which algebraic property deals with multiplying or adding a specific number so that you get what you started with?
1 answer:
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the rock will be at 11 meters from the ground level after 5.92 seconds
Step-by-step explanation:
The motion of the rock is a free-fall motion, since the rock is acted upon the force of gravity only. Therefore, it is a uniformly accelerated motion, so its position at time t is given by the equation:
where
h = 23 m is the initial height
u = 27 m/s is the initial velocity, upward
is the acceleration of gravity, downward
t is the time
We want to find the time t at which the position of the rock is
y = 11 m
Substituting and re-arranging the equation, we find
This is a second-order equation, which has solutions:
So
The first solution is negative so we neglect it: therefore, the rock will be at 11 meters from the ground level after 5.92 seconds.
Learn more about free fall:
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Answer:
Step-by-step explanation:
We will use 2 coordinates from the table along with the standard form for an exponential function to write the equation that models that data. The standard form for an exponential function is
where x and y are coordinates from the table, a is the initial value, and b is the growth/decay rate. I will use the first 2 coordinates from the table: (0, 3) and (1, 1.5)
Solving first for a:
. Sine anything in the world raised to a power of 0 is 1, we can determine that
a = 3. Using that value along with the x and y from the second coordinate I chose, I can then solve for b:
. Since b to the first is just b:
1.5 = 3b so
b = .5
Filling in our model:
Since the value for b is greater than 0 but less than 1 (in other words a fraction smaller than 1), this table represents a decay function.