First we will convert those radian angles to degrees, since my mind works better with degrees. Let's work one at a time. First,

. If we start at the positive x-axis and measure out 315 we end up in the 4th quadrant with a reference angle of 45 with the positive x-axis. The side across from the reference angle is -1, the side adjacent to the angle is 1, and the hypotenuse is sqrt2. The cotangent of this angle, then is 1/-1 which is -1. As for the second one, converting radians to degrees gives us that

. Sweeping out that angle has us going around the origin more than once and ending up in the first quadrant with a reference angle of 30° with the positive x-axis. The side across from the angle is 1, the side adjacent to the angle is √3, and the hypotenuse is 2. Therefore, the secant of that angle is 2/√3.
7978 years
Step-by-step explanation:
A = A02^(-t/hl)
where hl = half-life.
Dividing both sides by A0 and taking the logarithm, we get
ln(A/A0) = -(t/hl)ln2
or solving for t,
t= -(hl)ln(A/A0)/ln2
note that A/A0 = 0.38
t = -(5715 yrs)[ln(0.38)/ln2]
= 7978 years
Answer:
The closed linear form of the given sequence is 
Step-by-step explanation:
Given that the first term
and 
To find the closed linear form for the given sequence
The formula for arithmetic sequence is
(where d is the common difference)
The above equation is of the given form 
Comparing this we get d=0.75
With
and d=0.75
We can substitute these values in



Rewritting as below

Therefore 
Therefore the closed linear form of the given sequence is 
Answer:
11
Step-by-step explanation:
7,8,10,12,15,16
12+10=22÷2=11