I need help please help me
1 answer:
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Answer:
3.189 seconds
Step-by-step explanation:
You want f(t) = 0, so ...
0 = -16t^2 +13.4t +120
0 = t^2 -0.8375t -7.5 . . . . divide by -16
0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*
0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square
√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root
t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875
It will take the rock about 3.189 seconds to hit the ground.
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* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...
(t^2 -2at +a^2) = (t -a)^2
Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.
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<em>Comment on the question</em>
We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...
Answer:
The domain is:
x: (-∞, 0] U (0, ∞)
The range is
y: [0, ∞)
Step-by-step explanation:
These types of functions are known as piecewise functions. It has two pieces of functions, you must graph both pieces for each interval.
First, graph:
y = -x for x from -∞ to x = 0
Note that y = -x is the equation of a negative slope line = -1 that passes through the origin
Second, graph:
y = x for x from x = 0 to ∞
Note that y = x is the equation of a positive slope line = 1 that passes through the origin.
The graph of this function is shown in the attached image. Note that it matches the absolute value graph of x.
y = | x |
In this function y it is always positive, and x can be any real number.
Therefore the domain is:
x: (-∞, 0] U (0,∞)
The range is:
y: [0, ∞)
