On a piece of paper, use a protractor to construct a triangle with angle measures of 30° and 50º.
1 answer:
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To find the amplitude and period you need to be familiar with the following equation. Also you need to know that the standard cos has a period of 
and the midline is a line that runs between the max and min of the y-values of the function.
Equations:
f(x) = A cos(Bx +C) + D
f(x) = -4 cos(2x -n) + 3
A = amplitude = |-4| = 4
B = 2
C = phase shift = n = 0
D = vertical shift = midline = 3
Amplitude = 4
Find the period:
Find the midline:
We know that the amplitude is 4 so we have a range from -4 to 4. The standard y = cos(x) has its midline at 0 so y = 0. This is also true for y = -4 cos(x). In your equation though, you have a vertical shift of +3 so this changes our midline. With an amplitude of 4, which gives us a range from -4 to 4(our y-values), the shift moves this up by 3 so that means we will have new y-values and a range of -1 to 7. Now we need to find the midline(the middle of our y-values) of our new range. We can find this by using the following formula
Midline:
y = 3
Note, in the following equations that D = 3 = midline
y = A (Bx+C) + D
y = -4 (2x + n) + 3
Also, the picture that is attached is what your equation looks like when graphed.
Equations:
f(x) = A cos(Bx +C) + D
f(x) = -4 cos(2x -n) + 3
A = amplitude = |-4| = 4
B = 2
C = phase shift = n = 0
D = vertical shift = midline = 3
Amplitude = 4
Find the period:
Find the midline:
We know that the amplitude is 4 so we have a range from -4 to 4. The standard y = cos(x) has its midline at 0 so y = 0. This is also true for y = -4 cos(x). In your equation though, you have a vertical shift of +3 so this changes our midline. With an amplitude of 4, which gives us a range from -4 to 4(our y-values), the shift moves this up by 3 so that means we will have new y-values and a range of -1 to 7. Now we need to find the midline(the middle of our y-values) of our new range. We can find this by using the following formula
Midline:
y = 3
Note, in the following equations that D = 3 = midline
y = A (Bx+C) + D
y = -4 (2x + n) + 3
Also, the picture that is attached is what your equation looks like when graphed.
Answer:
<h2>The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles.</h2>Step-by-step explanation:
According to the graph, the dependent variable is Distance in miles, because it's on the vertical axis. Additionally, the independent variable is time in hours, because it's on the horizontal axis. However, you always put time as independent, because nothing affects time.
To find the equation, we just need to find the slope, using two points (0,0) and (2,40).
Therefore, the equation is , which shows a direct proportion between variables.
Now, in 24 hours, it would travel
It would travel 480 miles.
Therefore, the right answer is the second choice.