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=12+105x-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 pumpkin's maximum height is 184.27 feet and it hits the ground after 3.28 seconds. b: the pumpkin's maximum height is 3.28 feet and it hits the ground after 6.67 seconds. c: the pumpkin's maximum height is 184.27 feet and it hits the ground after 6.67 seconds d: the pumpkin's maximum height is 3.28 feet and it hits the ground after 184.27 seconds

 C. The pumpkin's maximum height is 184.27 feet and it hits the ground after 6.67 seconds

Step-by-step explanation:

Since, the given function that shows the height,

 ------- (1)

Where x is the time in seconds.

Since, the given function is a parabola,

Therefore the maximum height of the parabola is found at the vertex.

And, the vertex of the parabola =

Where a is the coefficient of and b is the coefficient of x.

Thus, the vertex of the given parabola =

Therefore, the maximum height of the pumpkin = feet ≈ 184.27 feet

Now, the pumpkin hits the ground when f(x)= 0,

⇒

⇒ x = 6.675 seconds ≈ 6.67 seconds

Thus, Option C is correct.

answer: the value of x is 7cm

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.