Use the arc length formula to find the length of the curve y = 5x − 1, −3 ≤ x ≤ 2. check your answer by noting that the curve is a line segment and calculating its length by the distance formula.

  length = 5√26

Step-by-step explanation:

The arc length of f(x) on the interval [a, b] is given by ...

In the present case, we have ...

  f(x) = 5x -1

  f'(x) = 5

on the interval [a, b] = [-3, 2]. Then the arc length is ...

_____

Check

We're looking for the distance between the points ...

  (-3, f(-3)) = (-3, -16)

and

  (2, f(2)) = (2, 9)

Using the distance formula, the distance is ...

  d = √((2-(-3))² +(9-(-16))²) = √(5² +25²) = 5√(1+5²)

  d = 5√26 . . . . . matches the integral result

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl