The transformation from 1 to 2 is a translation, as the shape is moved from one point to another with no rotation, reflection, or change in size.
The transformation from 2 to 3 is a reflection, as the shape is now upside down. It is still the same distance from the y-axis.
The answer is D. translation, then reflection.
I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.
X= -2 + the root of 5
OR
x= -2 - the root of 5
Answer:
Step-by-step explanation:
Which sentence shows the correct use of personal pronouns?
"This is Silvia. She is my best friend. Next week, we will go to school together."
"This is Silvia. Her is my best friend. Next week, we will go to school together."
"This is Silvia. She is my best friend. Next week, us will go to school together."
"This is Silvia. She is my best friend. Next week, they will go to school together."
Answer:
The range of the function will be (- ∞, 4].
Step-by-step explanation:
See the graph attached.
Here we have to get the range of the graphed function.
The value of y in the graphed function varies in the range of less than or equal to 4.
Because the graph of the function does not move beyond 4 towards +∞.
Therefore, the range of the function will be (- ∞, 4]. (Answer)
