Vastor

let's me explain you about the use of bracket and others that u should know... [math] xy^5 = x^1y^5 = (x)^1(y)^5[/math] based on the equation, u can see that the '1' actually not shown becoz everything would result the same [math] () = * [/math] in different way, let's see [math] a = xy [/math] [math] a^5 = (xy)^5 = (x)^5*(y)^5 \neq xy^5 = (x)^1(y)^5 = x^1*y^5 [/math] () usually used to substitute an unknown while having the same effect of * which is multiply

ridiculous.... [math]xy = x*y[/math] so [math] xy^5 = x*y*y*y*y*y [/math] and, bracket always important. [math] xy * xy * xy * xy * xy * xy = (xy)^5 = x^5y^5[/math] actually, the exponent simplify multiplication... i dun think it's happen the other way

does [math]log\sqrt{x^3} = \frac{3}{2} log x[/math] ?? just need confirmation of my understanding

I think it's not relevant to start new topic about this... ok let's start.. this is the law of log that i learn at school :- [math] log_a mn = log_a m + log_a n [/math] [math]log_a\frac{m}{n} = log_a m - log_a n[/math] [math]log_a m^n = n log_a m [/math] [math]log_a a = 1[/math] [math]log_a 1 = 0[/math] [math]log_a b = \frac{log_c b}{log_c a}[/math] [math]log_a b = \frac{1}{log_b a}[/math] there any more laws? how about law of multiply and dividing between log???

thnx all, i got it.. this give much of the understanding. however, how about the equation you give? [math]x^2 + x^4 = 28[/math] can't keep 'x' in one term, hard to adjust it. anyway, i need to improve my algebra skill especially in distributive law, e.g. before this I even thought that distribute 2x(5 + 2) and 2x(5 * 2) is same

[math]x^2 + x^4 = 28[/math] [math]\frac{x^2}{x^2} + \frac{x^4}{x^2} = \frac{28}{x^2}[/math] [math] 1 + x^2 = \frac{28}{x^2}[/math] [math] x^2 = \frac{28}{x^2} -1[/math] [math] \sqrt{x^2} = \sqrt{\frac{28}{x^2} -1}[/math] [math] x = \sqrt{\frac{28}{x^2} -1} [/math] soo... what? i'm not get it...

the question is, Solve the equation [math]2^{x+2} - 2^{x-1} = 28[/math] so, I do the calculation... [math]2^{x+2} - 2^{x-1} = 28[/math] [math]2^{x+2+1} - 2^{x-1+1} = 28 * 2[/math] [math]2^{x+3} - 2^x = 56[/math] [math]2^{x+3} = 2^x + 56[/math] [math]2^x * 8 = 2^x + 56[/math] [math]2^x = \frac{2^x + 56}{8}[/math] [math]2^x = \frac{2^x}{8} + 7[/math] [math]2^x = 2^{x-3} + 7[/math] now i'm stucked, i solve it, but does it's can only be done by wild guess, like this.. let x = 3 [math]2^3 = 2^{3-3} + 7[/math] [math]2^3 = 2^0 + 7[/math] [math]2^3 = 8[/math] x = 3 # or there any alternative calculation for this?

almost 1 day already and i need the answer or at least some clue :/

[math] =a([x+\frac {b}{2a}]^2 - [\sqrt {\frac {b^2-4ac}{4a^2}}]^2)[/math] [math] =a( {[x+\frac {b}{2a}] + [\sqrt {\frac {b^2-4ac}{4a^2}}]} { [x+\frac {b}{2a}] - [\sqrt {\frac {b^2-4ac}{4a^2}}] })[/math] how come this happen? [math] =a([x+\frac {b}{2a}]^2 - [\sqrt {\frac {b^2-4ac}{4a^2}}]^2) [/math] should be [math] =a([x+\frac {b}{2a}] - [\sqrt {\frac {b^2-4ac}{4a^2}}])^2[/math] [math] =a( ([x +\frac {b}{2a}] - [\frac {\sqrt {b^2-4ac}}{2a}])( [x+\frac {b}{2a}] - [\frac {\sqrt{b^2-4ac}}{2a}] ))[/math] doesn't it?

so p> plus minus 10? so, from the grap p > 10 and p < -10 so, how come p > plusminus 10 = p < -10??

