) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick is given by δ(r)=401+r2 kilograms per square meter. Find the exact value of the mass of the oil slick if the slick extends from r=0 to r=5 meters.

Therefore the mass of the of the oil is 409.59 kg.

Step-by-step explanation:

Let us consider a circular disk. The inner radius of the disk be r and the outer diameter of the disk be (r+Δr).

The area of the disk

=The area of the outer circle - The area of the inner circle

=

Since (Δr)² is very small, So it is ignorable.

∴

The density

We know,

Mass= Area× density

Total mass

Therefore

                     = 409.59 kg (approx)

Therefore the mass of the of the oil is 409.59 kg.

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

= ← substitute values

= ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2