Evaluate the triple integral ∭ 8x^2 dV, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)

2/15

Step-by-step explanation:

given that the triple integral = ∫∫∫ 8x^2 dv

and T is the solid tetrahedron with vertices :  (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)

hence the equation of the plane: x + y + z = 1

T [ (X,Y,Z) : 0≤x≤1, 0≤y≤1-x, 0≤z≤1-x-y ]

attached below is the detailed solution ( we multiply our answer after evaluation with the coefficient of  8 as attached to the initial expresssion)

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)