HELPP! Geometry volume practice
1 answer:
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To solve this we are going to use the kinematic equation for final velocity: 
where
is the final velocity
is the initial velocity
is the acceleration
is the time
We know for our problem that the the velocity at the beginning of the slope is
, so 
. We also know that the speed ad the bottom of the slope is 
, so 
. We also know that the acceleration is 
, so 
. Lets replace those values in our formula and solve for :
seconds
We can conclude that it takes the roller coaster 3 seconds to reach the bottom of the slope.
where
We know for our problem that the the velocity at the beginning of the slope is
We can conclude that it takes the roller coaster 3 seconds to reach the bottom of the slope.
Answer:
tex]M=\beta ln(2)[/tex]
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate).
Solution to the problem
For this case we can use the following Theorem:
"If X is a continuos random variable of the exponential distribution with parameter for some
"
Then the median of X is
Proof
Let M the median for the random variable X.
From the definition for the exponential distribution we know the denisty function of X is given by:
Since we need the median we can put this equation:
If we evaluate the integral we got this:
And that's equal to:
And if we solve for M we got:
If we apply natural log on both sides we got:
And then