Respuesta :

The arc length of the curve on the given interval is 31.241.

Explain the term Parametric Equations?

  • Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are characterized as continuous functions of a parameter and independent of other variables.

Parametric Equations

  • x = 6t + 5,  
  • y = 7 − 5t            

Interval: −1 ≤ t ≤ 3

dx/dt = d/dx(6t + 5)

dx/dt = 6

And, dy/dt = d/dt(7 − 5t )

dy/dt = -5

The arc length of curve is estimated as;

L = ∫√(dx/dt)² + (dy/dt)²).dt

L = ∫√(36 + 25t)     Interval: [−1 ≤ t ≤ 3]

L = √61  x  (3 + 1)

L = 31.241

Thus, the arc length of the curve on the given interval is 31.241.

To know more about the Parametric Equations, here

https://brainly.com/question/21845570

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