a sine function has the following key features:
frequency = 18π
amplitude = 6
midline: y = 3
y-intercept: (0,3)
the function is not a reflection of its parent function over the x-axis.
use the sine tool to graph the function. the first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

We want to get a point on the midline and the next maximum or minimum to that point, we will get: (0, 3) as a point on the midline, and (1/36, 9) as the next maximum to it.

A general sine function is written as:

f(x) = A*sin(w*x + p) + M

Where:

A is the amplitude.

w is the angular frequency.

M is the midline

p is the phase shift.

Here we know that:

Frequency  = 18π = w

Amplitude = 6 = A

Midline; y = 3 = M

Then we have:

f(x) = 6*( 18π*x + p) + 3

We also know that when x = 0, the function is equal to 3, this implies that the sine has no phase shift, then p = 0, and the function is:

f(x) = 6*(18π*x) + 3

Now we need to get:

A point on the midline; (0, 3) is on the midline so we use that.

A second point must be a maximum or a minimum closest to the first point.

We know that the sine function has a maximum at sin(x =  π/2)

Then we must solve:

18π*x = π/2

18*x = 1/2

x = 1/2*18 = 1/36

Then we have a maximum at: (1/36, 9)

Where the y-value of the maximum is just given by the midline plus the amplitude.

If you want to learn more, you can read:

link

Point on Midline (0,3)

Maximum (9π/2,3)

Minimum (-9π/2,-3)

Step-by-step explanation:

in the given sine function which is in the form of f(x) = a sin(bx+c) +d

a = amplitude

period = frequency = 18π

Therefore b = 2π/18π = 1/9

Y intercept = vertical shift = 3

Horizontal shift = d = 0

Therefore the sine function will be

f(x) = 6 sin(x/9) + 3

Now first point on the midline is (0,3)

Second point is maximum (9π/2,9)

Third point be a minimum value ( -9π/2,-3)

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

s

step-by-step explanation: