A right circular cylinder has a radius of 40 cm and a height of 100 cm. Use differentials to estimate the change in volume of the cylinder if its height and radius are both increased by 1 cm. Give an exact answer.

The change in volume is equal to pi*81cm^3

Step-by-step explanation:

The volume of a cilinder can be obtained by the integral:

where i stands for initial values, and f for final values, a is the angle, that goes from 0  to 2*pi.,

the initial values are:

R = 40cm, Z = 100cm

the final ones are:

R = 41cm, Z = 101 cm

that integral is equal to:

((r^2)/2)*z*a) valuated between the initial and final values, exept for the angle a.

Change in volume  = (((41cm^2) - (40cm)^2)/2)*(101cm - 100cm)*(2*pi - 0)

=2*pi*1cm*40.5cm^2 = pi*81cm^3

idk

step-by-step explanation:

i don't know

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180