Find the length of the curve yequalsthree fourths x Superscript 4 divided by 3 Baseline minus three eighths x Superscript 2 divided by 3 Baseline plus 9 for 1less than or equalsxless than or equals8.

Length of the curve = 1.207 units

Step-by-step explanation:

y = for 1 ≤x≤8

The formula for finding the length of a curve is:

Length of a curve =

To compute the length we need (dy/dx)². So,

dy/dx =

dy/dx =

(dy/dx)² = ()²

(dy/dx)² =

Length of a curve =

                              =

                              = [(1 + x^(2/3) - (1/16)(x^-2/3)]^1/2 dx

                              = 2/3 [(1 + x^(2/3) - (1/16)(x^-2/3)]^3/2 * [(2/3)*x^-1/3 + (1/24)*x^(-5/3)]

Applying limits 1 to 8:

(2/3)*[(1 + (8)^(2/3) - (1/16)(8)^(-2/3)]^3/2 * [(2/3)*(8)^(-1/3) + (1/24)*(8)^(-5/3)] -  (2/3)*[(1 + (1)^(2/3) - (1/16)(1)^(-2/3)]^3/2 * [(2/3)*(1)^(-1/3) + (1/24)*(1)^(-5/3)]

= (2/3)*(11.12)*(0.3346) - (2/3)*(2.6968)*(0.7083)

= 2.4805 - 1.2734

Length of the curve = 1.207 units

answer: 21$

step-by-step explanation:

$42 / $14 = 3   (ratio 3: 1)

$7 x 3 = $21

the first one, all those points on the line just make a strait line.