O-Level Additional Math

[Alarmchain]

MathIzzzFun:

Alarmchain:

Yes, that was what I did.


But I was wondering how the same values for A, B and C can be gotten from the 3 simultaneous equations.

Thanks.

255/7 = 36R3, B = 36
304/7 = 43R3, C = 43

or with A = 24 and
1) B - A = 12
2) C - B = 7

you can also get B= 36, C = 43

cheers.

My apologies, MathIzzzFun. I may have caused some confusion with my unclear question.

With 3 unknowns, we usually can find the unknowns using algebra, if we have 3 simultaneous equations.

In this instance, the 3 equations were:
1) B - A = 12
2) C - B = 7
3) C - A = 19

Yes, if we know that A= 24, we can substitute it into equations 1 and 2 to find the values of B and C. However, we got A by doing 171 / 7 first, which is perfectly ok for this problem.

But my question is, are we able to find A, B and C with just the above 3 simultaneous equations, without resorting to finding any one of them initially, by using 171 / 7 or 255 / 7 or 304 / 7.

Very sorry, my question is not just about this problem per se, but to correct a possible misunderstanding on my part, that Y unknowns can be found if we have Y number of simultaneous equations.

If it cannot be done, does it mean that when solving unknowns using simultaneous equations, it is not always true that all the Y unknowns can be found even if we have Y number of simultaneous equations given.

Again, very sorry for any confusion caused.

[MathIzzzFun]

Alarmchain:

MathIzzzFun:

[quote=\"Alarmchain\"]Yes, that was what I did.


But I was wondering how the same values for A, B and C can be gotten from the 3 simultaneous equations.

Thanks.

255/7 = 36R3, B = 36
304/7 = 43R3, C = 43

or with A = 24 and
1) B - A = 12
2) C - B = 7

you can also get B= 36, C = 43

cheers.

My apologies, MathIzzzFun. I may have caused some confusion with my unclear question.

With 3 unknowns, we usually can find the unknowns using algebra, if we have 3 simultaneous equations.

In this instance, the 3 equations were:
1) B - A = 12
2) C - B = 7
3) C - A = 19

Yes, if we know that A= 24, we can substitute it into equations 1 and 2 to find the values of B and C. However, we got A by doing 171 / 7 first, which is perfectly ok for this problem.

But my question is, are we able to find A, B and C with just the above 3 simultaneous equations, without resorting to finding any one of them initially, by using 171 / 7 or 255 / 7 or 304 / 7.

Very sorry, my question is not just about this problem per se, but to correct a possible misunderstanding on my part, that Y unknowns can be found if we have Y number of simultaneous equations.

If it cannot be done, does it mean that when solving unknowns using simultaneous equations, it is not always true that all the Y unknowns can be found even if we have Y number of simultaneous equations given.

Again, very sorry for any confusion caused.[/quote]In this case, although there are 3 equations :
1) B - A = 12
2) C - B = 7
3) C - A = 19

there are only 2 independent equations
eg with 1) and 2), we can get 3)
or with 2) and 3), we can get 1)
this is why the variables cannot be solved with the 3 equations.

In short, to solve for Y unknowns, you need Y independent equations.

cheers.

[Alarmchain]

Thank you so much! It is very clear now.


BTW, is there a way for a child to see and immediately tell that equations given are dependent or independent, like some kind of rule of thumb thingy? Unlike this example where the dependence was quite easy to visualise, not sure if there are such "tricks" or "tips" to help a child for more complicated examples.

Thanks again!

[S-H]

Hi, please kindly help me on this question:-


Find the equation of the circle,C, which passes through the points (0,5) and
(4, -3) and has its centre lying on the line y=3x+2. Hence, determine by calculation, whether the point (6,1) lies inside or outside C.

Thank you very much.

[MathIzzzFun]

S-H:

Hi, please kindly help me on this question:-


Find the equation of the circle,C, which passes through the points (0,5) and
(4, -3) and has its centre lying on the line y=3x+2. Hence, determine by calculation, whether the point (6,1) lies inside or outside C.

Thank you very much.

here are the pointers to the solution..

http://i46.tinypic.com/30navph.png\">

here are some websites that you can learn more about equations of circles (or you can google other sites)
- http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm
- http://www.mathsisfun.com/algebra/circle-equations.html

cheers.

[S-H]

Hi MathIzzzfun,


Thank you so much for your answer and notes on circles. Can you please explain to me why when the pt(6,1) lies outside the circle, the value is positive and when it lies inside it, the value is negative?

There is one more question that I cannot solve too, can u pls help me again, so sorry to trouble you again.

The question is :-

Find the possible equations of the circle which touches both coordinate axes and passes through (2,1).

Thank you very much.

[lost boy]

Please help to solve sec 3 amath


Use the substitution u =4^x to solve each of the following equations.
a) 2(4^x) + 4^x+2 = 9(4^-0.5)
b) 4^x-1 + 16^x = 66

Please show me the working

Thanks in advance

[MathIzzzFun]

S-H:

Hi MathIzzzfun,


Thank you so much for your answer and notes on circles. Can you please explain to me why when the pt(6,1) lies outside the circle, the value is positive and when it lies inside it, the value is negative?

There is one more question that I cannot solve too, can u pls help me again, so sorry to trouble you again.

The question is :-

Find the possible equations of the circle which touches both coordinate axes and passes through (2,1).

Thank you very much.

http://i47.tinypic.com/4l0p36.png\">

cheers.

[MathIzzzFun]

S-H:

Hi MathIzzzfun,


Thank you so much for your answer and notes on circles. Can you please explain to me why when the pt(6,1) lies outside the circle, the value is positive and when it lies inside it, the value is negative?

There is one more question that I cannot solve too, can u pls help me again, so sorry to trouble you again.

The question is :-

Find the possible equations of the circle which touches both coordinate axes and passes through (2,1).

Thank you very much.

The equation of circle centred on (a,b) with a radius r is:

(x-a)² + (x-b)² = r²

for any point (a1,b1) inside the circle
(a1-a)² + (b1-b)² = r1² < r²

so the expression

(a1-a)² + (b1-b)² - r² < 0

similarly for any point (a2,b2) outside the circle
(a2-a)² + (b2-b)² = r2² > r²

so the expression

(a2-a)² + (b2-b)² - r² > 0

cheers.

[S-H]

Thank you very much!! MathIzzzFun. :thankyou: