Question

question 13 of 16 (1 point) | question attempt: 1 of unlimited
$y=-0.39x^{2}+58.4x-352.5$
$y=-0.12x^{2}+22x+1400$
$y=15.2x+48.2$
(a) which curve fits the data best?
figure 1 $\bigcirc$ figure 2 $\bigcirc$ figure 3
(b) use the equation of the best fitting curve from part (a) to predict the depth of the trench 90 feet from the buoy. give an exact answer, not a rounded

Explanation:

Step1: Identify best fit curve

The data points in Figure 1 follow the downward-opening parabola shape of its equation, matching the curved trend of the points better than the other curves.

Step2: Substitute x=90 into the equation

Use the equation from Figure 1: $y=-0.39x^2 + 58.4x - 352.5$. Replace $x$ with 90.
First calculate each term:
$(-0.39)\times90^2 = (-0.39)\times8100 = -3159$
$58.4\times90 = 5256$
Then combine all terms:
$y = -3159 + 5256 - 352.5$

Step3: Compute the final value

Calculate the sum/difference step by step:
$-3159 + 5256 = 2097$
$2097 - 352.5 = 1744.5$

Answer:

(a) Figure 1
(b) $1744.5$