a tennis ball is thrown into a swimming pool from the top of a tall hotel. the height of the ball from the…

a tennis ball is thrown into a swimming pool from the top of a tall hotel. the height of the ball from the pool is given by ( d(t)=-16 t^{2}-4 t + 702 ) feet where ( t ) is the time, in seconds, after the ball was thrown. graphically find the ( t )-intercepts for this function. interpret the value(s) that make sense in this problem context. interpret the ( t )-intercept value(s) that make sense in this problem context. a. the ball will strike the pool after 6.5 seconds. -6.75 is meaningless. b. the ball will strike the pool after 13.25 seconds. c. the ball will strike the pool after 702 seconds. d. the ball will strike the pool after falling 702 feet.

a tennis ball is thrown into a swimming pool from the top of a tall hotel. the height of the ball from the pool is given by ( d(t)=-16 t^{2}-4 t + 702 ) feet where ( t ) is the time, in seconds, after the ball was thrown. graphically find the ( t )-intercepts for this function. interpret the value(s) that make sense in this problem context. interpret the ( t )-intercept value(s) that make sense in this problem context. a. the ball will strike the pool after 6.5 seconds. -6.75 is meaningless. b. the ball will strike the pool after 13.25 seconds. c. the ball will strike the pool after 702 seconds. d. the ball will strike the pool after falling 702 feet.

Answer

Explanation:

Step1: Analyze the function (D(t)=-16t^{2}-4t + 702)

The (t -)intercepts of the function (y = D(t)) are found by setting (D(t)=0), i.e., (-16t^{2}-4t + 702=0). Multiply through by (- 1) to get (16t^{2}+4t - 702 = 0). Using the quadratic formula (t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}) for a quadratic equation (ax^{2}+bx + c = 0). Here (a = 16), (b = 4), (c=-702).

Step2: Calculate the discriminant (\Delta=b^{2}-4ac)

(\Delta=(4)^{2}-4\times16\times(-702)=16 + 44928=44944)

Step3: Find the values of (t)

(t=\frac{-4\pm\sqrt{44944}}{2\times16}=\frac{-4\pm212}{32})

We have two solutions: (t_{1}=\frac{-4 + 212}{32}=\frac{208}{32}=6.5) (t_{2}=\frac{-4-212}{32}=\frac{-216}{32}=-6.75)

Since time (t\geq0) (time cannot be negative in this context), we discard (t=-6.75)

Answer:

A. The ball will strike the pool after 6.5 seconds, - 6.75 is meaningless.