Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 8x+y+z= 4.

Volume = cubic units

Step-by-step explanation: Given the equation find the limits:

For z:

8x + y + z = 4

z = 4 - 8x - y

limits 0 < z < 4-8x-y

For y:

4 - 8x - y = 0

y = 4 - 8x

limits: 0 < y < 4-8x

For x:

4 - 8x = 0

x = 1/2

limits: 0 < x < 1/2

Calculating triple integral and determining volume:

V =

V =

V =

V =

V =

V =

V =

V =

V =

Volume of the solid is V = cubic units.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

is there any photos or whatever?