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).
Answer:
Option (3).
Step-by-step explanation:
Attached figure is the graph of a function,
f(x) = -
Since domain of any function is the set of all possible input values of the function,
Therefore, Domain of the function is,
Domain : x ≤ 0 Or (-∞, 0]
And range of the function is the set of all possible output values (y-values) of the function.
Therefore, Range of the function will be,
Range : y ≤ 0 Or (-∞, 0]
Therefore, Domain and range of this function is same.
Option (3) will be the answer.
For this case we have a function of the form:
Where,
m: slope of the line
b: cutting point with the y axis.
The line cuts to the y-axis at the point:
Therefore, the value of b is given by:
We now look for the slope of the line.
For this, we use the following equation:
Substituting values we have:
Rewriting:
Then, the equation of the line is:
Answer:
the rule that matches the function shown in the graph is:
Answer:
12.
Explanation:
Use the distance formula to determine the distance between two points.
