1. Independent variable: the variable that can be modified and regulated.
the nail polish on Sarah's nails
2. Dependent variable: outcomes that result from the changes in the independent variable.
the duration of the nail polish's longevity
3. <span> Hypothesis: Different brands of nail polish have varied durations before they chip.
</span> 4. Control group: the <span> independent variable remains unchanged in this setup, not subject to variations.
</span> the schedule of when Sarah applies her nail polish (Sarah colors her nails every Sunday for a month)
the specific base coat and top coat (she <span> applies the same bottom coat and top coat with every kind of nail polish)
weekly habits (she ensures the same routine each week so her nails are not treated more harshly on some weeks).
</span> Experimental group: <span> the independent variable is altered for this group
type of nail polish (Essie, OPI, and Sally Hansen)
</span> 6. Constants: the experimenter (Sally), duration of study (one week), her weekly routine, <span> base coat and top coat, </span>
The angle formed with the positive x-axis is 120 degrees. We can assume that this angle is determined in a counterclockwise direction from the positive x-axis. The x-component of the vector can be calculated as: x-component = 10 cos(120) = -5. The vector's y-component is determined as: y-component = 10 sin(120) = 8.66. The x-component equates to -5 while the y-component equals 8.66.
assuming north-south is along the Y-axis and east-west along the X-axis
X = total X-displacement
from the graph, total displacement in the X-direction is computed as
X = 0 - 20 + 60 Cos45 + 0
X = 42.42 - 20
X = 22.42 m
Y = total Y-displacement
from the graph, total displacement in the Y-direction is computed as
Y = 40 + 0 + 60 Sin45 + 50
Y = 90 + 42.42
Y = 132.42 m
To calculate the magnitude of the net displacement vector, we apply the Pythagorean theorem, yielding
magnitude: Sqrt(X² + Y²) = Sqrt(22.42² + 132.42²) = 134.31 m
Direction: tan⁻¹(Y/X) = tan⁻¹(132.42/22.42) = 80.4 deg north of east