before getting started... i know how to use discriminant for Quadratic Equation/Function which is when [math] b^2 - 4ac > 0 [/math] so, the root(x) would have 2 intersect point and [math] b^2 - 4ac = 0 [/math] so, the root would have 1/equal intersect point and [math] b^2 - 4ac < 0 [/math] so, there are no root. but, I can't get the relation between those.. I mean, why [math] b^2?[/math], why [math]-4?[/math] why a and c?, why > or = or < ??? http://www.coolmath....arabolas-01.htm this website give me good concept of understanding the Quadratic Equation/Function in General Form/Vertex Form, but I found none for 'discriminant' would be glad if anyone can help

and this is what she said... [math]y = 2x + p[/math] [math]x^2 + y^2 = 20[/math] [math]x^2 + (2x+p)^2 = 20[/math] [math]x^2 + 4x^2 + 4px + p^2 = 20[/math] [math]5x^2 + 4px + p^2 -20 = 0[/math] then, used discriminant [math] b^2 - 4ac < 0[/math] because it doesn't intersect [math](4p)^2 -4(5)(p^2-20) < 0[/math] [math]16p^2 -20p^2 + 400 < 0[/math] [math]-4p^2 < -400[/math] [math]p^2 < 100[/math] [math]p < 10[/math] and this is my first calculation(or second) for this question , i ask here because p < 10 would make the graph intersect doesn't ???

ha3, it's seems I fail to understand the concept that you guys try to tell me, well, nevermind, tomorrow, I can ask my teacher. ^^ anyway, thanks all

and [math]y = +/- 2[/math] which would result to [math] p = +/- 6[/math] and [math]p = +/- 10[/math] ok, now what? I'm lost..

[math] y = -\frac{1}{2}x + 0[/math] [math] x^2 + (- \frac{1}{2}x)^2 = 20[/math] [math] x^2 + \frac{1}{4}x^2 = 20[/math] [math] (1 + \frac{1}{4}) x^2 = 20[/math] [math] (\frac{4}{4} + \frac{1}{4}) x^2 = 20[/math] [math] (\frac{5}{4}) x^2 = 20[/math] [math] x^2 = 16[/math] [math] x = 4[/math] [math] x^2 + y^2 = 20 [/math] [math] (4)^2 + y^2 = 20 [/math] [math] 16 + y^2 = 20 [/math] [math] y^2 = 4 [/math] [math] y = 2 [/math] and, the point-slope form is, [math] y - 2 = 2(x - 4)[/math] [math] y = 2x - 6 [/math] [math] y = 2x + p[/math] so, [math] p = -6[/math] ???

nvm, i found it ^^

second and third picture is like direct copy from text book(it's only contain word, thought), this part, like the textbook, is very messy, and hard to get the concept [i get the concept(a bit)], and there is a side note in textbook for this which say, "explain mathematically why [math] f(x) = a(x + p)^2 [/math] has a minimum value when [math] a > 0[/math] and a maximum value when [math]a < 0[/math] and I don't want direct answer for this, I just want some clue or 'image' on how this statement can be explain mathematically, so that I can grab the concept, and use it to adjust my note. and maybe the explanation for [math] f(x) = ax2 + bx + c [/math] too, if there any...

ermm, can't think of any line I ever learn that 'just touch' the circle so, i google and found... tangent?, and i only know about tan because it's appear on calculator (not really know about it, what it's use for etc) "what angle is it to the radius?" well, i hope i know what is that and how to calculate that after think so hard, the only thing that i can expect is all of you trying to say that y = p +2x is tangent to the circle?

and the 'unlucky' part about this is, i never learn this type of graph, so, there's no way i can plot it by using my knowledge. but, wth this came as my question -,- or maybe there any alternative way, a type of calculation or formula where i can get the answer without knowing what the graph actually about?

i'm not get this, the question is in chapter of Quadratic Function, and Q.F. without parabola?

so, here the graph, so p > 21 ? and any calculation to get the result?

the Question say, Find the range of value of p for which the straight line [math]y = 2x + p[/math] does not intersect the curve [math]x^2 + y^2 = 20 [/math] so, i dun have any idea how to start.. the textbook don't tell me anything.. so, help anyone?

ermm.. so u can do 'rearrange' part??? the point is, i never know that, that's why i use calculator, thnx for the calculation and yes, it's helpful

i think i should move to the 'real question', because [math] log_3(9) [/math] is just my creation. So it's said Evaluate [math] log_2 9 * log_3 4 * log_4 8 [/math] 2marks if I'm not wrong, converting log base would be using this formula [math] log_a(b) = \frac {log_c b}{log_c a} [/math] so [math] log_2(9) = \frac {log_10(9)}{log_10(2)} [/math] * [math] log_3(4) = \frac {log_10(4)}{log_10(3)} [/math] * [math] log_4(8) = \frac {log_10(8)}{log_10(4)} [/math] don't know how to 'zoom out' the '0', lol the things is I turn those log base to 10 so, using my calculators.... = 6 the answer???

ermm, another problem... what i'm gonna do if [math] log_3 9 * log_4 5 [/math] i'm not learn anything about 'multiply' or 'dividing' logarithms yet, but it's appear to my exam just now