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 are able to retrieve your souvenir, how long do you have to hold your breath until you resurface? your answer this is a required question

Explanation:

Step1: Set y to -115 (depth)

$0.05x^2 - 4x - 38 = -115$

Step2: Rearrange to standard quadratic form

$0.05x^2 - 4x + 77 = 0$
Multiply by 20 to eliminate decimals: $x^2 - 80x + 1540 = 0$

Step3: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here $a=1$, $b=-80$, $c=1540$
$\Delta = (-80)^2 - 4(1)(1540) = 6400 - 6160 = 240$
$\sqrt{\Delta} = \sqrt{240} = 4\sqrt{15} \approx 15.49$

Step4: Calculate valid positive root

$x = \frac{80 + 15.49}{2} \approx 47.75$ (we take the larger root as it's the time to resurface)

Answer:

Approximately 47.75 seconds (or exactly $40 + 2\sqrt{15}$ seconds)