Question

you are interested in retrieving a souvenir from a shipwreck located 115 feet below the water. you do not have diving equipment, so your dive is limited by the equation $y = 0.05x^2 - 4x - 38$ assuming you can hold your breath for the duration of the dive; will you be able to retrieve your souvenir? yes no

Explanation:

Step1: Identify target depth

We need to check if the dive equation can reach $y = -115$ (negative because it's below water).

Step2: Set up the equation

Substitute $y=-115$ into $y=0.05x^2 - 4x - 38$:
$$-115 = 0.05x^2 - 4x - 38$$

Step3: Rearrange to standard quadratic form

Bring all terms to one side to get $ax^2+bx+c=0$:
$$0.05x^2 - 4x - 38 + 115 = 0$$
$$0.05x^2 - 4x + 77 = 0$$
Multiply all terms by 20 to eliminate decimals:
$$x^2 - 80x + 1540 = 0$$

Step4: Calculate discriminant

Use discriminant formula $\Delta = b^2 - 4ac$ where $a=1$, $b=-80$, $c=1540$:
$$\Delta = (-80)^2 - 4(1)(1540)$$
$$\Delta = 6400 - 6160 = 240$$
Since $\Delta > 0$, real solutions for $x$ exist, meaning the dive can reach 115 feet below water.

Answer:

Yes