College Discussion - View Single Post - How well do Princeton Review AND Barrons correleate to the Calc BC AP Test?

vader1990 · 04-26-2008, 08:16 PM

^NO, its not 128*sqrt 3, but close...

make sure you remember that its perpendicular about the y-axis, and that the cross-section is an equilateral triangle?

If you cannot figure it out just post here, and I'll post a detailed solution back ASAP

ANOTHER DISGUISED BUMP++

EDIT: ok, to save time here's the solution:
ok, so it says that x^2 = 8y, and y=4, and the area is a triangle equilateral

The area of an equilateral-triangle is side^2 * sqrt(3) / 4..and the side will equal the length of the bounded region (the length of the rectangular sub-interval)...

Now since it says that its about the y-axis I find it easier to convert y in terms of x; so x = +- sqrt(8y), between 0 and 4 (4 because y=4 is now x=4)...

so sqrt(3) / 4 INTEGRATION[from 0 to 4] of (2*sqrt(8y))^2 dy (I said 2 times the square root, because the function is plus and minus[above and below the x-axis] and they are both equal in are so, the length of the box will be the sum of both the areas so 2 *) will yield: 64 * sqrt(3)

04-26-2008, 08:16 PM	#6
vader1990 Member Join Date: Dec 2007 Posts: 367	^NO, its not 128sqrt 3, but close... make sure you remember that its perpendicular about the y-axis, and that the cross-section is an equilateral triangle? If you cannot figure it out just post here, and I'll post a detailed solution back ASAP ANOTHER DISGUISED BUMP++* EDIT: ok, to save time here's the solution: ok, so it says that x^2 = 8y, and y=4, and the area is a triangle equilateral The area of an equilateral-triangle is side^2 * sqrt(3) / 4..and the side will equal the length of the bounded region (the length of the rectangular sub-interval)... Now since it says that its about the y-axis I find it easier to convert y in terms of x; so x = +- sqrt(8y), between 0 and 4 (4 because y=4 is now x=4)... so sqrt(3) / 4 INTEGRATION[from 0 to 4] of (2sqrt(8y))^2 dy (I said 2 times the square root, because the function is plus and minus[above and below the x-axis] and they are both equal in are so, the length of the box will be the sum of both the areas so 2 ) will yield: *64 sqrt(3)** Last edited by vader1990; 04-26-2008 at 08:24 PM.