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#76 Re: Exercises » Pre-University Calculus - III » 2008-12-19 15:16:44
1.
I don't know any rules for calculus, I will be learning the quotient, product and all that next year.
So I've managed to solve all this with finding derivatives by rule and the binomial expansion:)
(3x^2-1)^3= (3x^2)^3 (-1)^0 = 27x^6
= 3(3x^2)^2 (-1)^1 = 27x^4
= 3(3x^2)^1 (-1)^2 = 9x^2
= 1(3x^2)^0 (-1)^3 = -3x^2
dy
-- (27x^6+27x^4+9x^2-3x^2)
dx
= 162x^5-108x^3+18x
#77 Re: Exercises » Complex Numbers - Pre University level I » 2008-12-19 14:49:47
1.
real part is 4
complex part is -i√3.
2.
the conjugate is
1/2+1/2*i
4.
5+5i 3+4i
------*------
3-4i 3+4i
= 15+20i+15i+20i^2
--------
25
= 15-20+20i+15i
-------
25
= -5+35i
------
25
= -1 7
---+---*i
5 5
Thats all I can do with my complex knowledge:)
#78 Re: Exercises » Logarithms - High school - II » 2008-12-19 13:58:56
1.
2^x=16
2^x=2^4
=4
2.
343^x=7
343^x=343^1/3
=1/3
4.
x^-1/2=9/16
x^-1/2=256/81^-1/2
x=256/81
#79 Re: Help Me ! » Pyramids » 2008-12-19 13:53:13
Hmm I'm following your logic for question 2 mathsy but I get the answer wrong.
The answer according to my sheet is root18.
so do you use the pythagoras theorem for question 2 as follows:
c^2-b^2=a^2
6^2-root18^2=18
root18=3root2
Am I doing something wrong here?
#80 Re: Exercises » Logarithms - High school Level » 2008-12-19 13:44:19
1.
7^x=1/343
7^x=7^-3
x=-3
2.
root8^x=10/3
x=2log(10/3)
-------------
3log(2)
x=1.12
3. I'm assuming you use a calculator, I've never encountered a question like that non-tech.
=2/3
Thats all I got so far:)
#81 Re: Help Me ! » Pyramids » 2008-12-19 13:18:37
Thanks for the quick reply careless25 that makes alot more sense now, why didn't I think of that
.
Any ideas for the second question?
thanks again.
#82 Help Me ! » Pyramids » 2008-12-19 12:49:39
- glenn101
- Replies: 8
I'm having trouble working out thse 2 questions related to right pyramids with square bases.
1. A right pyramid with a square base is shown in the diagram. The height of the pyramid is 5cm and the square base has sides of length 10cm. The length of a sloping edge in centimetres is.
2. A right pyramid with a square base is shown (sorry can't draw diagram). The square base has sides of length 6cm. The length of each sloping edge is also 6cm. The height of the pyramid in centimetres is.
Could you please explain methods of solving these equations and explain the formula's your using, I havn't done questions related to pyramids in years I've forgotten it all.
Thanks in advance,
Glenn.
#83 Introductions » Hello Again! » 2008-12-17 20:13:34
- glenn101
- Replies: 5
Its been a while, I havn't been here for almost a year as I've had a busy year as a year 11 student. For those who don't know me or forget I live in Melbourne, Australia and am 17 years old. I'm now entering year 12 soon and I want to achieve the best I possibly can in methods CAS and maths specialist. I've been considering going to melbourne uni for a course in a bachelor of mechatronics which leads on to a masters in mechatronics; I need an ENTER of 85+ to get in. Next year is definatly going to be stressful but I just have to put up with it and constantly review and seek help with any troubles I have with maths. I really hope I do well. I look forward to posting again!:D
#84 Re: Dark Discussions at Cafe Infinity » Where to learn higher calculus? » 2008-08-07 19:16:05
Thanks again for the reply Identity:)
Thanks for putting forward your incite into Melbourne uni's engineering, I was considering going there but from what you said, Monash sounds to be the better choice, so I will see what Monash has to offer, so thanks for that.:D
Oh and what is La Trobe uni like? they also have engineering as well as Deakin.
