Question

You are interested in retrieving a souvenir from a shipwreck located 115 feet below the water. The path of your dive is modeled by the equation y = 0.05x2 - 4x - 38. Assuming you can hold your breath for the duration of the dive, will you be able to retrieve your souvenir? why?

Answer 1

In order to find out if we will be able to retrieve the souvenir, let's use y = -115 (negative because it's below the water) in the equation and calculate the value of x.

If there is at least one real solution, we will be able to retrieve the souvenir.

To solve this quadratic equation, let's use the quadratic formula:

`\begin{gathered} y=0.05x^2-4x-38 \\ -115=0.05x^2-4x-38 \\ 0.05x^2-4x-38+115=0 \\ 0.05x^2-4x+77=0 \\ a=0.05,b=-4,c=77 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_1=\frac{-(-4)+\sqrt[]{(-4)^2-4\cdot0.05\cdot77}_{}}{2\cdot0.05} \\ x_1=\frac{4+\sqrt[]{16-15.4}_{}}{0.1} \\ x_1=(4+0.77)/(0.1)=47.7 \\ x_2=(4-0.77)/(0.1)=32.3 \end{gathered}`

Since there are real solutions for x, the answer is YES.