The circumference of a sphere was measured to be 72 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) 22.91 Correct: Your answer is correct. cm2 What is the relative error

dA(s) = 22,917 cm²     maximum error

dA(s) /A(s) = 0,01389   or 1,38 %    relative error

Step-by-step explanation:

The Volume of a sphere is:

V(s) = 4/3)*π*r³       where  r is the  radius of circumference

If the length of circumference is 72 cm then

L (c) = 72   = 2*π*r

r  = 72/2*π

r = 72/ 6,28      ⇒  r = 11,46 cm

And

L(c)  = 2*π*r

Differentiation on both sides of the equation give:

dL (c) = 2*π*dr    

dr  =  dL(c) /2*π

dr = 0,5 / 6,28     ⇒  dr = 0,07961

The surface area Is:

A (s) = 4*π*r²

And the maximum or absolute error is

dA(s)  = 8*π*r*dr

dA(s) = 22,917 cm²

The relative error is   dA(s) /A(s)  

dA(s) /A(s) = 8*π*r*dr/ 4*π*r²

dA(s) /A(s) = 2*(0,07961)/ (11,46)

dA(s) /A(s) = 0,01389   or 1,38 %

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.