Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the wate

Question

Luba_88 [7]

3 years ago

12

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the wate

r is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Mathematics

1 answer:

Masja [62] · Answer 1 · 2022-05-16T00:34:37+03:00

Answer: a. 112 feet, b= 3 seconds, c= 256 feet, d = 6 seconds

Step-by-step explanation:

Here is the complete question:

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the water is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Find the actual value(s) now to each question. Use the solution from the previous question to assist you with what you are actual solving for.

(a) From what height was the quarter tossed?

The quarter was tossed at 112 feet.

(b) How long does it take the quarter to reach its maximum height?

It will take ________ seconds for the quarter to reach its maximum height.

(c) What is the maximum height of the quarter?

The maximum height of the quarter is ________ feet.

(d) How much time does it take for the quarter to hit the water?

It will take ______ seconds for the quarter to hit the water.

a. Since the function is

d(t) = −16t² + 96t + 112,

The coin is tossed at 112 feet. This is because it is the the initial value of the function. It is the constant term and does not depend on any other variable.

b. To calculate the maximum height, we have to find vertex of the function, that has coordinates of h,k and,

h = -b/2a and k = f(h).

From the question, we are aware that,

a = -16, b = 96, c = 112

Using the values, the vertex will be:

h = -b/2a

= -96/(2 × -16)

= -96/-32

= 3

k = f(3)

= 16t² + 96t + 112

= -16(3)² + 96(3) + 112