Answer:
- See the graphs attached and the explanation below
Explanation:
The most simple sine function, considered the parent function, is:

That function has:
- Midline, also known as rest or equilibrium position: y = 0
- Minimum: - 1
- Maximum: 1
- Amplitude: the distance between a minimum or a maximum and the midline = 1
- period: the interval of repetition of the function = 2π
The more general sine function is:

That function has:
- Midline: y = D (it is a vertical shift from the parent function)
- Minimum: - A + D
- Maximum: A + D
- Amplitude: A
- period: 2π/B
- phase shift: C (it is a horizontal shift of the from the parent function)
Now, you have to draw the sine function with the given key features:
- Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
- midline y = - 1 ⇒ D = - 1
Substitute the know values and use the y-intercept to find C:

Substitute (0, -1)

Hence, the function to graph is:

To draw that function use this:
- Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
- Minima: 3(-1) - 1 = - 3 - 1 = -4
- y-intercept: (0, - 1)
- x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
- first point of the midline: (0, -1) it is the same y-intercept
With that you can understand the graphs attached.
The answer will be 41,185 Hopes this help. :)
Answer:
32, consecutive interior angles are supplementary.
Step-by-step explanation:
We know that the two angles add up to 180, because consecutive interior angles are supplementary. So let's set up an equation equal to 180.
2x + 3x + 20 = 180
Now let's add like terms.
5x + 20 = 180
Now let's subtract 20 from both sides.
5x = 160
Now let's divide both sides by 5.
x = 32
Answer: See below
Step-by-step explanation:
<u>Area of the square</u> = l*w = 11*11 = 121
<u>Area of the circle</u> = pi r^2 = pi*1^2 = 3.142
<u>Part A</u>
P(hitting the circle) = 3.142 / 121 = 0.026 which is closer to 0.
<u>Part B</u>
P(hitting the outside portion) = 1 - 0.026 = 0.974 which is closer to 1.