Create a bucket by rotating around the y axis the curve y=5 ln(x-2) from y=0 to y=4. If this bucket contains a liquid with density 760 kg/m3 filled to a height of 3 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity.

The work will be "1909212.015 J". The further explanation is given below.

Step-by-step explanation:

The given values are:

Liquid's density

= 760 kg/m³

Height

= 3 meters

Gravity

g = 3.8 m/s²

Value of y is:

y = 5 log (x-2)

y = 0

y = 4

As we know,

⇒  

⇒  

⇒  

⇒  

⇒  

Now,

So that,

⇒  

The required work will be:

⇒  

answer is 144

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)