I am not a student, I am a parent trying to help my son. I understand why you do not want to solve the questions, but can you please help me set them up correctly so I can try?
h = -16t(exponent 2) + 60t where t is the time in seconds.
A) Factor the expression
B) What is the height of the rocket after 2 seconds?
C) What is the height of the rocket after 3.75 seconds? Explain the solution.
*any help would be greatly appreciated!
what do u me by exponent 2
is it
h=-16t²+60t?
h(t) = -16t^2 + 60t = 4t(-4t+15)
h(2) = 4*2(-4*2+15) = 8(7) = 56
now just plug in 3.75 for t.
Or, note that
h(t) = 0 when
-4t+15=0
t = 15/4 = 3.75
so, what does that mean?
Of course, I'm happy to help you set up the problem correctly!
The equation you provided is: h = -16t^2 + 60t
A) To factor the expression, we can start by taking out the common factor, which is t. The equation becomes: h = t(-16t + 60). Now, let's factor out the greatest common factor from the remaining expression inside the parentheses. Dividing both terms by -4, we get: h = t(-4t + 15). Hence, the factored form of the given expression is h = t(-4t + 15).
B) To find the height of the rocket after 2 seconds, we need to substitute t = 2 into the equation h = -16t^2 + 60t. Plugging in t = 2, we get: h = -16(2)^2 + 60(2). Simplifying this expression, we have: h = -16(4) + 120. Continuing the calculation, we find: h = -64 + 120. Adding -64 and 120, we get: h = 56. Therefore, the height of the rocket after 2 seconds is 56 units (which could be in feet or meters depending on the context of the problem).
C) Similarly, to find the height of the rocket after 3.75 seconds, we substitute t = 3.75 into the same equation h = -16t^2 + 60t. Plugging in t = 3.75, we have: h = -16(3.75)^2 + 60(3.75). To simplify, we calculate: h = -16(14.0625) + 225. Performing the multiplication, we obtain: h = -224.9 + 225. Adding -224.9 and 225, we find: h = 0.1. Therefore, the height of the rocket after 3.75 seconds is 0.1 units.
I hope this explanation helps you understand the process of setting up and solving these types of problems. Let me know if you have any further questions!