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.

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -

chemists are often responsible for designing a chemical reaction and analyzing the products obtained from it. one significant part of designing a chemical reaction is determining the amount of each reactant that is needed and the amount of each product that will be produced. in order to do so, chemists use stoichiometry, the quantitative relationships between reactants and products.