dmakoule27
contestada

Johnny rode his bicycle down a hill. It took him 15 seconds to ride from the top of the hill to the bottom of the hill. The equation h = -3t + 45 models his height, h, in feet, above the bottom of the hill as a function of the time, t, in seconds, after he started riding down the hill. Part A: What is the average rate of change in Johnny’s height? Part B: What is the height of the hill? Part C: How long will it take Johnny to travel 1/3 of the distance down the hill?

Respuesta :

From the height function, we get that:

a) The average rate of change is of -3 feet per second.

b) The height of the hill is of 45 feet.

c) It will take Johnny 5 seconds to travel 1/3 of the distance down the hill.

-------------------------------

The height, after t seconds, is given by:

[tex]h(t) = -3t + 45[/tex]

-------------------------------

  • The height of the hill is [tex]h(t)[/tex] when [tex]t = 0[/tex], thus [tex]h(0) = -3(0) + 45 = 45[/tex]. 45 feet, which means that the the answer for option B is 45 feet.

-------------------------------

Item a:

  • The initial height is of 45 feet, at [tex]t = 0[/tex] seconds.
  • The final height is of 0 feet, at [tex]t = 15[/tex] seconds.
  • Thus, the average rate of change is given by:

[tex]A = \frac{0 - 45}{15 - 0} = -\frac{45}{15} = -3[/tex]

The average rate of change is of -3 feet per second.

-------------------------------

Item c:

  • One-third of the distance of 45 feet is [tex]\frac{1}{3}45 = 15[/tex] feet, thus, we have to find the time at which he is at 30 feet, that is, t for which [tex]h(t) = 30[/tex]

[tex]h(t) = -3t + 45[/tex]

[tex]30 = -3t + 45[/tex]

[tex]3t = 15[/tex]

[tex]t = \frac{15}{3}[/tex]

[tex]t = 5[/tex]

It will take Johnny 5 seconds to travel 1/3 of the distance down the hill.

A similar problem is given at https://brainly.com/question/20732437

Otras preguntas