What is the probability of a die coming up with the number 10?
1 answer:
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<h3>Answer:</h3>
x/tan(x) is an even function
sec(x)/x is an odd function
<h3>Explanation:</h3><em>x/tan(x)</em>
For f(x) = x/tan(x), consider f(-x).
... f(-x) = -x/tan(-x)
Now, we know that tan(x) is an odd function, so tan(-x) = -tan(x). Using this, we have ...
... f(-x) = -x/(-tan(x)) = x/tan(x) = f(x)
The relation f(-x) = f(x) is characteristic of an even function, one that is symmetrical about the y-axis.
_____
<em>sec(x)/x</em>
For g(x) = sec(x)/x, consider g(-x).
... g(-x) = sec(-x)/(-x)
Now, we know that sec(x) is an even function, so sec(-x) = sec(x). Using this, we have ...
... g(-x) = sec(x)/(-x) = -sec(x)/x = -g(x)
The relation g(-x) = -g(x) is characeristic of an odd function, one that is symmetrical about the origin.
Answer:
The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.
Step-by-step explanation:
Here, we note the following
Let the person walking way fom the elevator be X
Let the other person going up in the elevator be Y
Therefore after 15 seconds, their positions will be;
For X, 2 ft/sec × 15 s = 30 ft away from the elevator
For Y, 7 ft/sec × 15 s = 105 ft up in the elevator
At that instant, the distance between them is given as
d² = x² + y²
= 30² +105² = 11925 ft²
d = √11925 ft² = 109.202 ft
The rate of change of the distance between the two peopl, X and Y is given as
Therefore, or
Since is given as 2 ft/sec and
= 7 ft/sec
Then