Question

100 pts. & will give brainliest! answer asap

every year in delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. the equation y = 15 + 110x - 16x^2 can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. what is the maximum height that the pumpkin reaches? how many seconds have passed when the pumpkin hits the ground? (hint: if the pumpkin hits the ground, its height is 0 feet)

a. the pumpkins maximum height is 204.06 feet and it hits the ground after 7.01 seconds.

b. the pumpkins maximum height is 3.44 feet and it hits the ground after 7.01 seconds.

c. the pumpkins maximum height is 204.06 feet and it hits the ground after 3.44 seconds

d. the pumpkins maximum height is 3.44 feet and it hits the ground after 204.05 seconds.

Answer 1

First we need to differentiate y

$\\ \sf\Rrightarrow \dfrac{dy}{dx}$

$\\ \sf\Rrightarrow \dfrac{d}{dx}(-16x^2-110x+15)$

$\\ \sf\Rrightarrow -32x-110$

Now let it be 0

$\\ \sf\Rrightarrow -32x-110=0$

$\\ \sf\Rrightarrow -32x=110$

$\\ \sf\Rrightarrow x=|110/-32$

$\\ \sf\Rrightarrow x=3.44s$

Put it in y

$\\ \sf\Rrightarrow y=15-110(3.44)-16(3.44)^2$

$\\ \sf\Rrightarrow y=204.05ft$