a sinusoid always function has an amplitude of 3, a frequency of 1/8pi, and a midline at 2. Which of the following equations satisfies these conditions? a. f(x)=3sin x/8pi +2 b. f(x)=3sin(4x) +2 c. f(x)=3sin(8pi x) +2 d. f(x)=3sin x/4 +2

The correct option is;

f(x) = 3·sin x/8·π + 2

Step-by-step explanation:

The given parameters for the sinusoidal function are;

Amplitude of oscillation = 3

Frequency of oscillation = 1/8·π

Midline of oscillation= 2

The general form of sinusoidal equation is y = A·sin(B(x - C)) + D

Where;

A = The amplitude

B = The frequency

C = The horizontal shift

D = The midline or vertical shift

Substituting the given values into the general form of sinusoidal equation, we have;

f(x) = y =  3·sin(1/8·π(x - 0)) + 2 = 3·sin(x/8·π) + 2

Which gives;

f(x) = 3·sin(x/8·π) + 2.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1