my last troubles (1 Viewer)

[chooke]

ok now i have one last question and then im finished my assessment. how do i do this question;

The region in the first quadrant bounded by the graphs of f(x)=1/8 x^3 and
g(x)=2x is rotated about the y-axis. Find the volume of the solid so formed.

 

[klaw]

Find the points of intersection by solving simultaneous equations, then just put those points as your limits of the volume formula.

 

[Riviet]

ok now i have one last question and then im finished my assessment. how do i do this question;

The region in the first quadrant bounded by the graphs of f(x)=1/8 x^3 and
g(x)=2x is rotated about the y-axis. Find the volume of the solid so formed.

Hello again. ^^

To find point of intersection of both curves,

let f(x)=g(x)
x³/8=2x
x³/8-2x=0
x(x²/8-2)=0
x(x/sqrt8 + sqrt2)(x/sqrt8 - sqrt2)=0 , by difference of 2 squares
x=0, x=(-sqrt2)(sqrt8), x=(sqrt2)(sqrt8)
x=0, 4, -4

The one we take is 4 because only this one is in the first quadrant.

So now the volume is given by:

4
/
| pi{[g(x)]² - [f(x)]² dx}= (see next line)
/
0

4
/
| pi{4x² - x⁶/64 dx}= (see next line)
/
0

pi{4x³/3 - x⁷/448]} from 0->4 = pi[256/3 - 16384/448 - 0]

= 65536pi/1344 units³

If the question doesn't ask for any rounding, then leave it in this exact form.

No need to say good luck since you've already done it.

 

[chooke]

oh my god u r my saviour thank you so much

 

[Riviet]

Lol, no problem.

 

[klaw]

This pisses me off. A hand-in maths assessment... people are just gonna get their family/friends/BOS to do Qs that they can't do. I know that I would have done the same thing if I was in that situation but it's stuffed up how schools give these assessments. I feel sorry for anybody who doesn't get 100%

 

[chooke]

hey sorry dude but im just doing what im told to do...i have heard everyone sayin its unusual. My teacher was going to make it a test but decided against it, i must say it was a little hard to do it by myself so it is easy to get answers but still.

 

[Riviet]

So... you've finished your assignment right?

 

[klaw]

yeah I'm not pissed off at you, anybody who cares about their marks, including me, would have done the same thing, but it's stuffed up how schools give these assessments. The whole purpose of assessments is to differentiate between students, and with assessments like these you're gonna get 99% of students getting 100%, and the people who don't have smart friends/family or know of BOS are gonna be disadvantaged.

 

[chooke]

yes riviet i have finished but i still think i have done part of a question wrong. And Klaw he did make it hard and the teacher said he will be lookin to take marks off and be real picky not like hsc markers where they look to add marks

 

[klaw]

That makes it even worse. A hard test means that there WILL be variation in marks between students, but not due to the mathematical ability of the student, but rather how smart the student's friends/family/contacts are.

 

[Riviet]

Yeah that is true. Only the student is supposed to be tested/assessed, not his/her friends, family, contacts like us lol.