of the derivative at each of those points. Hint: When you are solving the simultaneous, you will end up with this quadratic:
Solving that will give you the two x-value components of your two solutions (substitute back into one of the others to get the y-coordinates, as usual) ;)
Edit: Whoops, Rui posted too, oh well ;)
Post by: RuiAce on September 17, 2016, 01:27:37 pm
Mate, use /Delta not /bigtriangleup :P
Edit: Whoops, Rui posted too, oh well ;)
Edit:: Soz, hit modify not quote :P
Post by: jamonwindeyer on September 17, 2016, 01:34:13 pm
Mate, use /Delta not /bigtriangleup :P
Hmm, this one isn't too bad, but in general I like the formatting of \bigtriangleup a little better! I remember writing an exam for a student with \Delta and having the triangles just reduce to nothing if I did anything tricky, so I got into a (probably bad) habit, because the triangle is bigger (ironically) ;)
Post by: anotherworld2b on September 18, 2016, 04:29:27 pm
Our teacher simply told us its on 'patterns' so I'm not sure what to study.
Would series and sequences, combinatorics fit under 'patterns?'
Post by: jamonwindeyer on September 18, 2016, 04:39:27 pm
I have a methods test on 'patterns' but I'm not sure what topics would fit under this topic.
Our teacher simply told us its on 'patterns' so I'm not sure what to study.
Would series and sequences, combinatorics fit under 'patterns?'
Loosely, I'd say yes, but only someone who is doing/has done the WACE would know for sure :P you should consult your syllabus!
Be sure to clarify this sort of stuff with your teacher in the first instance too! Like, you deserve to know what topics to study for your test, aha ;D
Post by: anotherworld2b on September 18, 2016, 05:59:27 pm
Leaving this post unfinished for you to do some work yourself. Come back later if you tried and still couldn't finish
Is there a particular way to prove and make a conjecture? I never seem to have an idea how to start :-\
Post by: anotherworld2b on September 18, 2016, 06:01:40 pm
Loosely, I'd say yes, but only someone who is doing/has done the WACE would know for sure :P you should consult your syllabus!
Be sure to clarify this sort of stuff with your teacher in the first instance too! Like, you deserve to know what topics to study for your test, aha ;D
Will do ;D
Post by: RuiAce on September 18, 2016, 06:09:35 pm
Is there a particular way to prove and make a conjecture? I never seem to have an idea how to start :-\In general, conjecturing something is hard and requires the mindset of a third year uni student at the least.
For this question, however, try to figure out why instead of 12, if we used 6 the statement would be true...
(If you can figure out why it's true, then you can figure out my inspiration as to why I picked 6)
Proving a conjecture is just a fancy way of saying "proving something I made up myself"
Post by: anotherworld2b on September 22, 2016, 07:48:35 pm
Post by: MightyBeh on September 22, 2016, 08:03:10 pm
Hi i was just wandering if my answers to these two questions are correect because the answer is different in my book.seems fine to me, but don't forget your f'(x) in your working out. I wasn't sure what you were doing for a sec. :)
Post by: RuiAce on September 22, 2016, 08:38:23 pm
Post by: anotherworld2b on September 22, 2016, 11:39:01 pm
Post by: jamonwindeyer on September 22, 2016, 11:42:29 pm
Could i get help with q35 and 36 please?
Sure thing! So 35 is in two parts; first, what is the gradient of that line?
So in gradient intercept form, it is easier to see that \(m=\frac{41}{16}\) :) now, we simply use the derivative to find the gradient:
For what values of \(x\) is that derivative equal to \(\frac{41}{16}\)?
So Question 36 is more of a test of algebraic manipulation than anything else, it's using the definition that you've written and that's all! It can be tough though, I'll show you the first one for \(f(x)=\frac{1}{x}\) :)
Notice that I used cross multiplication in the middle there to express the numerator as a single fraction! See if that algebra makes sense, and have a go at manipulating the second one!
HINT: For Q36(b), there is a not so obvious trick. You'll arrive at an expression containing:
Try multiplying the top and bottom by \(\sqrt{x+h}+\sqrt{x}\), and see where it gets you ;)
Post by: anotherworld2b on September 23, 2016, 10:05:49 am
I will try to redo them later ;D
I was also wondering could i get help to understand these two questions? ive tried to understand the answers for these 2 questions but i still dont understand it
Sure thing! So 35 is in two parts; first, what is the gradient of that line?
