Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

The function f(t) = −5t 2 + 20t + 60 models the approximate height of an object
t seconds after it is launched. How many seconds does it take the object to hit the
ground?

Sagot :

kayt91
f(t) = -5t^2 + 20t + 60
-5(t^2 - 4t - 12)
-5(t + 2) (t - 6)
t = -2 or t = 6

6 seconds

Answer:

6 seconds.

Step-by-step explanation:

We have been given a function formula [tex]f(t)=-5t^2+20t+60[/tex] that models the approximate height of an object  t seconds after it is launched.

To find the number of seconds it will take the object to hit the ground, we need to find the zeros of our given function.

[tex]-5t^2+20t+60=0[/tex]

Upon dividing our equation by -5 we will get,

[tex]t^2-4t-12=0[/tex]

We will factor our given equation by splitting the middle term as:

[tex]t^2-6t+2t-12=0[/tex]

[tex]t(t-6)+2(t-6)=0[/tex]

[tex](t-6)(t+2)=0[/tex]

[tex](t-6)=0\text{ or }(t+2)=0[/tex]

[tex]t=6\text{ or }t=-2[/tex]

Since time cannot be negative, therefore, it will take the object 6 seconds to hit the ground.

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.