#85 Re: Dark Discussions at Cafe Infinity » Where to learn higher calculus? » 2008-08-04 22:07:25
Thanks identity for your reply:)
yes I am in year 11 at the moment, but how do I apply for uni maths next year? does it become one of my 5 subjects and replace another? how does it work?
I really enjoy maths methods and maths specialist, I want to go into electronic engineering in uni as I like electronics and the engineering part goes into advanced maths. So would this uni maths subject be good?
#86 Re: Dark Discussions at Cafe Infinity » Where to learn higher calculus? » 2008-08-02 12:11:11
Well I understand what your saying Ricky,
in my maths class our calculus section was small.
These are the chapters we did:
Rates of change first (without differentiation)
Differentiation (first principles, derivatives by rule, antidifferentiation) *no integration*
and then applications of differentiation ie stationary points, maximums and minimums.
Its not really a calulus oriented textbook I mean we have done
Quadratics, Polynomials, Cubics, quartics, probability and our next topic is circular functions.
So we only really covered the basics, but I was intrigued to learn more after it.
All this is done in my maths methods class by the way, and I do 2 different maths classes. Here in Australia we have 3 different levels of maths in year 11,12 there is;
starting from easiest to hardest:
maths further,
maths methods,
maths specialist.
I do methods and specialist, but my specialist class is in someway unstructured it doesn't seem like we are doing those hard aspects, we have done;
Matrices, Simultaneous Triples, Partial Fractions, Transformations, and now logarithms and difference equations. In specialist we havn't done any calculus as such, but I hear next year we do integration and differential equations etc.
So yeah, I'm just interested to learn more calculus, as when I finish I am going to enter an engineering stream, most definatly electronic engineering like Zhero:)
#87 Dark Discussions at Cafe Infinity » Where to learn higher calculus? » 2008-08-01 12:44:32
- glenn101
- Replies: 11
Hey guys,
So far in my maths class we have finished up calculus for the year, but I want to continue to learn.
All we covered was;
Limits,
Finding the derivative by first principles,
Finding the derivative by rule,
and antidifferentiation (indefinate integrals).
Any ideas of where to study higher from where I am?
#88 Re: Introductions » About me.. » 2008-08-01 12:20:15
Can't wait!
#89 Re: Introductions » About me.. » 2008-07-30 20:52:23
Electronics engineering, I want to do that myself when I finish school, is it really interesting? I love electronics, and is there lots of maths involved? I hope there is some at least I like maths:)
#90 Re: Help Me ! » Calculus » 2008-07-30 20:45:04
Thanks alot guys:D
Any ideas where I can learn higher calculus though? I'm interested in calculus:)
#91 Help Me ! » Calculus » 2008-07-28 22:17:35
- glenn101
- Replies: 5
Hi, I'm just beginning calculus, all we have learned at the moment is limits, finding the derivative (by first principles and by rule not including the chain rule) and antidifferentiation (indefinite integrals) I have 2 questions which I just cannot get, please help!
find:
*indefiniteintegral5x^4+4x^3-2x^2/2x^2 dx
and
Find the equations of the tangent and the normal to the curve with equation y=3x^2-7x+2 at the point where the tangent is parallel to the line with the equation y=2x+5.
Thank you
P.S where can I learn higher level calculus? know of any websites? that just go on from where I finished not start at integrals etc, Thanks!
#92 Re: Help Me ! » another polynomial identity quadratic response question » 2008-04-26 15:46:33
ah that makes much better sense, thanks for clearing it up jane.
#93 Re: Help Me ! » the last of the identities, quadratics and partial fractions response » 2008-04-26 15:45:45
Thank you Jane,
you described them exactly as I wanted, thank you so much:D
#94 Re: Help Me ! » another polynomial identity quadratic response question » 2008-04-26 14:02:43
Thank you for your response John.