So in gradient intercept form, it is easier to see that \(m=\frac{41}{16}\) :) now, we simply use the derivative to find the gradient:
For what values of \(x\) is that derivative equal to \(\frac{41}{16}\)?
So Question 36 is more of a test of algebraic manipulation than anything else, it's using the definition that you've written and that's all! It can be tough though, I'll show you the first one for \(f(x)=\frac{1}{x}\) :)
Notice that I used cross multiplication in the middle there to express the numerator as a single fraction! See if that algebra makes sense, and have a go at manipulating the second one!
HINT: For Q36(b), there is a not so obvious trick. You'll arrive at an expression containing:
Try multiplying the top and bottom by \(\sqrt{x+h}+\sqrt{x}\), and see where it gets you ;)
Post by: RuiAce on September 23, 2016, 10:06:54 am
I will try to redo them later ;DIs there something about induction in itself that you find difficult to grasp?
I was also wondering could i get help to understand these two questions? ive tried to understand the answers for these 2 questions but i still dont understand it
Post by: jamonwindeyer on September 23, 2016, 10:25:13 am
Post by: anotherworld2b on September 23, 2016, 10:47:35 pm
Is there something about induction in itself that you find difficult to grasp?
Post by: anotherworld2b on September 23, 2016, 11:17:30 pm
This guide might be worth a read for induction! ;D
Thank you for the guide :)
I will read and see if i understand the questions now. Are there guides for other proofs such as proof by exhaustion?
I did parts a and b for q13 but im not sure what to do for c and d. I am also unsure how to do part b for q14. Could i get some advice please?
Post by: jamonwindeyer on September 23, 2016, 11:47:01 pm
Thank you for the guide :)
I will read and see if i understand the questions now. Are there guides for other proofs such as proof by exhaustion?
Proof by exhaustion just means proving every single possible case! For example, proving every year that the Olympics are held is divisible by four, by going through every year and checking that it is divisible by 4. It's (as you'd expect), fair exhausting ;)
I did parts a and b for q13 but im not sure what to do for c and d. I am also unsure how to do part b for q14. Could i get some advice please?
Sure! Here are some rough guides :)
For Part C, the total units produced after \(t\) hours is:
Note that the amount of units produced in the final hour is just the number produced after 8 hours, minus the number produced after 7 hours. That is:
For Part D, the production rate is given by the derivative (remember, a derivative is a rate of change!). So, the derivative being:
We just evaluate that for \(t=1,2,3\) as the question requires :)
Question 14 is similar, we are given a function telling us how much water has leaked after \(t\) minutes:
For Part A, we just substitute the given values for \(t\) into the equation! Remember that the second value is given in hours, so you'll need to convert it into minutes first! :)
Part B is identical to 13D, we find the derivative as a means for finding the rate of leakage (remember, derivatives are rate of change, if you take one thing from these examples THIS must be it):
Again, substitute the given values for \(t\) to obtain your solutions ;D
Post by: anotherworld2b on September 24, 2016, 11:24:48 pm
Could i please get help with part e and f?
Proof by exhaustion just means proving every single possible case! For example, proving every year that the Olympics are held is divisible by four, by going through every year and checking that it is divisible by 4. It's (as you'd expect), fair exhausting ;)
Sure! Here are some rough guides :)
For Part C, the total units produced after \(t\) hours is:
Note that the amount of units produced in the final hour is just the number produced after 8 hours, minus the number produced after 7 hours. That is:
For Part D, the production rate is given by the derivative (remember, a derivative is a rate of change!). So, the derivative being:
We just evaluate that for \(t=1,2,3\) as the question requires :)
Question 14 is similar, we are given a function telling us how much water has leaked after \(t\) minutes:
For Part A, we just substitute the given values for \(t\) into the equation! Remember that the second value is given in hours, so you'll need to convert it into minutes first! :)
Part B is identical to 13D, we find the derivative as a means for finding the rate of leakage (remember, derivatives are rate of change, if you take one thing from these examples THIS must be it):
Again, substitute the given values for \(t\) to obtain your solutions ;D
Post by: jamonwindeyer on September 25, 2016, 04:29:47 pm
Thank you for you help.
