Given that
, we have
, so that

Take the derivative and find the critical points of
:

Take the second derivative and evaluate it at the critical point:

Since
is positive for all
, the critical point is a minimum.
At the critical point, we get the minimum value
.
The horizontal stretch is the correct answer. A period is the distance on the x-axis that it takes for the tangent or cotangent function to repeat itself. Stretching it out horizontally will lengthen that distance and therefore change the period.
Answer:
About 15.3%!
Step-by-step explanation:
ill explain in comments, i hope this helps you out
Answer:
50% of the number is 40
Step-by-step explanation:
8 * 5 = 40
Answer:
D 21.80°
Step-by-step explanation:
Let x = measure of the angle
Tan x = 12000/30000 = .4
Arctan .4 = 21.80°