A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h = –5t2+ 92t + 16. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary. (1 point)

Wrong.

Given a quadratic equation, the x-value that will always yield the maximum y-value is given by the equation:

x = -b/2a

So, in this case...
t = -(92)/2(-5) = 9.2 sec

Therefore, the boulder will reach it's maximum height at 9.2 sec. Now, just plug n' chug it into the function...

h = -5(9.2)² + 92(9.2) + 16
h = 439.20 m

You can also make a logical assumption. Think about it: you are launching a boulder 92 m/s in the air...the max height is bound to be great.

Thanks that really helped <3

thanksssss so much

So it’s d?

However, the catapult cannot really launch a 90 kilogram object over 300 meters.

correct answer should be :

D. Reaches a maximum height of 439.20 meters in 9.2 seconds.

thx

You're welcome! Don't hesitate to ask if you have any more questions.

To find the time it takes for the boulder to reach its maximum height, we need to consider the quadratic function h = -5t^2 + 92t + 16. The maximum height is achieved when the boulder reaches the vertex of the parabolic curve.

The formula for the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c is given by x = -b/2a.

In this case, a = -5 and b = 92. Plugging these values into the formula, we have x = -92/(2*(-5)) = -92/(-10) = 9.2 seconds. So, it takes 9.2 seconds for the boulder to reach its maximum height.

To find the maximum height, we need to substitute the value of t = 9.2 into the equation for h. Plugging t = 9.2 into the equation h = -5t^2 + 92t + 16, we get h = -5*(9.2)^2 + 92*(9.2) + 16.

Calculating this expression, we have h = -5*(84.64) + 846.4 + 16 = -423.2 + 846.4 + 16 = 439.2.

Therefore, the boulder's maximum height is 439.2 meters.

So, none of the given options for the maximum height and time to reach the maximum height are correct. The correct answers are:

It takes 9.2 seconds to reach the maximum height.
The boulder's maximum height is 439.2 meters.