Your answer seems logical and everything however, my book says otherwise:(
meters, I don't understand how they get this answer:(
#95 Help Me ! » the last of the identities, quadratics and partial fractions response » 2008-04-26 13:32:46
- glenn101
- Replies: 2
Here are the final questions I just cannot get at all, I've tried so many times but have had no success whatsoever.
Here is the first question:
Two trains are travelling at uniform speeds. The slower train takes a hours longer to cover b km. It travels 1km less than the faster one in c hours.
a) What is the speed of the faster train in terms of a,b and c.
b) if a, b and c, and the speeds of the trains, are rational numbers, find five sets of values for a,b and c. Choose and discuss two sensible sets of values.
Here is the second question:
A tank can be filled using two pipes. The smaller pipe alone will take a minutes longer than the larger pipe alone to fill the tank. Also the smaller pipe will take b minutes longer to fill the tank then when both pipes are used.
a) Find, in terms of a and b, how long it will take each of the pipes to fill the tank.
b) If a = 24 and b = 32, find how long it takes for each of the pipes to fill the tank.
c) If a and b are consecutive positive integers, find five pairs of values of a and b such that b^2-ab is a perfect square. Interpret these results in the context of this tank problem.
I would be so grateful for any help at all, I really am stuck.
Thanks greatly in advance,
Glenn.
#96 Help Me ! » another polynomial identity quadratic response question » 2008-04-25 16:20:01
- glenn101
- Replies: 4
This is another question which I just don't understand.
An upholster purchased some fabric for $a. If he had brought the fabric from another supplier who charged $b per meter more he would have received b meters less for the same amount of money.
a) How many metres did he purchase, in terms of a and b?
b) If a and b, and the number of metres purchased, are natural numbers, find the possible values of a given a <100.
I don't understand how they come to the answers, for a) it ends as a quadratic formula and for b) it becomes some massive table.
Thanks,
Glenn
#97 Re: Help Me ! » help with a polynomial identity and quadratic response question » 2008-04-25 11:57:50
Thanks so much for your time guys.
That helps alot,
thanks,
Glenn.
#98 Help Me ! » help with a polynomial identity and quadratic response question » 2008-04-24 19:57:01
- glenn101
- Replies: 3
Ok, so far I have managed to do parts a and b of question 1 but I do not understand c.
Here is the question:
1. A train completes a journey of 240km at a constant speed.
a) If it had travelled 4km/h slower, it would have taken two hours more for the journey. Find the actual speed of the train.
I got this for a)
and so x = 24, so the actual speed of the train is 24km/h
b) If it had travelled a km/h slower, and still taken two hours more for the journey of 240km, what would have been the actual speed?(Answer is terms of a.) Discuss the practical possible values of a and also the possible values for the speed of the train.
I got this for b)
and so I got this. I can't do it in latex, I've tried for 30mins and have had no success,hopefully you can understand.
x= a+√a(a+480) or in another way a+√a(a+480)/2
----------------
2
x>0, if a=60, x=120.
Now for part c.
If the train had travelled a km/h slower, and taken a hours more for the journey of 240km, and if a is an integer and the speed is an integer, find the possible values for a and the speed of the train.
My text book I am using does show an answer in the textbook which appears to be displayed as a table of values of a and speed. But I am unsure of how they derived there answer. Please help.
Regards,
Glenn.
#99 Help Me ! » Quadratics and a graphic question » 2008-04-14 10:29:53
- glenn101
- Replies: 3
This question is related to quadratics
Make x the subject in each of the following and give the values for t for which real solutions to the equation can be found.
2x^2-4t=x
this is the graphing question.
x-y=5
xy=126
describe in a detailed way, as I am going to be tested on this tomorrow:(
Thanks in advance,
Glenn
#100 Re: Help Me ! » Polyomials and simultaneous equations graphs » 2008-04-14 10:24:00
Thank you identity, that helps alot:D