Asolid lies between planes perpendicular to the x-axis at x=0 and x=8. the cross-sections perpendicular to the axis on the interval 0

The volume of the solid is 256 cubic units.

Step-by-step explanation:

Given:

The solid lies between planes

The cross section of the solid is a square with diagonal length equal to the distance between the parabolas .

The distance between the parabolas is given as:

Now, we know that, area of a square with diagonal 'D' is given as:

Plug in . This gives,

Now, volume of the solid is equal to the product of area of cross section and length . So, we integrate it over the length from . This gives,

Therefore, the volume of the solid is 256 cubic units.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4