Answer:
sin
(
x/
2
) = -
√
3
/2
Take the inverse sine of both sides of the equation to extract x
from inside the sine.
x/
2
=
arcsin
(
−
√
3/
2
)
The exact value of arcsin
(
−
√
3
/2
) is −
π
/3
.
/x
2
=
−
π
/3
Multiply both sides of the equation by 2
.
2
⋅
x
/2
=
2
⋅
(
−
π
/3
)
Simplify both sides of the equation.
x
=
−
2
π
/3
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from 2
π
, to find a reference angle. Next, add this reference angle to π to find the solution in the third quadrant.
x
/2
=
2
π
+
π/
3
+
π
Simplify the expression to find the second solution.
x
=
2
π
/3
4
π
Add 4
π to every negative angle to get positive angles.
x
=
10
π
/3
The period of the sin
(
x
/2
) function is 4
π so values will repeat every 4
π radians in both directions.
x
=2
π
/3
+
4
π
n
,
10
π/
3
+
4
π
n
, for any integer n
Exclude the solutions that do not make sin
(
x
/2
)
=
−
√
3/
2 true.
x
=
10
π
/3
+
4
π
n
, for any integer n
Answer:
m= -13
Step-by-step explanation:
step1: left part times 26 is m
step2: right part times 26 is -13
so m= -13
Factor and set each factor equal to zero:
x = -3, 3, 2i, -2i
Step-by-step explanation:
oh, come on. you can just use common sense.
a local minimum is a point where the curve goes down to, and then turns around and starts to go up again. that point in the middle, where it turns around and does not go down any further, is the minimum.
for the maximum the same thing applies, just in the other direction (the curve goes up and turns around to go back down again).
a)
the local minimum values (y) are
-2, -1
b)
the values of x where it had these minimum values are
-1, +3
Answer:
B. x < $5 or x > $15
Step-by-step explanation:
The "or" in the problem statement gives you a clue that answer choices C and D can be rejected.
If x is the stock value, then value per share "below $5" means x < $5. This corresponds with answer choice B. Of course, "above $15" means x > $15, also corresponding to answer choice B.
