Question

Hard Problem**
Double Integral
volume of tetrahedron bounded by
4x+4y+7z=112
x=15y
x=0
z=0

Answer 1

image included

Answer 2

k so i have the plane's intercepts at y = -16, x=-26, and z = -16

Answer 3

not exactly sure how to set up the limits of integration

Answer 4

so wait it would have to be split up with two integrals then

Answer 5

Hey, I'm thnking layman's method here, so don't trust me.
Er..have you tried just pluggin in the values?

Answer 6

aww wait. I see how complex this is. So, vectors is not my thing.

Answer 7

\[\int\limits_{-26}^{-1680/67}\int\limits_{-4/7*x-16}^{0}(-4/7)*x-y-16dydx\]

Answer 8

that should be the first equation

Answer 9

then add + \[\int\limits_{-1680/67}^{0}\int\limits_{(1/15)x}^{0}(-4/7)x-y-16dydx\]

Answer 10

right?

Answer 11

i got this by finding the equation of the line that goes from the intercepts y=-16 to x=-26
**basically just the equation of the plane 4x+7y+7z=112 and setting z=0

Answer 12

then the problem is that it intercepts y=1/15x so you'd have to find the interception of above with y=1/15x
aka 1/15x=-4/7x-16
again, where -4/7x-16 is from taking the above equation and setting z = 0 and solving for y

Answer 13

is this right?

Answer 14

answer = -(1225024/9849)

Answer 15

could very easily be completely wrong on this

Answer 16

Sam, please say you got something on this.

Answer 17

:0

Answer 18

it can't have negative area tho right?

Answer 19

er wait it should because it's in the um 8th quadrant

Answer 20

er crap yeah just put it in and it's wrong

Answer 21

Honestly, I have no idea.

Answer 22

yeah, think i'm going to have to take this to the math lab
guarantee everyone is going to get this one wrong

Answer 23

eh that's ok, thank you for the help

Answer 24

yeah. sorry bro

Answer 25

u can try ask yahoo answers