Could i please get help with part e and f?
For Part E, just find when the derivative of the function is equal to zero! That should tell you when deflation has stopped.
For Part F, \(a=0\). This is by definition, we can't have negative times! The upper limit \(b\) occurs when the turning point you find in Part E occurs, because after this, the deflation is negative (which doesn't make sense) ;D
Post by: anotherworld2b on September 25, 2016, 05:30:12 pm
I am not sure how to do it
For Part E, just find when the derivative of the function is equal to zero! That should tell you when deflation has stopped.
For Part F, \(a=0\). This is by definition, we can't have negative times! The upper limit \(b\) occurs when the turning point you find in Part E occurs, because after this, the deflation is negative (which doesn't make sense) ;D
Post by: RuiAce on September 25, 2016, 05:31:04 pm
how exactly can I find when the derivative of the function is equal to zero?You find dV/dt and let it equal to 0
I am not sure how to do it
Post by: jamonwindeyer on September 25, 2016, 06:47:14 pm
how exactly can I find when the derivative of the function is equal to zero?
I am not sure how to do it
Pretty much!! So we find the derivative:
Then we set that equal to zero:
And there's your answer ;D
Post by: anotherworld2b on September 25, 2016, 08:42:58 pm
I also tried this question but I still get how to do it the secind part
Post by: RuiAce on September 25, 2016, 08:46:09 pm
Thank you very much for your help.
I also tried this question but I still get how to do it
Post by: anotherworld2b on September 29, 2016, 12:58:53 am
Post by: ml125 on September 29, 2016, 03:36:19 am
Im sorry but im still confused how to do it? :-\
Post by: anotherworld2b on September 30, 2016, 11:47:25 am
Also how would you do this question?
Post by: Syndicate on September 30, 2016, 12:34:21 pm
Oh i get it now :)
Also how would you do this question?
In order to locate the turning points of a cubic, you need to differentiate it's given equation.
- Now you basically need to solve for x
a) Since part a of the question wants you to justify that (5,-195) is a turning point of the given cubic, just sub in x = 5 into the equation.
Therefore (5, -195) is a minimum T.P. of the given cubic.
b) Well since only two x-values were discovered (and that there are two T.P.s), it means that the turning points displayed on the graphs are the only existing turning points of the function.
c) Using the same method utilised in part a of the question, you can determine the exact location of the maximum T.P (by subbing-in x= 3 into the equation).
Therefore, the exact location of the local maximum point is (-3, 61). Which seems correct, since the x coordinate has to be negative, and the y coordinate has to be positive (as seen on the graph).
Post by: RuiAce on September 30, 2016, 01:50:42 pm
Might want to consider \text{}
:)
Post by: anotherworld2b on September 30, 2016, 04:58:29 pm
I was wondering how to do this question as well
In order to locate the turning points of a cubic, you need to differentiate it's given equation.
- Now you basically need to solve for x
a) Since part a of the question wants you to justify that (5,-195) is a turning point of the given cubic, just sub in x = 5 into the equation.
Therefore (5, -195) is a minimum T.P. of the given cubic.
b) Well since only two x-values were discovered (and that there are two T.P.s), it means that the turning points displayed on the graphs are the only existing turning points of the function.
c) Using the same method utilised in part a of the question, you can determine the exact location of the maximum T.P (by subbing-in x= 3 into the equation).
Therefore, the exact location of the local maximum point is (-3, 61). Which seems correct, since the x coordinate has to be negative, and the y coordinate has to be positive (as seen on the graph).
Post by: Syndicate on September 30, 2016, 06:47:28 pm
Thank you for your help
I was wondering how to do this question as well
Please excuse my handwriting :P
Spoiler
(https://s10.postimg.org/iy3yqbkdl/Full_Size_Render_67304.jpg)
Moderator edit: Added spoiler to image
Post by: anotherworld2b on October 04, 2016, 06:56:44 pm
Could i aldo get help with this question as well please?
Please excuse my handwriting :PSpoiler(https://s10.postimg.org/iy3yqbkdl/Full_Size_Render_67304.jpg)
Moderator edit: Added spoiler to image
Post by: ml125 on October 04, 2016, 11:47:37 pm
Thank you
Could i aldo get help with this question as well please?
