Answer:
Step-by-step explanation:
Given the system of two equations:
Multiply the first equation and the second equation by 60 to get rid of fractions:
Now multiply the first equation by 4 and the second equation by 5:
Subtract them:
Substitute it into the first equation:
The solution is
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:
x = -1 or 2
Step-by-step explanation:
Taking the antilog, you have the quadratic ...
x^2 -x -1 = 1
x^2 -x -2 = 0 . . . . subtract 1
(x -2)(x +1) = 0 . . . factor
The values of x that make these factors zero are the solutions to the equation.
x = 2 or x = -1
