stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height…

stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height, $h(t)$, in meters (as it relates to sea level), of the sunglasses after $t$ seconds, is shown in the table. during its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. to the nearest meter, what is difference in elevation between stefano and the climber? height of sunglasses over time\n|$t$|$h(t)$|\n|----|----|\n|0|10|\n|1|5.1|\n|2|-9.6|\n|3|-34.1|\n|4|-68.4|\n|5|-112.5|\n|6|-166.4|\n|7|-230.1|\n166 meters\n176 meters\n230 meters\n240 meters

stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height, $h(t)$, in meters (as it relates to sea level), of the sunglasses after $t$ seconds, is shown in the table. during its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. to the nearest meter, what is difference in elevation between stefano and the climber? height of sunglasses over time\n|$t$|$h(t)$|\n|----|----|\n|0|10|\n|1|5.1|\n|2|-9.6|\n|3|-34.1|\n|4|-68.4|\n|5|-112.5|\n|6|-166.4|\n|7|-230.1|\n166 meters\n176 meters\n230 meters\n240 meters

Answer

Explanation:

Step1: Identify initial height

The initial height when $t = 0$ is $h(0)=10$ meters. This is Stefano's height relative to sea - level (where the sunglasses start).

Step2: Identify height at 6 seconds

When $t = 6$ seconds, the height of the sunglasses is $h(6)=- 166.4$ meters. This is the climber's height relative to sea - level.

Step3: Calculate height difference

The difference in elevation $\Delta h=h(0)-h(6)$. Substitute the values: $\Delta h = 10-(-166.4)=10 + 166.4=176.4\approx176$ meters.

Answer:

176 meters