Spoiler
(https://cdn.pbrd.co/images/aTFeoPrTC.jpg)
Post by: jamonwindeyer on October 04, 2016, 11:52:07 pm
Spoiler(https://cdn.pbrd.co/images/aTFeoPrTC.jpg)
Legend! Awesome answer, questions like this are great revision for Circle Geometry ;)
Post by: anotherworld2b on October 05, 2016, 12:41:59 am
I was wondering if i could also get help.with these two questions
Spoiler(https://cdn.pbrd.co/images/aTFeoPrTC.jpg)
Post by: ml125 on October 05, 2016, 09:38:47 pm
Thank you for your help ;DFor the first question:
I was wondering if i could also get help.with these two questions
Spoiler
(https://cdn.pbrd.co/images/bg8y2FiDY.png)
Not 100% sure about the next one, so I'll leave that for the others :)
Post by: anotherworld2b on October 07, 2016, 11:02:01 am
Post by: RuiAce on October 08, 2016, 12:30:48 pm
Can u get help with these questions please?
Post by: Syndicate on October 08, 2016, 01:37:53 pm
Can u get help with these questions please?Q1)
However, only x = 30, 210 work as we squared the equation in order to get the solutions. Make sure you always check your solutions by substituting them back into the original equation (sin(x+30) = cosx).
Post by: RuiAce on October 08, 2016, 01:42:02 pm
Q1)Didn't have to square here. Just apply an auxiliary angle transformation, or divide by cos(x) and test x=90o, 270o separately.
However, only x = 30, 210 work as we squared the equation in order to get the solutions. Make sure you always check your solutions by substituting them back into the original equation (sin(x+30) = cosx).
I'd avoid squaring when solving equations, in general. Better ways out than just eliminating the mistakes.
More LaTeX advice: You can use \implies or \Rightarrow to create the arrow you need.
Post by: anotherworld2b on October 09, 2016, 06:16:35 pm
I was wondering is there a guide on graphing functions such as quadratics, cubics and trigonometric graphs on ATARNotes?
I am having trouble understanding how to graph these functions and finding the equation from a given graph
Post by: anotherworld2b on October 11, 2016, 07:42:26 pm
Post by: Syndicate on October 11, 2016, 10:16:40 pm
Could i get help with these questions please? I tried q5 but i couldnt get the answer.Line 3: X(95-x) expands out to 95x-x^2 not 95 -x^2.
Post by: anotherworld2b on October 11, 2016, 10:55:34 pm
Post by: anotherworld2b on October 11, 2016, 10:58:40 pm
Post by: Syndicate on October 15, 2016, 04:16:35 pm
I tried q7 but couldnt get part b. I also wanted to check whether how I solved q8 was mathematically correct. I was also wondering if i could get help with q10 and 11 because im not sure where to start
Q8 seems fine.
Q7b)
Therefore the maximum area = 1250 m^2, when x = 50. So the dimensions of the fenced area is 25 x 50 .
Q10) Hint: since the box is a cube, length would equal the width. Each side's length = 60 - 2x.
Q11) The second part of the question is missing.
Post by: anotherworld2b on October 16, 2016, 04:45:26 pm
I was wondering if i could get help with q30 and 32
Q8 seems fine.
Q7b)
Therefore the maximum area = 1250 m^2, when x = 50. So the dimensions of the fenced area is 25 x 50 .
Q10) Hint: since the box is a cube, length would equal the width. Each side's length = 60 - 2x.
Q11) The second part of the question is missing.
Post by: anotherworld2b on August 23, 2017, 01:12:23 am
Post by: jamonwindeyer on August 23, 2017, 11:08:41 am
Can I have help with q 21 and q22c please?
For Q21, you are given the mean and standard deviation of the normal distribution of the fruit juice. You can standardise it using the formula:
And then use a table to find the normalised probability that the juice contains less than the daily recommended intake. 110% is 44mg, so we are looking for \(X<44\) (use the formula above to convert to a Y-value, that's what you use in the table) :)
Q22, you should already have your distribution normalised to use with a table. Look for the values of the normalised variable that give:
Those values, \(X_1,X_2\) correspond to the lower and upper limits of the middle 40%. Then just use the formula you used to be able to use the table, in reverse, to get back to original scores ;D
Post by: anotherworld2b on August 26, 2017, 07:00:03 pm
Post by: Syndicate on August 26, 2017, 07:23:26 pm
Can I have help with q32 b?
