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Im stuck on two integration questions, but i guess if see how one of them is answered i might understand how to do the other: Find the volume of the solid when the region between the curves y = x^2 and y = 2 - x^2 in the x-y plane is rotated about the y axis. I sketched and found the two...

Well i dont have to worry bout the 2 unit test..... so i guess yeah...its just that because we graph manually its not very clear how close the curve ever gets 5. For example if the graph was y = cos x + sin x, the two graphs drawn seperately would intersect when x = pi/4 and it is evident that...

Nevermind i found out for myself that yeah it is 5..just another question then.. How are you to calculate the amplitude?

Hey um, just asking another question considering the graphs of trigonometric functions. y = 4cos x + 3sin x. I calculated the amplitude being 7root2 / 2 equaling 4.95 (corred to 2.d.p). The amplitude in the back of the book is given as being 5. Just wondering, is their answer due to rounding off...

oh well i see we both figured it out... thanks anyway though!!! oh well i ALSO see that there was no point doing the diameter...just the radius is sufficient... i feel like an idiot..i do 4 unit..but i cant even do this simple 2 unit crap... :(

No, well the answer says the approximate area is 16 cm2 where the exact (well to 4.d.p) is 16.3501 cm2 . Working backwards: 16 = 2/3(12)h 16 = 8h h = 2 cm So...i dunno then... OH just as i write this i think i figured it out... the height of the triangle formed by the chord and...

hahaha no no my problem was i didnt know what a major segment was. I was thinking the major segment was the section within a sector other then the minor segment. But i see now that the major segment is the rest of the circle apart from the minor segment, not just the sector. Thanks for that though.

Theres a question in my book that states: "What is the area of the major segment of a circle in which the minor segment subtends a central angle of 5pi/6 and the radius is 7cm?" For this question i applied the formula A = 1/2(ab)sinC for the major arc: A = 1/2(7)2sin5pi/6 = 12.25 cm2...

Oh yeah the book had that a - d, a, a + d for the arithmetic progression. I jsut didnt get the geometric progression question. Thanks.

The questions were: Solve the equation x^3 - 12x^2 + 39x - 28 = 0 if the roots are in arithmetic progression. (Following the example i was able to do this). Solve the equation x^3 - 14x^2 + 56x - 64 = 0 if the roots are in geometric progression.

Hmmmm why the hell do they have to ask stuff like that in polynomials?!?! I dont really understand it.. ah well maybe i can just skip the question.. Its only one question.

Hmm.. that sucks for me then. I havent done series and sequence. I saw the book im using has an example with arithmetic progression, (sorry for asking before checking) but nothing on geometric progression. When you say increasing exponentially do you mean ax, where a is a constant? Or..well...

I have another question!!!! What do the terms "arithmetic progression" and "geometric progression" mean, relating to polynomials?

No no no, i wasnt asking cuz i "knew". Before i did the question i suspected such because of the relation between min/max t.p.s and double roots, and then it turned out to work out in that question. I was asking generally, do triple roots mean a point of inflexion (or horizontal point of inflexion).

Just to test it out, i derived and ect. and for the question i was doing it turned out to be a horizontal point of inflexion. Also your statement of a single root being a point of inflexion is false, such as condsidering e.g. y = (x + 1)(x - 1), we know for a fact that it as a parabola...

Also id like to ask if this is true about roots, as the book doesnt actually tell you. Are: Double roots are min/max turning points and, Triple roots are points of inflexion? Thanks in advance.

hmm i tried that but i couldnt get anything usable..maybe i screwed it up. When you divide by say (x -1)(x-2), you expand it right? EDIT: Yeah i screwed it up i did a +3 instead of a -3 somewhere. Thanks all.

I dont get that. P(2) = - Q(x), Is the - sign a typo? If P(x) = (x - 1)Q(x) then P(2) = (2 - 1)Q(x) = Q(x) I dont get tat bit either. Could you please explain? Thanks.

Show that 1 and 2 are zeros of the polynomail P(x) = x4 - 2x3 + 5x2 - 16x +12 and hence that (x-1)(x-2) is a factor of P(x). I showed that 1 and 2 are the zeros of the polynomail and hence the factors are (x - 1) and (x - 2). But how do you show that (x-1)(x-2) is a factor? Does this make...

I did something wrong before. And now i cant get any answer...