Step-by-step explanation:
Rise of y-value = (-4) - (3) = -7.
Run of x-value = (8) - (6) = 2.
Slope of the line = Rise / Run = (-7) / (2) = -3.5.
Answer:
Check below for a lucid explanation.
Step-by-step explanation:
The independent variable is the variable whose variation does not depend on another external variable. It is the variable on the x-axis which in this case is the growth of the baby.
Note: The diagram you attached to this question does not include the calibration on the x - axis which will give us the independent variable at point
This, nevertheless, is a very simple task. Locate the point A on the graph and trace it downwards to the x - axis, the value written where the line coincides with the x -axis is the value of the independent variable( growth of the baby) at point A.
It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.
Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is
<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)
The cosine of the angle between the vectors can be obtained from the dot product identity,
<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>) ==> cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)
so that
<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)
For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is
<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))
==> <em>W</em> ≈ 5.12 J
(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).
5.4 yards for each dress. This number lies between 5 and 6