If we take the square of x and square of y and then subtract them:
(csc t)²-(cot t)²=1 ( this eq. gets from basic identity
x²-y²=1......a 1+cot²x=csc²x)
equation 'a' represent the equation of hyperbola which is (x²/a²)-(y²/b²) =1 with given conditions( a=1,b=1)
So, option D is correct
Answer:
Step-by-step explanation:
The correct statements regarding the behavior of a quadratic function are:
- The function in increasing for all real values of x where -6 < x < -2.
- The function is decreasing for all real values of x where x < -6 or x > -2.
<h3>When is a quadratic function increasing or decreasing?</h3>
A quadratic function with roots
and
is defined by:
![y = a(x - x_1)(x - x_2)](https://tex.z-dn.net/?f=y%20%3D%20a%28x%20-%20x_1%29%28x%20-%20x_2%29)
In which a is the leading coefficient.
The coefficient influences the behavior, as follows:
- If a < 0, the function is increasing between the roots, and decreasing otherwise.
- If a > 0, the function is decreasing between the roots, and increasing otherwise.
In this problem, the function is:
f(x) = -(x + 6)(x + 2).
The roots are x = -6 and x = -2, and the leading coefficient is of a = -1 < 0, hence:
- The function in increasing for all real values of x where -6 < x < -2.
- The function is decreasing for all real values of x where x < -6 or x > -2.
More can be learned about quadratic functions at brainly.com/question/24737967
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Answer:
B
Step-by-step explanation:
If we imagine this is on a clock, then point P is at the 9-o'clock position. When we rotate it 90 degrees clockwise, that's a quarter rotation, so P' will be at the 12-o'clock position. So the coordinates of P' will be (0, 5).