Question

Find the arc length of the following curve on the given interval. x equals 8 t minus 7 comma y equals 15 t minus 6x=8t−7, y=15t−6​, 0 less than or equals t less than or equals 40≤t≤4 The length of the curve is nothing. ​(Type an integer or a​ fraction.)

Answer 1

612

Explanation:

Both x and y are linear functions of t, so for each increment of t, the x- and y-coordinates will increment by 8 and 15, respectively. The length of a line segment joining points 8 units in the horizontal direction and 15 units in the vertical direction is given by the Pythagorean theorem as ...

d = √(8² +15²) = 17

From t=4 to t=40, there are 36 increments in t, so the length of the line segment defined by the given functions is ...

36×17 = 612 . . . units