Answered

Find the best solutions to your problems with the help of IDNLearn.com's expert users. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.

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 :

Kayt91idn
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.

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.