Answer:
A = π/6 + kπ, or A = 2π/3 + kπ
Step-by-step explanation:
tan A / (1 − tan² A) = √3 / 2
Cross multiply and simplify:
√3 (1 − tan² A) = 2 tan A
√3 − √3 tan² A = 2 tan A
3 − 3 tan² A = 2√3 tan A
0 = 3 tan² A + 2√3 tan A − 3
Solve with quadratic formula:
tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)
tan A = [ -2√3 ± √(12 + 36) ] / 6
tan A = (-2√3 ± √48) / 6
tan A = (-2√3 ± 4√3) / 6
tan A = -√3 or √3/3
Solve for A:
A = 2π/3 + kπ, or A = π/6 + kπ
Full rotation= 360 degrees
360(5/6)= 300 degrees
The answer is 300 degrees.
Hope this helps!
Answer:
2nd graph (image)
Step-by-step explanation:
The function to graph is:
It follows the general pattern of the function: 
, which is general shape and in 1st and 3rd quadrants. So, we can eliminate 3rd and 4th choices (because of quadrants).
The answer is either 1st, or 2nd graph.
Now, we simply can check a point in both.
lets take x = 4, so the function would be:
f(4) = 4/4 = 1
Hence, point is:
(4,1)
The first graph doesn't go through this point. The second graph does.
hence, we can successfully choose the 2nd graph as our answer.
Answer:
9.21954445729
Step-by-step explanation:
use distance formula
Answer:
A
Step-by-step explanation:
First, the definition of a floor function is that you round down, whereas for a ceiling function, you round up no matter what.
So, since C and D have the definitions totally wrong inherently, we can eliminate those.
Looking at the graph, we see that all the segments have their leftmost circle filled in. This indicates that the smaller number is counted. So, it's a floor function graph.
Thus, the answer is A.
Hope this helps!