Using a CAS calculator, I got that a (where a is the point at which Pr(Z<a) = 0.015) is equal to -2.17009
a = (x - u)/(sd(x) (Note: u is the population mean, and x is the value being tested)
sd(x) = (x-u)/a
= (490-500)/-2.17009
therefore sd(x) = 4.608 (as per Shadow's correction)
Post by: anotherworld2b on August 27, 2017, 09:56:11 am
Using a CAS calculator, I got that a (where a is the point at which Pr(Z<a) = 0.015) is equal to -2.17009
a = (x - u)/(sd(x) (Note: u is the population mean, and x is the value being tested)
sd(x) = (x-u)/a
= (490-500)/-2.71009
therefore sd(x) = 3.69
Post by: Shadowxo on August 27, 2017, 10:05:50 am
the answer for a is 2.3% while the answer for b is 4.6?His method is right, he just used a as -2.71 instead of -2.17
sd(x) = (x-u)/a
= (490-500)/-2.17009
=4.608 = 4.6
Post by: Syndicate on August 27, 2017, 10:52:09 am
His method is right, he just used a as -2.71 instead of -2.17
sd(x) = (x-u)/a
= (490-500)/-2.17009
=4.608 = 4.6
Haha thanks for the correction :P
Post by: anotherworld2b on August 29, 2017, 10:46:10 pm
Post by: RuiAce on August 29, 2017, 10:48:53 pm
I was wondering how do you these questions. How do you find b for q18? How do you find a and k for q16?
_______________________________
These are the ingredients set up for you. Have a go at the actual computations and come back if you need further help
Post by: anotherworld2b on August 30, 2017, 12:03:52 am
I got ( x^2 x e^ - bc) divided by 8
I was wondering where do u get the second equation from in q16?
So I far I have 8a/ 3 + 2k = 0.4
_______________________________
These are the ingredients set up for you. Have a go at the actual computations and come back if you need further help
Post by: jamonwindeyer on August 30, 2017, 09:13:42 pm
I manually integrated q18 and substituted he upper and lower boundaries but I'm not sure what to do from there.
I got ( x^2 x e^ - bc) divided by 8
I was wondering where do u get the second equation from in q16?
So I far I have 8a/ 3 + 2k = 0.4
For Question 18, you shouldn't have any x'es left after the substitution:
In 16, we know we can integrate from 0 to 1 to find the probability, \(P\left(X\le1\right)\). And we know it is equal to 0.2 from the question - That is where the second equation comes from ;D
Post by: anotherworld2b on September 08, 2017, 11:19:15 pm
Post by: RuiAce on September 08, 2017, 11:45:05 pm
I was wondering if I could have help with this question please. We just started to learn about sample proportions but I'm really confused about this topic in general
(1,1) (1,2) (2,1) (1,3) (3,1) (2,2) (1,4) (2,3) (3,2) (4,1) (1,5) (2,4) (3,3) (4,2) (5,1) (1,6) (2,5) (3,4) (4,3) (5,2) (6,1) (2,6) (3,5) (4,4) (5,3) (6,2) - 26 outcomes
(Of course, a frequency histogram or something would've made this a lot faster)
_____________________________
In practice, such a thing is an "estimator" for the theoretical probability.
_____________________________
Admittedly, at this point I'm not too confident (no pun intended) anymore. I might get things wrong from here, so please comment the correct answers if that does happen.
_____________________________
Post by: anotherworld2b on September 09, 2017, 11:56:16 am
Population proportion: is the experimental probability
sample proportion: is practical probability?
I was also wondering for part d when I typed it into my calculator it gave -1.1978 but when I put 0.0448 instead of the square root of 13/6840 it gave me -1.1656?
(1,1) (1,2) (2,1) (1,3) (3,1) (2,2) (1,4) (2,3) (3,2) (4,1) (1,5) (2,4) (3,3) (4,2) (5,1) (1,6) (2,5) (3,4) (4,3) (5,2) (6,1) (2,6) (3,5) (4,4) (5,3) (6,2) - 26 outcomes
(Of course, a frequency histogram or something would've made this a lot faster)
_____________________________
In practice, such a thing is an "estimator" for the theoretical probability.
