Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Answer:
a) The ball reaches it's maximum height after 3 seconds.
b) The maximum height of the ball is of 151 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
The height of the ball is modeled by:
[tex]h(t) = -16t^2 + 96t + 7[/tex]
So a quadratic equation with [tex]a = -16, b = 96, c = 7[/tex]
a) After how many seconds will the ball reach its maximum height?
t-value of the vertex. So
[tex]t_{v} = -\frac{96}{2(-16)} = 3[/tex]
The ball reaches it's maximum height after 3 seconds.
b) What is that maximum height?
h of the vertex.
[tex]\Delta = b^2 - 4ac = (96)^2 - 4(-16)(7) = 9664[/tex]
[tex]h_{v} = -\frac{9664}{4(-16)} = 604[/tex]
The maximum height of the ball is of 151 feet.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
