Question

Please answer ASAP. A baseball is hit upward from a platform that is m high at an initial speed of 29m/s. The approximate height of the baseball, h meters, after x seconds is given by the equation: h - 1= -5x^2 + 29x a) determine the time period for which the baseball is higher than 18m. Give the answer to the nearest tenth of a second. Explain your strategy. b) What are the restrictions on the domain and range of the related function?

Answer 1

Answer:

a) about 0.7 seconds to 5.1 seconds.

b) Listed below.

Step-by-step explanation:

h - 1 = -5x^2 + 29x

h = -5x^2 + 29x + 1

a) We will find the amount of time it takes to get to 18 meters.

18 = -5x^2 + 29x + 1

-5x^2 + 29x + 1 = 18

-5x^2 + 29x - 17 = 0

We will then use the quadratic formula to find the answer.

[please ignore the A-hat; that is a bug]

$\frac{-29±\sqrt{29^2 - 4 * -5 * -17} }{2 * -5}$

= $\frac{-29±\sqrt{841 - 340} }{-10}$

= $\frac{-29±\sqrt{501} }{-10}$

= $\frac{-29 ± 22.38302929}{-10}$

= $\frac{-6.616970714}{-10}$ and $\frac{-51.38302929}{-10}$

= 0.6616970714 and 5.138302929

So, the time period for which the baseball is higher than 18 metres ranges from about 0.7 seconds to 5.1 seconds.

b) Restrictions on the domain and range of the function are that the domain and range can never be negative, since time cannot be negative, and height cannot be negative. The height cannot exceed the vertex of the parabola, since that is the highest the ball will ever go. It cannot exceed that height since gravity will cause the ball to fall down.

Hope this helps!