_____________________________
Admittedly, at this point I'm not too confident (no pun intended) anymore. I might get things wrong from here, so please comment the correct answers if that does happen.
_____________________________
Post by: RuiAce on September 09, 2017, 01:50:52 pm
I was wondering would it be correct to say thatI thought "experimental" and "practical" meant the same thing (unless I was taught that part wrong).
Population proportion: is the experimental probability
sample proportion: is practical probability?
I was also wondering for part d when I typed it into my calculator it gave -1.1978 but when I put 0.0448 instead of the square root of 13/6840 it gave me -1.1656?
I call the first one the "theoretical" probability.
_______________________________________
There's a typo. 6840 should be 6480.
Post by: anotherworld2b on September 09, 2017, 04:52:49 pm
Can I also have some help with this question please?
I thought "experimental" and "practical" meant the same thing (unless I was taught that part wrong).
I call the first one the "theoretical" probability.
_______________________________________
There's a typo. 6840 should be 6480.
Post by: anotherworld2b on September 11, 2017, 09:07:02 am
Post by: RuiAce on September 11, 2017, 09:49:14 am
I was wondering what particular formulas I would need to know. I'm quite sure what the formula is for p or p hatYour previous question involved a confidence interval. That formula is one you need to know.
There isn't a rule of thumb as to how to actually find \(p\) or \(\hat{p}\). That will depend entirely on the question given to you.
It just so happens that all of your previous questions involved the binomial distribution, so the method of finding \(p\) and \(\hat{p}\) are pretty much the same.
_________________________________________________
Also, you can show this via explicit computation, but in general if you want a larger percent confidence interval, the interval will be wider. The intuitive explanation to this is that if you want to be more confident (that your true value lies in the confidence interval), you have to relax your restriction instead. By relaxing your interval, you're really just making it larger.
Post by: anotherworld2b on September 11, 2017, 11:31:31 am
Your previous question involved a confidence interval. That formula is one you need to know.
There isn't a rule of thumb as to how to actually find \(p\) or \(\hat{p}\). That will depend entirely on the question given to you.
It just so happens that all of your previous questions involved the binomial distribution, so the method of finding \(p\) and \(\hat{p}\) are pretty much the same.
_________________________________________________
Also, you can show this via explicit computation, but in general if you want a larger percent confidence interval, the interval will be wider. The intuitive explanation to this is that if you want to be more confident (that your true value lies in the confidence interval), you have to relax your restriction instead. By relaxing your interval, you're really just making it larger.
I see :D
I was wondering does E[^p) stand for the mean of p hat?
E[^p]=E[P/100]
E[p] = mean of population portion?
I was wondering is it always 1/100 x E[p] x 100?
=1/100E[P]
=1/100 ×(100×13/18)
=13\18
Post by: RuiAce on September 11, 2017, 12:05:54 pm
I see :DWell basically yeah. For the binomial distribution this does tend to be the case.
I was wondering does E[^p) stand for the mean of p hat?
E[^p]=E[P/100]
E[p] = mean of population portion?
I was wondering is it always 1/100 x E[p] x 100?
=1/100E[P]
=1/100 ×(100×13/18)
=13\18
And I'm fairly sure yes, in general the mean of the sample is the same as the mean of the population proportion.
Post by: anotherworld2b on September 11, 2017, 12:16:23 pm
Post by: Shadowxo on September 11, 2017, 02:28:55 pm
I am having trouble with commenting on the results for part c. I'm not quite sure what to compare and focus onYou wouldn't normally have to answer a question as ambiguous as this, but things you could mention are
- p^ is quite different to p. Reasons for this discrepancy could include
-Small sample size (only 240)
-Not a random sample - it's from "a particular region in the country" so doesn't represent the population as a whole
Post by: anotherworld2b on September 14, 2017, 08:59:14 pm
Post by: anotherworld2b on September 14, 2017, 09:00:30 pm
Post by: jamonwindeyer on September 14, 2017, 11:22:48 pm
Hi I was wondering if I could get help with question 14
The first bit is literally just substituting the maximum and minimum values from the expression of \(0.241\pm0.06\).
