Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=-4.9t2+64t+136.
The rocket will reach its peak height of 345 meters above sea level at _____ second

Sagot :

Using the vertex of the quadratic equation, it is found that:

The rocket will reach its peak height of 345 meters above sea level at 6.53 seconds.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

  • If a < 0, the vertex is a maximum point.
  • If a > 0, the vertex is a minimum point.

In this problem, the equation is given by:

h(t) = -4.9t² + 64t + 136.

The coefficients are a = -4.9 < 0, b = 64, c = 136, hence the instant of the maximum height is given by, in seconds:

[tex]t_v = -\frac{64}{2(-4.9)} = 6.53[/tex]

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

#SPJ1

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.