So a general harmonic equation is Asin(2πt/T). Little t is just a variable. 6 inches is the height of one maximum and one minimum from equilibrium, so that is the amplitude A. T is the period, or the time of one cycle (or wavelength), which is 2 seconds.
The equation is therefore (in terms of seconds and inches), 6*sin(2πt/2), or 6*sin(πt).
Answer:
Step-by-step explanation:
y = -4x - 2
slope of line = -4
slope of perpendicular to line = ¼
Point-slope equation for line of slope ¼, passing through (4,-4):
y+4 = ¼(x-4)
In slope-intercept form:
y = ¼x - 5
X/4 + 1 = -6
x/4 = -6 -1
x/4 = -7
x= -28
To find r, first write out the equation:

Next, multiply both sides by 2:

Now, subtract both sides by 4:

Divide both sides by 3:

The answer to this problem is
r = 2. Hope this helps and have a phenomenal day!
Answer:

Step-by-step explanation:
To get the equation in the slope-intercept form first, put the equation in slope-point form using the information given. The slope-point form is
. Then solve for y.
Distribute -3 to
,

Then, add -2 to both sides,

This is your final answer; the slope is -3 and the y-intercept is 4. There are also a few other ways to solve but I find this the easiest.