As for the second bit, it's been a year since I've done confidence intervals, but pretty sure this is the job for a large scale confidence interval?
It might also be the t-distribution since variance is unknown - Sorry, I'm pretty rusty on this. Whatever style interval you have been using will likely work again, you'll be taking the 0.06 from the expression and putting it equal to the expression being added/subtracted to get the endpoints of your interval. You'll be able to draw values out of there I'm fairly certain :)
Second one should be similar, your answer for (c) would have endpoints that are more than 3% from the mean. You want them to be 3%, that is, the endpoints need to be \(\bar{x}\pm0.03\bar{x}\). Find the value for \(n\) that achieves this with everything else the same :)
Post by: anotherworld2b on September 29, 2017, 12:31:07 am
Post by: RuiAce on September 29, 2017, 12:36:58 am
Can I have help with part a and b?
________________________
________________________
Post by: anotherworld2b on September 29, 2017, 09:06:58 am
Can I also have help with this question
Post by: RuiAce on September 29, 2017, 10:05:20 am
c) is now quite easily doable because it's just plugging in numbers to find the expected value
Post by: anotherworld2b on September 29, 2017, 02:07:22 pm
I was also hoping to get help with this question please
Post by: RuiAce on September 29, 2017, 02:09:22 pm
Thank you :)All you need to do here is to add the areas of the rectangles
I was also hoping to get help with this question please
Post by: jamonwindeyer on September 29, 2017, 02:09:48 pm
Thank you :)
I was also hoping to get help with this question please
The estimate for the area under the curve just comes from summing the areas of each rectangle. So, use the scales on the axes to get the widths and heights, find the areas, and add em up ;D
Edit:
All you need to do here is to add the areas of the rectangles^ What he said :)
Post by: anotherworld2b on September 29, 2017, 07:30:19 pm
The estimate for the area under the curve just comes from summing the areas of each rectangle. So, use the scales on the axes to get the widths and heights, find the areas, and add em up ;D
Edit: ^ What he said :)
Post by: jamonwindeyer on September 29, 2017, 07:35:29 pm
When I added all the areas of the rectangles I got 9 sq units but the ans says ~8.7 sq units?
I get about 8.7 - Show us your working? :)
Post by: anotherworld2b on September 29, 2017, 09:10:40 pm
I get about 8.7 - Show us your working? :)
Post by: Eric11267 on September 29, 2017, 09:19:06 pm
For the fourth rectangle you incorrectly subbed in the x value as 2.5, when you needed x=3
Post by: anotherworld2b on September 29, 2017, 11:02:33 pm
For the fourth rectangle you incorrectly subbed in the x value as 2.5, when you needed x=3
Post by: anotherworld2b on September 30, 2017, 11:48:26 am
Post by: RuiAce on September 30, 2017, 11:51:03 am
I'm not quite sure what to do for this questionYou will need to provide the information under that text.
Post by: anotherworld2b on September 30, 2017, 06:03:03 pm
You will need to provide the information under that text.
Post by: RuiAce on September 30, 2017, 06:17:02 pm
Post by: anotherworld2b on September 30, 2017, 11:09:32 pm
Post by: RuiAce on September 30, 2017, 11:39:06 pm
Here's the solutionSee, based off the information you had provided I have no idea how they got 1.8 or 1.85. So unless this question had a previous part to it, it was severely lacking in information
Post by: anotherworld2b on October 19, 2017, 10:36:01 am
Post by: Shadowxo on October 19, 2017, 10:43:18 am
I Am having a bit of trouble anti differentiating this question
You should be able to go from there :) Let me know if you're still stuck
Post by: anotherworld2b on October 19, 2017, 12:13:53 pm
Post by: RuiAce on October 19, 2017, 12:15:40 pm
Would this be correct ?Yes.
Just don't forget the +C.
Post by: anotherworld2b on October 19, 2017, 05:24:38 pm
Post by: Shadowxo on October 19, 2017, 07:27:05 pm
I tried to differentiate this question. Would this be correct?Yep :)
Post by: anotherworld2b on October 19, 2017, 08:20:36 pm
Yep :)
Post by: Shadowxo on October 19, 2017, 08:39:00 pm
But the answer is this apparently?They just put it into a different form (a single fraction)
Which is their answer